Entrants' Sample Solutions

CSE 1.5

Sample solution for SEU140+2

% SZS output start Proof
%ClaNum:116(EqnAxiom:34)
%VarNum:417(SingletonVarNum:163)
%MaxLitNum:4
%MaxfuncDepth:2
%SharedTerms:12
%goalClause: 37 38 55
%singleGoalClaCount:3
[35]P1(a1)
[36]P1(a2)
[37]P3(a3,a5)
[38]P2(a5,a6)
[54]~P1(a13)
[55]~P2(a3,a6)
[40]P3(a1,x401)
[43]P3(x431,x431)
[56]~P4(x561,x561)
[39]E(f12(a1,x391),a1)
[41]E(f16(x411,a1),x411)
[42]E(f12(x421,a1),x421)
[44]E(f16(x441,x441),x441)
[46]E(f12(x461,f12(x461,a1)),a1)
[49]E(f12(x491,f12(x491,x491)),x491)
[45]E(f16(x451,x452),f16(x452,x451))
[47]P3(x471,f16(x471,x472))
[48]P3(f12(x481,x482),x481)
[50]E(f16(x501,f12(x502,x501)),f16(x501,x502))
[51]E(f12(f16(x511,x512),x512),f12(x511,x512))
[52]E(f12(x521,f12(x521,x522)),f12(x522,f12(x522,x521)))
[57]~P1(x571)+E(x571,a1)
[61]~P3(x611,a1)+E(x611,a1)
[62]P5(f7(x621),x621)+E(x621,a1)
[60]~E(x601,x602)+P3(x601,x602)
[63]~P5(x632,x631)+~E(x631,a1)
[64]~P4(x641,x642)+~E(x641,x642)
[65]~P1(x651)+~P5(x652,x651)
[70]~P4(x701,x702)+P3(x701,x702)
[71]~P2(x712,x711)+P2(x711,x712)
[74]~P5(x742,x741)+~P5(x741,x742)
[75]~P4(x752,x751)+~P4(x751,x752)
[76]~P3(x762,x761)+~P4(x761,x762)
[67]~P3(x671,x672)+E(f12(x671,x672),a1)
[69]P3(x691,x692)+~E(f12(x691,x692),a1)
[72]~P3(x721,x722)+E(f16(x721,x722),x722)
[78]P1(x781)+~P1(f16(x782,x781))
[79]P1(x791)+~P1(f16(x791,x792))
[80]P3(x801,x802)+P5(f8(x801,x802),x801)
[81]P2(x811,x812)+P5(f14(x811,x812),x812)
[82]P2(x821,x822)+P5(f14(x821,x822),x821)
[96]P3(x961,x962)+~P5(f8(x961,x962),x962)
[88]~P2(x881,x882)+E(f12(x881,f12(x881,x882)),a1)
[89]~P3(x891,x892)+E(f16(x891,f12(x892,x891)),x892)
[90]~P3(x901,x902)+E(f12(x901,f12(x901,x902)),x901)
[95]P2(x951,x952)+~E(f12(x951,f12(x951,x952)),a1)
[104]P2(x1041,x1042)+P5(f4(x1041,x1042),f12(x1041,f12(x1041,x1042)))
[99]~P3(x991,x993)+P3(f12(x991,x992),f12(x993,x992))
[106]~P2(x1061,x1062)+~P5(x1063,f12(x1061,f12(x1061,x1062)))
[107]~P3(x1071,x1073)+P3(f12(x1071,f12(x1071,x1072)),f12(x1073,f12(x1073,x1072)))
[58]~P1(x582)+~P1(x581)+E(x581,x582)
[73]P4(x731,x732)+~P3(x731,x732)+E(x731,x732)
[77]~P3(x772,x771)+~P3(x771,x772)+E(x771,x772)
[97]E(x971,x972)+P5(f15(x971,x972),x972)+P5(f15(x971,x972),x971)
[103]E(x1031,x1032)+~P5(f15(x1031,x1032),x1032)+~P5(f15(x1031,x1032),x1031)
[83]~P3(x833,x832)+P5(x831,x832)+~P5(x831,x833)
[84]~P3(x841,x843)+P3(x841,x842)+~P3(x843,x842)
[91]~P2(x913,x912)+~P5(x911,x912)+~P5(x911,x913)
[98]~P3(x982,x983)+~P3(x981,x983)+P3(f16(x981,x982),x983)
[108]P5(f10(x1082,x1083,x1081),x1081)+P5(f10(x1082,x1083,x1081),x1082)+E(x1081,f12(x1082,x1083))
[111]P5(f10(x1112,x1113,x1111),x1111)+~P5(f10(x1112,x1113,x1111),x1113)+E(x1111,f12(x1112,x1113))
[113]~P5(f9(x1132,x1133,x1131),x1131)+~P5(f9(x1132,x1133,x1131),x1133)+E(x1131,f16(x1132,x1133))
[114]~P5(f9(x1142,x1143,x1141),x1141)+~P5(f9(x1142,x1143,x1141),x1142)+E(x1141,f16(x1142,x1143))
[105]~P3(x1051,x1053)+~P3(x1051,x1052)+P3(x1051,f12(x1052,f12(x1052,x1053)))
[109]P5(f11(x1092,x1093,x1091),x1091)+P5(f11(x1092,x1093,x1091),x1093)+E(x1091,f12(x1092,f12(x1092,x1093)))
[110]P5(f11(x1102,x1103,x1101),x1101)+P5(f11(x1102,x1103,x1101),x1102)+E(x1101,f12(x1102,f12(x1102,x1103)))
[85]~P5(x851,x854)+P5(x851,x852)+~E(x852,f16(x853,x854))
[86]~P5(x861,x863)+P5(x861,x862)+~E(x862,f16(x863,x864))
[87]~P5(x871,x873)+P5(x871,x872)+~E(x873,f12(x872,x874))
[92]~P5(x924,x923)+~P5(x924,x921)+~E(x921,f12(x922,x923))
[100]~P5(x1001,x1003)+P5(x1001,x1002)+~E(x1003,f12(x1004,f12(x1004,x1002)))
[112]P5(f9(x1122,x1123,x1121),x1121)+P5(f9(x1122,x1123,x1121),x1123)+P5(f9(x1122,x1123,x1121),x1122)+E(x1121,f16(x1122,x1123))
[115]P5(f10(x1152,x1153,x1151),x1153)+~P5(f10(x1152,x1153,x1151),x1151)+~P5(f10(x1152,x1153,x1151),x1152)+E(x1151,f12(x1152,x1153))
[116]~P5(f11(x1162,x1163,x1161),x1161)+~P5(f11(x1162,x1163,x1161),x1163)+~P5(f11(x1162,x1163,x1161),x1162)+E(x1161,f12(x1162,f12(x1162,x1163)))
[93]~P5(x931,x934)+P5(x931,x932)+P5(x931,x933)+~E(x932,f12(x934,x933))
[94]~P5(x941,x944)+P5(x941,x942)+P5(x941,x943)+~E(x944,f16(x943,x942))
[102]~P5(x1021,x1024)+~P5(x1021,x1023)+P5(x1021,x1022)+~E(x1022,f12(x1023,f12(x1023,x1024)))
%EqnAxiom
[1]E(x11,x11)
[2]E(x22,x21)+~E(x21,x22)
[3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
[4]~E(x41,x42)+E(f12(x41,x43),f12(x42,x43))
[5]~E(x51,x52)+E(f12(x53,x51),f12(x53,x52))
[6]~E(x61,x62)+E(f16(x61,x63),f16(x62,x63))
[7]~E(x71,x72)+E(f16(x73,x71),f16(x73,x72))
[8]~E(x81,x82)+E(f11(x81,x83,x84),f11(x82,x83,x84))
[9]~E(x91,x92)+E(f11(x93,x91,x94),f11(x93,x92,x94))
[10]~E(x101,x102)+E(f11(x103,x104,x101),f11(x103,x104,x102))
[11]~E(x111,x112)+E(f15(x111,x113),f15(x112,x113))
[12]~E(x121,x122)+E(f15(x123,x121),f15(x123,x122))
[13]~E(x131,x132)+E(f8(x131,x133),f8(x132,x133))
[14]~E(x141,x142)+E(f8(x143,x141),f8(x143,x142))
[15]~E(x151,x152)+E(f10(x151,x153,x154),f10(x152,x153,x154))
[16]~E(x161,x162)+E(f10(x163,x161,x164),f10(x163,x162,x164))
[17]~E(x171,x172)+E(f10(x173,x174,x171),f10(x173,x174,x172))
[18]~E(x181,x182)+E(f9(x181,x183,x184),f9(x182,x183,x184))
[19]~E(x191,x192)+E(f9(x193,x191,x194),f9(x193,x192,x194))
[20]~E(x201,x202)+E(f9(x203,x204,x201),f9(x203,x204,x202))
[21]~E(x211,x212)+E(f14(x211,x213),f14(x212,x213))
[22]~E(x221,x222)+E(f14(x223,x221),f14(x223,x222))
[23]~E(x231,x232)+E(f4(x231,x233),f4(x232,x233))
[24]~E(x241,x242)+E(f4(x243,x241),f4(x243,x242))
[25]~E(x251,x252)+E(f7(x251),f7(x252))
[26]~P1(x261)+P1(x262)+~E(x261,x262)
[27]P5(x272,x273)+~E(x271,x272)+~P5(x271,x273)
[28]P5(x283,x282)+~E(x281,x282)+~P5(x283,x281)
[29]P3(x292,x293)+~E(x291,x292)+~P3(x291,x293)
[30]P3(x303,x302)+~E(x301,x302)+~P3(x303,x301)
[31]P2(x312,x313)+~E(x311,x312)+~P2(x311,x313)
[32]P2(x323,x322)+~E(x321,x322)+~P2(x323,x321)
[33]P4(x332,x333)+~E(x331,x332)+~P4(x331,x333)
[34]P4(x343,x342)+~E(x341,x342)+~P4(x343,x341)

%-------------------------------------------
cnf(117,plain,
   (E(x1171,f16(x1171,x1171))),
   inference(scs_inference,[],[44,2])).
cnf(121,plain,
   (~P2(a6,a3)),
   inference(scs_inference,[],[55,44,39,2,95,71])).
cnf(125,plain,
   (~P5(x1251,a1)),
   inference(scs_inference,[],[55,35,44,39,46,2,95,71,69,65])).
cnf(129,plain,
   (~P5(x1291,f16(a1,a1))),
   inference(scs_inference,[],[55,35,44,39,46,2,95,71,69,65,64,63])).
cnf(130,plain,
   (E(f16(x1301,x1301),x1301)),
   inference(rename_variables,[],[44])).
cnf(132,plain,
   (~E(a5,a3)),
   inference(scs_inference,[],[38,55,35,44,39,46,2,95,71,69,65,64,63,31])).
cnf(137,plain,
   (E(f16(x1371,x1371),x1371)),
   inference(rename_variables,[],[44])).
cnf(139,plain,
   (E(f16(x1391,x1391),x1391)),
   inference(rename_variables,[],[44])).
cnf(140,plain,
   (~P5(x1401,f16(f12(x1402,f12(x1402,a1)),a1))),
   inference(scs_inference,[],[43,40,38,55,35,54,44,130,137,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100])).
cnf(175,plain,
   (~P5(x1751,f12(a5,f12(a5,a6)))),
   inference(scs_inference,[],[37,43,40,38,55,35,54,44,130,137,139,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106])).
cnf(177,plain,
   (P5(f4(a3,a6),f12(a3,f12(a3,a6)))),
   inference(scs_inference,[],[37,43,40,38,55,35,54,44,130,137,139,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104])).
cnf(185,plain,
   (E(f12(a5,f12(a5,a6)),a1)),
   inference(scs_inference,[],[37,43,40,38,55,35,54,44,130,137,139,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88])).
cnf(187,plain,
   (P5(f14(a3,a6),a3)),
   inference(scs_inference,[],[37,43,40,38,55,35,54,44,130,137,139,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88,82])).
cnf(189,plain,
   (P5(f14(a3,a6),a6)),
   inference(scs_inference,[],[37,43,40,38,55,35,54,44,130,137,139,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88,82,81])).
cnf(210,plain,
   (E(f16(x2101,x2101),x2101)),
   inference(rename_variables,[],[44])).
cnf(211,plain,
   (~P2(a3,f16(a6,a6))),
   inference(scs_inference,[],[37,43,56,40,38,55,35,36,54,44,130,137,139,210,45,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88,82,81,79,78,76,74,72,67,60,57,34,33,32])).
cnf(212,plain,
   (E(f16(x2121,x2121),x2121)),
   inference(rename_variables,[],[44])).
cnf(213,plain,
   (~P5(x2131,f16(f16(a1,a1),f16(a1,a1)))),
   inference(scs_inference,[],[37,43,56,40,38,55,35,36,54,44,130,137,139,210,212,45,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88,82,81,79,78,76,74,72,67,60,57,34,33,32,28])).
cnf(214,plain,
   (E(f16(x2141,x2141),x2141)),
   inference(rename_variables,[],[44])).
cnf(223,plain,
   (~E(a3,f12(x2231,a3))),
   inference(scs_inference,[],[37,43,56,40,38,55,35,36,54,44,130,137,139,210,212,45,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88,82,81,79,78,76,74,72,67,60,57,34,33,32,28,111,108,105,98,92])).
cnf(231,plain,
   (~E(f12(a5,f12(a5,a6)),f16(x2311,a3))),
   inference(scs_inference,[],[37,43,56,40,38,55,35,36,54,44,130,137,139,210,212,45,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88,82,81,79,78,76,74,72,67,60,57,34,33,32,28,111,108,105,98,92,91,87,86,85])).
cnf(233,plain,
   (~P5(f14(a3,a6),f12(a3,f12(a3,a6)))),
   inference(scs_inference,[],[37,43,56,40,38,55,35,36,54,44,130,137,139,210,212,45,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88,82,81,79,78,76,74,72,67,60,57,34,33,32,28,111,108,105,98,92,91,87,86,85,83])).
cnf(235,plain,
   (~P3(a5,a3)),
   inference(scs_inference,[],[37,43,56,40,38,55,35,36,54,44,130,137,139,210,212,45,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88,82,81,79,78,76,74,72,67,60,57,34,33,32,28,111,108,105,98,92,91,87,86,85,83,73])).
cnf(237,plain,
   (~E(f12(a5,f12(a5,a6)),f12(a3,f12(a3,a3)))),
   inference(scs_inference,[],[37,43,56,40,38,55,35,36,54,44,130,137,139,210,212,45,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88,82,81,79,78,76,74,72,67,60,57,34,33,32,28,111,108,105,98,92,91,87,86,85,83,73,102])).
cnf(242,plain,
   (~P5(f14(a3,a6),f16(f16(a5,a5),f16(a5,a5)))),
   inference(scs_inference,[],[37,43,56,40,38,55,35,36,54,44,130,137,139,210,212,214,45,47,48,41,39,46,2,95,71,69,65,64,63,31,30,29,26,3,100,97,84,77,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,104,99,90,89,88,82,81,79,78,76,74,72,67,60,57,34,33,32,28,111,108,105,98,92,91,87,86,85,83,73,102,27,103,94])).
cnf(249,plain,
   (P5(f8(a5,a3),a5)),
   inference(scs_inference,[],[235,96,80])).
cnf(252,plain,
   (~P5(x2521,f12(a5,f12(a5,a6)))),
   inference(rename_variables,[],[175])).
cnf(255,plain,
   (~P5(x2551,a1)),
   inference(rename_variables,[],[125])).
cnf(256,plain,
   (~E(f12(a5,f12(a5,a6)),f16(x2561,a3))),
   inference(rename_variables,[],[231])).
cnf(257,plain,
   (~P5(x2571,f12(a5,f12(a5,a6)))),
   inference(rename_variables,[],[175])).
cnf(267,plain,
   (~P5(f14(a3,a6),f16(a5,a5))),
   inference(scs_inference,[],[45,125,235,231,129,189,213,242,175,252,237,96,80,110,112,62,82,91,86])).
cnf(268,plain,
   (E(f16(x2681,x2682),f16(x2682,x2681))),
   inference(rename_variables,[],[45])).
cnf(276,plain,
   (~E(a3,f12(x2761,a3))),
   inference(rename_variables,[],[223])).
cnf(280,plain,
   (~E(f12(a3,f12(a3,a6)),a1)),
   inference(scs_inference,[],[47,48,45,55,125,132,235,231,129,189,223,213,242,175,252,237,96,80,110,112,62,82,91,86,69,84,77,2,95])).
cnf(283,plain,
   (~P5(x2831,a1)),
   inference(rename_variables,[],[125])).
cnf(289,plain,
   (~P3(a3,f12(a3,a6))),
   inference(scs_inference,[],[47,48,45,38,55,125,255,132,235,231,129,189,223,213,242,175,252,237,96,80,110,112,62,82,91,86,69,84,77,2,95,81,74,71,67])).
cnf(293,plain,
   (~E(a6,a1)),
   inference(scs_inference,[],[47,48,45,38,55,125,255,132,235,231,129,189,223,213,242,175,252,237,96,80,110,112,62,82,91,86,69,84,77,2,95,81,74,71,67,65,63])).
cnf(298,plain,
   (E(f12(x2981,a1),x2981)),
   inference(rename_variables,[],[42])).
cnf(300,plain,
   (E(x3001,f16(x3001,x3001))),
   inference(rename_variables,[],[117])).
cnf(302,plain,
   (~P5(x3021,a1)),
   inference(rename_variables,[],[125])).
cnf(306,plain,
   (P3(x3061,x3061)),
   inference(rename_variables,[],[43])).
cnf(308,plain,
   (~E(a6,f12(x3081,f12(x3081,a1)))),
   inference(scs_inference,[],[37,42,43,47,48,45,38,55,125,255,283,302,132,235,117,231,129,189,223,276,213,242,175,252,237,96,80,110,112,62,82,91,86,69,84,77,2,95,81,74,71,67,65,63,57,31,3,108,105,100])).
cnf(309,plain,
   (~P5(x3091,a1)),
   inference(rename_variables,[],[125])).
cnf(314,plain,
   (P5(f15(f12(a5,f12(a5,a6)),f16(x3141,a3)),f16(x3141,a3))),
   inference(scs_inference,[],[37,42,43,306,47,48,45,38,55,125,255,283,302,132,235,117,231,256,129,189,223,276,213,242,175,252,257,237,96,80,110,112,62,82,91,86,69,84,77,2,95,81,74,71,67,65,63,57,31,3,108,105,100,98,97])).
cnf(321,plain,
   (E(f12(x3211,a1),x3211)),
   inference(rename_variables,[],[42])).
cnf(324,plain,
   (~P5(x3241,a1)),
   inference(rename_variables,[],[125])).
cnf(326,plain,
   (~E(a1,f12(a6,f12(a6,a6)))),
   inference(scs_inference,[],[37,42,298,52,43,306,47,48,45,38,55,125,255,283,302,309,324,132,235,117,231,256,129,189,223,276,213,242,175,252,257,237,177,96,80,110,112,62,82,91,86,69,84,77,2,95,81,74,71,67,65,63,57,31,3,108,105,100,98,97,92,87,83,102])).
cnf(327,plain,
   (~P5(x3271,a1)),
   inference(rename_variables,[],[125])).
cnf(330,plain,
   (E(f12(x3301,a1),x3301)),
   inference(rename_variables,[],[42])).
cnf(334,plain,
   (E(f12(x3341,a1),x3341)),
   inference(rename_variables,[],[42])).
cnf(339,plain,
   (E(x3391,f16(x3391,x3391))),
   inference(rename_variables,[],[117])).
cnf(341,plain,
   (E(f12(x3411,a1),x3411)),
   inference(rename_variables,[],[42])).
cnf(342,plain,
   (~P5(x3421,f12(x3422,f12(x3422,a1)))),
   inference(scs_inference,[],[37,42,298,321,330,334,52,43,306,47,48,45,268,38,55,125,255,283,302,309,324,327,132,235,117,300,231,256,129,189,223,276,213,242,175,252,257,237,177,140,96,80,110,112,62,82,91,86,69,84,77,2,95,81,74,71,67,65,63,57,31,3,108,105,100,98,97,92,87,83,102,94,93,60,32,29,85])).
cnf(348,plain,
   (E(f12(x3481,a1),x3481)),
   inference(rename_variables,[],[42])).
cnf(349,plain,
   (P5(f14(a3,a6),f12(a6,a1))),
   inference(scs_inference,[],[37,42,298,321,330,334,341,348,52,43,306,56,47,48,45,268,38,55,125,255,283,302,309,324,327,132,235,117,300,339,231,256,129,189,223,276,213,242,175,252,257,237,177,140,96,80,110,112,62,82,91,86,69,84,77,2,95,81,74,71,67,65,63,57,31,3,108,105,100,98,97,92,87,83,102,94,93,60,32,29,85,27,34,28])).
cnf(372,plain,
   (~P5(x3721,f12(x3722,f12(x3722,a1)))),
   inference(rename_variables,[],[342])).
cnf(375,plain,
   (~P5(x3751,a1)),
   inference(rename_variables,[],[125])).
cnf(383,plain,
   (~P5(x3831,a1)),
   inference(rename_variables,[],[125])).
cnf(404,plain,
   (E(f12(x4041,f12(x4041,x4042)),f12(x4042,f12(x4042,x4041)))),
   inference(rename_variables,[],[52])).
cnf(433,plain,
   ($false),
   inference(scs_inference,[],[38,49,50,51,40,117,41,42,52,404,43,48,35,45,121,293,267,314,349,289,249,187,211,342,372,233,185,280,308,326,125,375,383,140,189,80,110,58,82,109,62,86,84,74,71,63,108,92,91,87,94,93,67,69,77,2,81,65,31,102]),
   ['proof']).
% SZS output end Proof

CSE_E 1.4

Sample solution for SEU140+2

% SZS output start Proof
fof(t4_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~(in(X3,set_intersection2(X1,X2)))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2)))), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', t4_xboole_0)).
fof(t48_xboole_1, lemma, ![X1, X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', t48_xboole_1)).
fof(t63_xboole_1, conjecture, ![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', t63_xboole_1)).
fof(d1_xboole_0, axiom, ![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1))), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', d1_xboole_0)).
fof(d4_xboole_0, axiom, ![X1, X2, X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2))))), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', d4_xboole_0)).
fof(t3_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', t3_xboole_0)).
fof(d3_xboole_0, axiom, ![X1, X2, X3]:(X3=set_intersection2(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&in(X4,X2)))), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', d3_xboole_0)).
fof(l32_xboole_1, lemma, ![X1, X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2)), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', l32_xboole_1)).
fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(subset(X1,X2)&subset(X2,X1))), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', d10_xboole_0)).
fof(t36_xboole_1, lemma, ![X1, X2]:subset(set_difference(X1,X2),X1), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', t36_xboole_1)).
fof(t3_boole, axiom, ![X1]:set_difference(X1,empty_set)=X1, file('/home/ars01/Desktop/dist/problems/SEU140+2.p', t3_boole)).
fof(c_0_11, lemma, ![X1, X2]:(~((~disjoint(X1,X2)&![X3]:~in(X3,set_intersection2(X1,X2))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2)))), inference(fof_simplification,[status(thm)],[t4_xboole_0])).
fof(c_0_12, lemma, ![X226, X227, X229, X230, X231]:((disjoint(X226,X227)|in(esk10_2(X226,X227),set_intersection2(X226,X227)))&(~in(X231,set_intersection2(X229,X230))|~disjoint(X229,X230))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])).
fof(c_0_13, lemma, ![X223, X224]:set_difference(X223,set_difference(X223,X224))=set_intersection2(X223,X224), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_14, negated_conjecture, ~(![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), inference(assume_negation,[status(cth)],[t63_xboole_1])).
cnf(c_0_15, lemma, (~in(X1,set_intersection2(X2,X3))|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_16, lemma, (set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_13])).
fof(c_0_17, negated_conjecture, ((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])).
fof(c_0_18, plain, ![X1]:(X1=empty_set<=>![X2]:~in(X2,X1)), inference(fof_simplification,[status(thm)],[d1_xboole_0])).
fof(c_0_19, plain, ![X1, X2, X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~in(X4,X2)))), inference(fof_simplification,[status(thm)],[d4_xboole_0])).
fof(c_0_20, lemma, ![X1, X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), inference(fof_simplification,[status(thm)],[t3_xboole_0])).
cnf(c_0_21, lemma, (~disjoint(X2,X3)|~in(X1,set_difference(X2,set_difference(X2,X3)))), inference(rw,[status(thm)],[c_0_15, c_0_16])).
cnf(c_0_22, negated_conjecture, (disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_17])).
fof(c_0_23, plain, ![X126, X127, X128]:((X126!=empty_set|~in(X127,X126))&(in(esk1_1(X128),X128)|X128=empty_set)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])])).
fof(c_0_24, plain, ![X145, X146, X147, X148, X149, X150, X151, X152]:((((in(X148,X145)|~in(X148,X147)|X147!=set_intersection2(X145,X146))&(in(X148,X146)|~in(X148,X147)|X147!=set_intersection2(X145,X146)))&(~in(X149,X145)|~in(X149,X146)|in(X149,X147)|X147!=set_intersection2(X145,X146)))&((~in(esk4_3(X150,X151,X152),X152)|(~in(esk4_3(X150,X151,X152),X150)|~in(esk4_3(X150,X151,X152),X151))|X152=set_intersection2(X150,X151))&((in(esk4_3(X150,X151,X152),X150)|in(esk4_3(X150,X151,X152),X152)|X152=set_intersection2(X150,X151))&(in(esk4_3(X150,X151,X152),X151)|in(esk4_3(X150,X151,X152),X152)|X152=set_intersection2(X150,X151))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])])).
fof(c_0_25, plain, ![X154, X155, X156, X157, X158, X159, X160, X161]:((((in(X157,X154)|~in(X157,X156)|X156!=set_difference(X154,X155))&(~in(X157,X155)|~in(X157,X156)|X156!=set_difference(X154,X155)))&(~in(X158,X154)|in(X158,X155)|in(X158,X156)|X156!=set_difference(X154,X155)))&((~in(esk5_3(X159,X160,X161),X161)|(~in(esk5_3(X159,X160,X161),X159)|in(esk5_3(X159,X160,X161),X160))|X161=set_difference(X159,X160))&((in(esk5_3(X159,X160,X161),X159)|in(esk5_3(X159,X160,X161),X161)|X161=set_difference(X159,X160))&(~in(esk5_3(X159,X160,X161),X160)|in(esk5_3(X159,X160,X161),X161)|X161=set_difference(X159,X160))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])])).
fof(c_0_26, lemma, ![X212, X213, X215, X216, X217]:(((in(esk9_2(X212,X213),X212)|disjoint(X212,X213))&(in(esk9_2(X212,X213),X213)|disjoint(X212,X213)))&(~in(X217,X215)|~in(X217,X216)|~disjoint(X215,X216))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])])])).
fof(c_0_27, lemma, ![X174, X175]:((set_difference(X174,X175)!=empty_set|subset(X174,X175))&(~subset(X174,X175)|set_difference(X174,X175)=empty_set)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])).
cnf(c_0_28, negated_conjecture, (~in(X1,set_difference(esk12_0,set_difference(esk12_0,esk13_0)))), inference(spm,[status(thm)],[c_0_21, c_0_22])).
cnf(c_0_29, plain, (in(esk1_1(X1),X1)|X1=empty_set), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_30, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_intersection2(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_31, plain, (~in(X1,X2)|~in(X1,X3)|X3!=set_difference(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_32, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_17])).
cnf(c_0_33, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_26])).
fof(c_0_34, plain, ![X124, X125]:(((subset(X124,X125)|X124!=X125)&(subset(X125,X124)|X124!=X125))&(~subset(X124,X125)|~subset(X125,X124)|X124=X125)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])).
cnf(c_0_35, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_27])).
cnf(c_0_36, negated_conjecture, (set_difference(esk12_0,set_difference(esk12_0,esk13_0))=empty_set), inference(spm,[status(thm)],[c_0_28, c_0_29])).
fof(c_0_37, lemma, ![X205, X206]:subset(set_difference(X205,X206),X205), inference(variable_rename,[status(thm)],[t36_xboole_1])).
cnf(c_0_38, plain, (in(X1,X2)|X3!=set_difference(X4,set_difference(X4,X2))|~in(X1,X3)), inference(rw,[status(thm)],[c_0_30, c_0_16])).
cnf(c_0_39, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_27])).
cnf(c_0_40, negated_conjecture, (subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_17])).
fof(c_0_41, plain, ![X211]:set_difference(X211,empty_set)=X211, inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_42, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3)), inference(er,[status(thm)],[c_0_31])).
cnf(c_0_43, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk13_0)), inference(spm,[status(thm)],[c_0_32, c_0_33])).
cnf(c_0_44, plain, (X1=X2|~subset(X1,X2)|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_34])).
cnf(c_0_45, lemma, (subset(esk12_0,set_difference(esk12_0,esk13_0))), inference(spm,[status(thm)],[c_0_35, c_0_36])).
cnf(c_0_46, lemma, (subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_37])).
cnf(c_0_47, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2)))), inference(er,[status(thm)],[c_0_38])).
cnf(c_0_48, negated_conjecture, (set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_39, c_0_40])).
cnf(c_0_49, plain, (set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_41])).
cnf(c_0_50, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_51, negated_conjecture, (~in(esk9_2(esk11_0,esk13_0),set_difference(X1,esk13_0))), inference(spm,[status(thm)],[c_0_42, c_0_43])).
cnf(c_0_52, lemma, (set_difference(esk12_0,esk13_0)=esk12_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_46])])).
cnf(c_0_53, negated_conjecture, (in(X1,esk12_0)|~in(X1,esk11_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_49])).
cnf(c_0_54, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk11_0)), inference(spm,[status(thm)],[c_0_32, c_0_50])).
cnf(c_0_55, lemma, (~in(esk9_2(esk11_0,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_51, c_0_52])).
cnf(c_0_56, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_55]), ['proof']).
% SZS output end Proof

cvc5 1.0

Sample solution for SET014^4

% SZS output start Proof for SET014^4
(let ((_let_1 (not (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A (-> $$unsorted Bool))) (=> (and (@ (@ subset X) A) (@ (@ subset Y) A)) (@ (@ subset (@ (@ union X) Y)) A)))))) (let ((_let_2 (= misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) (let ((_let_3 (= meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (let ((_let_4 (= subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))) (let ((_let_5 (= disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ intersection X) Y) emptyset))))) (let ((_let_6 (= complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_7 (= setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))) (let ((_let_8 (= intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_9 (= excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (let ((_let_1 (@ Y U))) (let ((_let_2 (@ X U))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))) (let ((_let_10 (= union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_11 (= singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))) (let ((_let_12 (= unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))) (let ((_let_13 (= emptyset (lambda ((X $$unsorted)) false)))) (let ((_let_14 (= is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) (let ((_let_15 (= in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) (let ((_let_16 (forall ((BOUND_VARIABLE_607 $$unsorted)) (or (not (ho_1 skv_3 BOUND_VARIABLE_607)) (ho_1 skv_4 BOUND_VARIABLE_607))))) (let ((_let_17 (ho_1 skv_4 skv_5))) (let ((_let_18 (ho_1 skv_3 skv_5))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17))) (let ((_let_21 (ho_1 skv_2 skv_5))) (let ((_let_22 (not _let_21))) (let ((_let_23 (and _let_22 _let_19))) (let ((_let_24 (not _let_16))) (let ((_let_25 (forall ((BOUND_VARIABLE_588 $$unsorted)) (or (not (ho_1 skv_2 BOUND_VARIABLE_588)) (ho_1 skv_4 BOUND_VARIABLE_588))))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24 _let_23 _let_17))) (let ((_let_28 (forall ((BOUND_VARIABLE_721 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_718 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_714 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_588 $$unsorted)) (or (not (ho_1 BOUND_VARIABLE_721 BOUND_VARIABLE_588)) (ho_1 BOUND_VARIABLE_714 BOUND_VARIABLE_588)))) (not (forall ((BOUND_VARIABLE_607 $$unsorted)) (or (not (ho_1 BOUND_VARIABLE_718 BOUND_VARIABLE_607)) (ho_1 BOUND_VARIABLE_714 BOUND_VARIABLE_607)))) (and (not (ho_1 BOUND_VARIABLE_721 BOUND_VARIABLE_669)) (not (ho_1 BOUND_VARIABLE_718 BOUND_VARIABLE_669))) (ho_1 BOUND_VARIABLE_714 BOUND_VARIABLE_669))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (not _let_28))) (let ((_let_31 (ASSUME :args (_let_15)))) (let ((_let_32 (ASSUME :args (_let_14)))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (ASSUME :args (_let_10)))) (let ((_let_37 (ASSUME :args (_let_9)))) (let ((_let_38 (ASSUME :args (_let_8)))) (let ((_let_39 (ASSUME :args (_let_7)))) (let ((_let_40 (ASSUME :args (_let_6)))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31) :args ((= disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= emptyset (@ (@ intersection X) Y)))) SB_DEFAULT SBA_FIXPOINT))) _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31) :args ((not (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A (-> $$unsorted Bool))) (or (not (@ (@ subset X) A)) (not (@ (@ subset Y) A)) (@ (@ subset (@ (@ union X) Y)) A)))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A (-> $$unsorted Bool)) (BOUND_VARIABLE_669 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_588 $$unsorted)) (or (not (@ X BOUND_VARIABLE_588)) (@ A BOUND_VARIABLE_588)))) (not (forall ((BOUND_VARIABLE_607 $$unsorted)) (or (not (@ Y BOUND_VARIABLE_607)) (@ A BOUND_VARIABLE_607)))) (and (not (@ X BOUND_VARIABLE_669)) (not (@ Y BOUND_VARIABLE_669))) (@ A BOUND_VARIABLE_669)))) _let_30))))))) (let ((_let_42 (OR))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_41) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_28))) (REFL :args (_let_29)) :args _let_42)) _let_41 :args (_let_29 true _let_28)))) (let ((_let_44 (REFL :args (_let_27)))) (let ((_let_45 (not _let_20))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 3)) _let_43 :args ((not _let_17) true _let_27)))) (let ((_let_47 (or _let_22 _let_17))) (let ((_let_48 (_let_25))) (let ((_let_49 (skv_5 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_50 (_let_23))) (let ((_let_51 (_let_16))) (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_51) :args _let_49) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_17 _let_45))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_50) (CONG (REFL :args _let_50) (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_42)) :args ((or _let_21 _let_18 _let_23))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_22 _let_17 (not _let_47)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_48) :args _let_49) :args _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_42)) :args ((or _let_25 _let_27))) _let_43 :args (_let_25 true _let_27)) :args (_let_47 false _let_25)) :args (_let_22 true _let_17 false _let_47)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 2)) _let_43 :args ((not _let_23) true _let_27)) :args (_let_18 true _let_21 true _let_23)) _let_46 :args (_let_45 false _let_18 true _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 1)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_16))) :args _let_42)) :args ((or _let_16 _let_27))) _let_43 :args (_let_16 true _let_27)) :args (false true _let_20 false _let_16)) :args (_let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))
% SZS output end Proof for SET014^4

Sample solution for DAT013=1

% SZS output start Proof for DAT013=1
(let ((_let_1 (not (forall ((U array) (V Int) (W Int)) (=> (forall ((X Int)) (=> (and (<= V X) (<= X W)) (> (read U X) 0))) (forall ((Y Int)) (=> (and (<= (+ V 3) Y) (<= Y W)) (> (read U Y) 0)))))))) (let ((_let_2 (* (- 1) skv_5))) (let ((_let_3 (+ skv_3 _let_2))) (let ((_let_4 (>= _let_3 (- 2)))) (let ((_let_5 (>= _let_3 1))) (let ((_let_6 (>= (read skv_2 skv_5) 1))) (let ((_let_7 (>= (+ skv_4 _let_2) 0))) (let ((_let_8 (not _let_7))) (let ((_let_9 (forall ((X Int)) (or (not (>= (+ X (* (- 1) skv_3)) 0)) (>= (+ X (* (- 1) skv_4)) 1) (>= (read skv_2 X) 1))))) (let ((_let_10 (not _let_9))) (let ((_let_11 (or _let_10 _let_4 _let_8 _let_6))) (let ((_let_12 (not _let_4))) (let ((_let_13 (forall ((U array) (V Int) (W Int) (BOUND_VARIABLE_434 Int)) (let ((_let_1 (* (- 1) BOUND_VARIABLE_434))) (or (not (forall ((X Int)) (let ((_let_1 (* (- 1) X))) (or (>= (+ V _let_1) 1) (not (>= (+ W _let_1) 0)) (>= (read U X) 1))))) (>= (+ V _let_1) (- 2)) (not (>= (+ W _let_1) 0)) (>= (read U BOUND_VARIABLE_434) 1)))))) (let ((_let_14 (not _let_11))) (let ((_let_15 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_16 (OR))) (let ((_let_17 (not _let_13))) (let ((_let_18 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_15) :args (_let_17)) (REWRITE :args ((=> _let_17 (not (or (not (forall ((X Int)) (let ((_let_1 (* (- 1) X))) (or (>= (+ skv_3 _let_1) 1) (not (>= (+ skv_4 _let_1) 0)) (>= (read skv_2 X) 1))))) _let_4 _let_8 _let_6))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_13))) (REFL :args (_let_14)) :args _let_16)) _let_15 :args (_let_14 true _let_13)))) (let ((_let_19 (or _let_5 _let_8 _let_6))) (let ((_let_20 (REFL :args (_let_11)))) (let ((_let_21 (_let_9))) (let ((_let_22 (< _let_3 1))) (let ((_let_23 (_let_5))) (let ((_let_24 (ASSUME :args _let_23))) (let ((_let_25 (ASSUME :args (_let_12)))) (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_24 _let_25) :args (_let_12 _let_5)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_24 (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_25 :args ((< _let_3 (- 2))))) :args ((- 1.0) 1.0)) :args (false)) :args _let_23) :args (_let_22)) (MACRO_SR_PRED_TRANSFORM _let_24 :args ((not _let_22)))) :args (_let_5 _let_12)) :args ((not (and _let_12 _let_5)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_4))) (REFL :args ((not _let_5))) :args _let_16)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_8 _let_6 _let_5 (not _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 2)) (CONG _let_20 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_16)) :args ((or _let_7 _let_11))) _let_18 :args (_let_7 true _let_11)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_11 3)) _let_18 :args ((not _let_6) true _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_21) :args (skv_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((read skv_2 X)))) :args _let_21))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 0)) (CONG _let_20 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_16)) :args ((or _let_9 _let_11))) _let_18 :args (_let_9 true _let_11)) :args (_let_19 false _let_9)) :args (_let_5 false _let_7 true _let_6 false _let_19)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_11 1)) _let_18 :args (_let_12 true _let_11)) :args (false false _let_5 true _let_4)) :args ((forall ((U array) (V Int) (W Int)) (= (read (write U V W) V) W)) (forall ((X array) (Y Int) (Z Int) (X1 Int)) (or (= Y Z) (= (read (write X Y X1) Z) (read X Z)))) _let_1 true)))))))))))))))))))))))))))
% SZS output end Proof for DAT013=1

Sample solution for SEU140+2

% SZS output start Proof for SEU140+2
(let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (disjoint A B) (disjoint B A))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (subset A B) (forall ((C $$unsorted)) (=> (in C A) (in C B))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (and (in C A) (in C B)))))) (not (and (exists ((C $$unsorted)) (and (in C A) (in C B))) _let_1))))))) (let ((_let_4 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (subset A B) (disjoint B C)) (disjoint A C)))))) (let ((_let_5 (in skv_7 skv_4))) (let ((_let_6 (in skv_7 skv_5))) (let ((_let_7 (not _let_5))) (let ((_let_8 (or _let_7 _let_6))) (let ((_let_9 (in skv_7 skv_6))) (let ((_let_10 (not _let_9))) (let ((_let_11 (or _let_7 _let_10))) (let ((_let_12 (forall ((C $$unsorted)) (or (not (in C skv_4)) (not (in C skv_6)))))) (let ((_let_13 (not _let_11))) (let ((_let_14 (not _let_12))) (let ((_let_15 (disjoint skv_4 skv_6))) (let ((_let_16 (or _let_15 _let_14))) (let ((_let_17 (forall ((BOUND_VARIABLE_930 $$unsorted) (BOUND_VARIABLE_932 $$unsorted)) (or (disjoint BOUND_VARIABLE_930 BOUND_VARIABLE_932) (not (forall ((C $$unsorted)) (or (not (in C BOUND_VARIABLE_930)) (not (in C BOUND_VARIABLE_932))))))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (_let_17))) (let ((_let_20 (disjoint skv_5 skv_6))) (let ((_let_21 (not _let_20))) (let ((_let_22 (subset skv_4 skv_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_15))) (let ((_let_25 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (subset A B)) (not (disjoint B C)) (disjoint A C))))) (let ((_let_26 (not _let_24))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (OR))) (let ((_let_29 (not _let_25))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_27) :args (_let_29))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_25))) (REFL :args (_let_26)) :args _let_28)) _let_27 :args (_let_26 true _let_25)))) (let ((_let_31 (_let_14))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_31)) :args _let_31)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_12))) (REFL :args (_let_13)) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_14 (not _let_16)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 2)) _let_30 :args ((not _let_15) true _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_19) :args (skv_4 skv_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (disjoint BOUND_VARIABLE_930 BOUND_VARIABLE_932) true))))) :args _let_19)) (AND_ELIM _let_18 :args (0)) :args (_let_16 false _let_17)) :args (_let_14 true _let_15 false _let_16)) :args (_let_13 true _let_12)))) (let ((_let_33 (REFL :args (_let_11)))) (let ((_let_34 (forall ((C $$unsorted)) (or (not (in C skv_4)) (in C skv_5))))) (let ((_let_35 (= _let_22 _let_34))) (let ((_let_36 (forall ((A $$unsorted) (B $$unsorted)) (= (subset A B) (forall ((C $$unsorted)) (or (not (in C A)) (in C B))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (REFL :args (_let_24)))) (let ((_let_39 (_let_34))) (let ((_let_40 (not _let_6))) (let ((_let_41 (disjoint skv_6 skv_5))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_42 _let_10 _let_40))) (let ((_let_44 (forall ((BOUND_VARIABLE_945 $$unsorted) (BOUND_VARIABLE_947 $$unsorted) (BOUND_VARIABLE_961 $$unsorted)) (or (not (disjoint BOUND_VARIABLE_945 BOUND_VARIABLE_947)) (not (in BOUND_VARIABLE_961 BOUND_VARIABLE_945)) (not (in BOUND_VARIABLE_961 BOUND_VARIABLE_947)))))) (let ((_let_45 (_let_44))) (let ((_let_46 (or _let_21 _let_41))) (let ((_let_47 (forall ((A $$unsorted) (B $$unsorted)) (or (not (disjoint A B)) (disjoint B A))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_8)) :args ((or _let_7 _let_6 (not _let_8)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_10 _let_40 (not _let_43)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_21 _let_41 (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 1)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_28)) :args ((or _let_20 _let_24))) _let_30 :args (_let_20 true _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (skv_5 skv_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (disjoint A B) false))))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_41 false _let_20 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 1)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_28)) :args ((or _let_9 _let_11))) _let_32 :args (_let_9 true _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_45) :args (skv_6 skv_5 skv_7 QUANTIFIERS_INST_E_MATCHING ((not (= (disjoint BOUND_VARIABLE_945 BOUND_VARIABLE_947) false)) (not (= (in BOUND_VARIABLE_961 BOUND_VARIABLE_945) false))))) :args _let_45)) (AND_ELIM _let_18 :args (1)) :args (_let_43 false _let_44)) :args (_let_40 false _let_41 false _let_9 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_39) :args (skv_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (in C skv_4) false))))) :args _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_35)) :args ((or _let_23 _let_34 (not _let_35)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_28)) :args ((or _let_22 _let_24))) _let_30 :args (_let_22 true _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (skv_4 skv_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((subset A B)))) :args (_let_36))) _let_37 :args (_let_35 false _let_36)) :args (_let_34 false _let_22 false _let_35)) :args (_let_8 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 0)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_5))) :args _let_28)) :args ((or _let_5 _let_11))) _let_32 :args (_let_5 true _let_11)) :args (false true _let_6 false _let_8 false _let_5)) :args ((forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (subset A B) (subset C B)) (subset (set_union2 A C) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (empty A) (not (= A B)) (empty B)))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (not (and (in A B) (empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (set_difference A (set_difference A B)) (set_intersection2 A B))) (forall ((A $$unsorted)) (=> (empty A) (= A empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (subset A B) (= B (set_union2 A (set_difference B A))))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (subset A B) (proper_subset B A)))) (forall ((A $$unsorted)) (=> (subset A empty_set) (= A empty_set))) _let_3 (forall ((A $$unsorted)) (= (set_difference A empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= (set_difference A B) empty_set) (subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (set_difference (set_union2 A B) B) (set_difference A B))) (forall ((A $$unsorted) (B $$unsorted)) (subset (set_difference A B) A)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (in C (set_intersection2 A B)))))) (not (and (exists ((C $$unsorted)) (in C (set_intersection2 A B))) _let_1))))) (forall ((A $$unsorted)) (subset empty_set A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (in C A) (in C B))) (= A B))) (forall ((A $$unsorted)) (= (set_intersection2 A empty_set) empty_set)) (forall ((A $$unsorted)) (= (set_difference empty_set A) empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (subset A B) (= (set_intersection2 A B) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (subset A B) (subset (set_intersection2 A C) (set_intersection2 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (= (proper_subset A B) (and (subset A B) (not (= A B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (set_union2 A A) A)) (forall ((A $$unsorted)) (= (= A empty_set) (forall ((B $$unsorted)) (not (in B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (set_union2 A B) (set_union2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (set_intersection2 A A) A)) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (set_union2 A (set_difference B A)) (set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (subset A B) (subset B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (set_union2 A B)) (forall ((D $$unsorted)) (= (in D C) (or (in D A) (in D B)))))) (exists ((A $$unsorted)) (empty A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (set_intersection2 A B)) (forall ((D $$unsorted)) (= (in D C) (and (in D A) (in D B)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (set_intersection2 A B) (set_intersection2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (in A B) (not (in B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (set_difference A B)) (forall ((D $$unsorted)) (= (in D C) (and (in D A) (not (in D B))))))) (exists ((A $$unsorted)) (not (empty A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (proper_subset A B) (not (proper_subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (subset (set_intersection2 A B) A)) true (empty empty_set) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (empty A)) (not (empty (set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (empty A)) (not (empty (set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (subset A B) (subset B C)) (subset A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (subset A B) (subset (set_difference A C) (set_difference B C)))) (forall ((A $$unsorted)) (= (set_union2 A empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (not (proper_subset A A))) (forall ((A $$unsorted) (B $$unsorted)) (subset A (set_union2 A B))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (disjoint A B) (= (set_intersection2 A B) empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (set_difference A B) empty_set) (subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (subset A B) (= (set_union2 A B) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (subset A B) (subset A C)) (subset A (set_intersection2 B C))))))))))))))))))))))))))))))))))))))))))))))))))))))
% SZS output end Proof for SEU140+2

Sample solution for NLP042+1

% SZS output start FiniteModel for NLP042+1
(
; cardinality of $$unsorted is 4
; rep: (as @$$unsorted_0 $$unsorted)
; rep: (as @$$unsorted_1 $$unsorted)
; rep: (as @$$unsorted_2 $$unsorted)
; rep: (as @$$unsorted_3 $$unsorted)
(define-fun woman (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_3 $$unsorted) $x2)))
(define-fun female (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_3 $$unsorted) $x2)))
(define-fun human_person (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_3 $$unsorted) $x2)))
(define-fun animate (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_3 $$unsorted) $x2)))
(define-fun human (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_3 $$unsorted) $x2)))
(define-fun organism (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_3 $$unsorted) $x2)))
(define-fun living (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_3 $$unsorted) $x2)))
(define-fun impartial (($x1 $$unsorted) ($x2 $$unsorted)) Bool true)
(define-fun entity (($x1 $$unsorted) ($x2 $$unsorted)) Bool (or (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_1 $$unsorted) $x2)) (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_3 $$unsorted) $x2))))
(define-fun mia_forename (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_2 $$unsorted) $x2)))
(define-fun forename (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_2 $$unsorted) $x2)))
(define-fun abstraction (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_2 $$unsorted) $x2)))
(define-fun unisex (($x1 $$unsorted) ($x2 $$unsorted)) Bool (or (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2)) (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_2 $$unsorted) $x2)) (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_1 $$unsorted) $x2))))
(define-fun general (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_2 $$unsorted) $x2)))
(define-fun nonhuman (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_2 $$unsorted) $x2)))
(define-fun thing (($x1 $$unsorted) ($x2 $$unsorted)) Bool true)
(define-fun relation (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_2 $$unsorted) $x2)))
(define-fun relname (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_2 $$unsorted) $x2)))
(define-fun object (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_1 $$unsorted) $x2)))
(define-fun nonliving (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_1 $$unsorted) $x2)))
(define-fun existent (($x1 $$unsorted) ($x2 $$unsorted)) Bool (or (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_1 $$unsorted) $x2)) (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_3 $$unsorted) $x2))))
(define-fun specific (($x1 $$unsorted) ($x2 $$unsorted)) Bool (or (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_1 $$unsorted) $x2)) (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2)) (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_3 $$unsorted) $x2))))
(define-fun substance_matter (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_1 $$unsorted) $x2)))
(define-fun food (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_1 $$unsorted) $x2)))
(define-fun beverage (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_1 $$unsorted) $x2)))
(define-fun shake_beverage (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_1 $$unsorted) $x2)))
(define-fun order (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2)))
(define-fun event (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2)))
(define-fun eventuality (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2)))
(define-fun nonexistent (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2)))
(define-fun singleton (($x1 $$unsorted) ($x2 $$unsorted)) Bool true)
(define-fun act (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2)))
(define-fun of (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted)) Bool true)
(define-fun nonreflexive (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2)))
(define-fun agent (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted)) Bool (and (not (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2) (= (as @$$unsorted_1 $$unsorted) $x3))) (not (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2) (= (as @$$unsorted_0 $$unsorted) $x3))) (not (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2) (= (as @$$unsorted_2 $$unsorted) $x3)))))
(define-fun patient (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted)) Bool (not (and (= (as @$$unsorted_3 $$unsorted) $x1) (= (as @$$unsorted_0 $$unsorted) $x2) (= (as @$$unsorted_3 $$unsorted) $x3))))
(define-fun actual_world ((_arg_1 $$unsorted)) Bool true)
(define-fun past ((_arg_1 $$unsorted) (_arg_2 $$unsorted)) Bool true)
)
% SZS output end FiniteModel for NLP042+1

Sample solution for SWV017+1

% SZS output start FiniteModel for SWV017+1.tptp
(
; cardinality of $$unsorted is 2
; rep: (as @$$unsorted_0 $$unsorted)
; rep: (as @$$unsorted_1 $$unsorted)
(define-fun at () $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun t () $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun key (($x1 $$unsorted) ($x2 $$unsorted)) $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun a_holds (($x1 $$unsorted)) Bool true)
(define-fun a () $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun party_of_protocol (($x1 $$unsorted)) Bool true)
(define-fun b () $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun an_a_nonce () $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun pair (($x1 $$unsorted) ($x2 $$unsorted)) $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun sent (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted)) $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun message (($x1 $$unsorted)) Bool true)
(define-fun a_stored (($x1 $$unsorted)) Bool true)
(define-fun quadruple (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted) ($x4 $$unsorted)) $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun encrypt (($x1 $$unsorted) ($x2 $$unsorted)) $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun triple (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted)) $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun bt () $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun b_holds (($x1 $$unsorted)) Bool true)
(define-fun fresh_to_b (($x1 $$unsorted)) Bool true)
(define-fun generate_b_nonce (($x1 $$unsorted)) $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun generate_expiration_time (($x1 $$unsorted)) $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun b_stored (($x1 $$unsorted)) Bool true)
(define-fun a_key (($x1 $$unsorted)) Bool (= (as @$$unsorted_1 $$unsorted) $x1))
(define-fun t_holds (($x1 $$unsorted)) Bool true)
(define-fun a_nonce (($x1 $$unsorted)) Bool (= (as @$$unsorted_0 $$unsorted) $x1))
(define-fun generate_key (($x1 $$unsorted)) $$unsorted (as @$$unsorted_1 $$unsorted))
(define-fun intruder_message (($x1 $$unsorted)) Bool true)
(define-fun intruder_holds (($x1 $$unsorted)) Bool true)
(define-fun an_intruder_nonce () $$unsorted (as @$$unsorted_0 $$unsorted))
(define-fun fresh_intruder_nonce (($x1 $$unsorted)) Bool true)
(define-fun generate_intruder_nonce (($x1 $$unsorted)) $$unsorted (as @$$unsorted_0 $$unsorted))
)
% SZS output end FiniteModel for SWV017+1.tptp

Drodi 3.3.3

Sample solution for SEU140+2

% SZS status Theorem for SEU140+2: Theorem is valid
% SZS output start CNFRefutation for SEU140+2
fof(f4,axiom,(
  ((! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ))),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/SEU140+2.p')).
fof(f5,axiom,(
  ((! [A,B] :( A = B<=> ( subset(A,B)& subset(B,A) ) ) ))),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/SEU140+2.p')).
fof(f11,axiom,(
  ((! [A,B] :( disjoint(A,B)<=> set_intersection2(A,B) = empty_set ) ))),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/SEU140+2.p')).
fof(f33,lemma,(
  ((! [A,B,C] :( subset(A,B)=> subset(set_intersection2(A,C),set_intersection2(B,C)) ) ))),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/SEU140+2.p')).
fof(f37,lemma,(
  ((! [A] : subset(empty_set,A) ))),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/SEU140+2.p')).
fof(f51,conjecture,(
  ((! [A,B,C] :( ( subset(A,B)& disjoint(B,C) )=> disjoint(A,C) ) ))),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/SEU140+2.p')).
fof(f52,negated_conjecture,(
  ~(((! [A,B,C] :( ( subset(A,B)& disjoint(B,C) )=> disjoint(A,C) ) )))),
  inference(negated_conjecture,[status(cth)],[f51])).
fof(f63,plain,(
  ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
  inference(cnf_transformation,[status(esa)],[f4])).
fof(f64,plain,(
  ![A,B]: ((~A=B|(subset(A,B)&subset(B,A)))&(A=B|(~subset(A,B)|~subset(B,A))))),
  inference(NNF_transformation,[status(esa)],[f5])).
fof(f65,plain,(
  (![A,B]: (~A=B|(subset(A,B)&subset(B,A))))&(![A,B]: (A=B|(~subset(A,B)|~subset(B,A))))),
  inference(miniscoping,[status(esa)],[f64])).
fof(f68,plain,(
  ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
  inference(cnf_transformation,[status(esa)],[f65])).
fof(f108,plain,(
  ![A,B]: ((~disjoint(A,B)|set_intersection2(A,B)=empty_set)&(disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
  inference(NNF_transformation,[status(esa)],[f11])).
fof(f109,plain,(
  (![A,B]: (~disjoint(A,B)|set_intersection2(A,B)=empty_set))&(![A,B]: (disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
  inference(miniscoping,[status(esa)],[f108])).
fof(f110,plain,(
  ![X0,X1]: (~disjoint(X0,X1)|set_intersection2(X0,X1)=empty_set)),
  inference(cnf_transformation,[status(esa)],[f109])).
fof(f111,plain,(
  ![X0,X1]: (disjoint(X0,X1)|~set_intersection2(X0,X1)=empty_set)),
  inference(cnf_transformation,[status(esa)],[f109])).
fof(f151,plain,(
  ![A,B,C]: (~subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)))),
  inference(pre_NNF_transformation,[status(esa)],[f33])).
fof(f152,plain,(
  ![A,B]: (~subset(A,B)|(![C]: subset(set_intersection2(A,C),set_intersection2(B,C))))),
  inference(miniscoping,[status(esa)],[f151])).
fof(f153,plain,(
  ![X0,X1,X2]: (~subset(X0,X1)|subset(set_intersection2(X0,X2),set_intersection2(X1,X2)))),
  inference(cnf_transformation,[status(esa)],[f152])).
fof(f162,plain,(
  ![X0]: (subset(empty_set,X0))),
  inference(cnf_transformation,[status(esa)],[f37])).
fof(f193,plain,(
  (?[A,B,C]: ((subset(A,B)&disjoint(B,C))&~disjoint(A,C)))),
  inference(pre_NNF_transformation,[status(esa)],[f52])).
fof(f194,plain,(
  ?[A,C]: ((?[B]: (subset(A,B)&disjoint(B,C)))&~disjoint(A,C))),
  inference(miniscoping,[status(esa)],[f193])).
fof(f195,plain,(
  ((subset(sk0_10,sk0_12)&disjoint(sk0_12,sk0_11))&~disjoint(sk0_10,sk0_11))),
  inference(skolemization,[status(esa)],[f194])).
fof(f196,plain,(
  subset(sk0_10,sk0_12)),
  inference(cnf_transformation,[status(esa)],[f195])).
fof(f197,plain,(
  disjoint(sk0_12,sk0_11)),
  inference(cnf_transformation,[status(esa)],[f195])).
fof(f198,plain,(
  ~disjoint(sk0_10,sk0_11)),
  inference(cnf_transformation,[status(esa)],[f195])).
fof(f471,plain,(
  set_intersection2(sk0_12,sk0_11)=empty_set),
  inference(resolution,[status(thm)],[f110,f197])).
fof(f472,plain,(
  set_intersection2(sk0_11,sk0_12)=empty_set),
  inference(forward_demodulation,[status(thm)],[f63,f471])).
fof(f501,plain,(
  spl0_4 <=> empty_set=empty_set),
  introduced(split_symbol_definition)).
fof(f503,plain,(
  ~empty_set=empty_set|spl0_4),
  inference(component_clause,[status(thm)],[f501])).
fof(f506,plain,(
  $false|spl0_4),
  inference(trivial_equality_resolution,[status(esa)],[f503])).
fof(f507,plain,(
  spl0_4),
  inference(contradiction_clause,[status(thm)],[f506])).
fof(f568,plain,(
  ![X0]: (empty_set=X0|~subset(X0,empty_set))),
  inference(resolution,[status(thm)],[f162,f68])).
fof(f1330,plain,(
  ![X0]: (subset(set_intersection2(sk0_10,X0),set_intersection2(sk0_12,X0)))),
  inference(resolution,[status(thm)],[f153,f196])).
fof(f10117,plain,(
  ![X0]: (subset(set_intersection2(sk0_10,X0),set_intersection2(X0,sk0_12)))),
  inference(paramodulation,[status(thm)],[f63,f1330])).
fof(f13040,plain,(
  subset(set_intersection2(sk0_10,sk0_11),empty_set)),
  inference(paramodulation,[status(thm)],[f472,f10117])).
fof(f13608,plain,(
  empty_set=set_intersection2(sk0_10,sk0_11)),
  inference(resolution,[status(thm)],[f13040,f568])).
fof(f13735,plain,(
  spl0_255 <=> disjoint(sk0_10,sk0_11)),
  introduced(split_symbol_definition)).
fof(f13736,plain,(
  disjoint(sk0_10,sk0_11)|~spl0_255),
  inference(component_clause,[status(thm)],[f13735])).
fof(f13777,plain,(
  disjoint(sk0_10,sk0_11)|~empty_set=empty_set),
  inference(paramodulation,[status(thm)],[f13608,f111])).
fof(f13778,plain,(
  spl0_255|~spl0_4),
  inference(split_clause,[status(thm)],[f13777,f13735,f501])).
fof(f13779,plain,(
  $false|~spl0_255),
  inference(forward_subsumption_resolution,[status(thm)],[f13736,f198])).
fof(f13780,plain,(
  ~spl0_255),
  inference(contradiction_clause,[status(thm)],[f13779])).
fof(f13781,plain,(
  $false),
  inference(sat_refutation,[status(thm)],[f507,f13778,f13780])).
% SZS output end CNFRefutation for SEU140+2.p

Sample solution for BOO001-1

% SZS status Unsatisfiable for BOO001-1: Theory is unsatisfiable
% SZS output start CNFRefutation for BOO001-1
fof(f1,axiom,(
  (![V,W,X,Y,Z]: (( multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z)) )))),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/BOO001-1.p')).
fof(f2,axiom,(
  (![Y,X]: (( multiply(Y,X,X) = X )))),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/BOO001-1.p')).
fof(f3,axiom,(
  (![X,Y]: (( multiply(X,X,Y) = X )))),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/BOO001-1.p')).
fof(f5,axiom,(
  (![X,Y]: (( multiply(X,Y,inverse(Y)) = X )))),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/BOO001-1.p')).
fof(f6,negated_conjecture,(
  (  inverse(inverse(a)) != a )),
  file('/run/media/oscar/Elements/temp/TPTP-v7.3.0.b/Problems/BOO001-1.p')).
fof(f7,plain,(
  ![X0,X1,X2,X3,X4]: (multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4))=multiply(X0,X1,multiply(X2,X3,X4)))),
  inference(cnf_transformation,[status(esa)],[f1])).
fof(f8,plain,(
  ![X0,X1]: (multiply(X0,X1,X1)=X1)),
  inference(cnf_transformation,[status(esa)],[f2])).
fof(f9,plain,(
  ![X0,X1]: (multiply(X0,X0,X1)=X0)),
  inference(cnf_transformation,[status(esa)],[f3])).
fof(f11,plain,(
  ![X0,X1]: (multiply(X0,X1,inverse(X1))=X0)),
  inference(cnf_transformation,[status(esa)],[f5])).
fof(f12,plain,(
  ~inverse(inverse(a))=a),
  inference(cnf_transformation,[status(esa)],[f6])).
fof(f18,plain,(
  ![X0,X1,X2,X3]: (multiply(X0,X1,multiply(X2,X0,X3))=multiply(X2,X0,multiply(X0,X1,X3)))),
  inference(paramodulation,[status(thm)],[f8,f7])).
fof(f19,plain,(
  ![X0,X1,X2,X3]: (multiply(X0,X1,multiply(X2,multiply(X0,X1,X2),X3))=multiply(X0,X1,X2))),
  inference(paramodulation,[status(thm)],[f7,f9])).
fof(f481,plain,(
  ![X0,X1,X2]: (multiply(X0,X1,multiply(inverse(X1),X0,X2))=multiply(X0,X1,inverse(X1)))),
  inference(paramodulation,[status(thm)],[f11,f19])).
fof(f482,plain,(
  ![X0,X1,X2]: (multiply(X0,X1,multiply(inverse(X1),X0,X2))=X0)),
  inference(forward_demodulation,[status(thm)],[f11,f481])).
fof(f526,plain,(
  ![X0,X1,X2]: (multiply(inverse(X0),X1,multiply(X1,X0,X2))=X1)),
  inference(paramodulation,[status(thm)],[f18,f482])).
fof(f591,plain,(
  ![X0,X1]: (multiply(inverse(X0),X1,X0)=X1)),
  inference(paramodulation,[status(thm)],[f8,f526])).
fof(f623,plain,(
  ![X0]: (inverse(inverse(X0))=X0)),
  inference(paramodulation,[status(thm)],[f11,f591])).
fof(f653,plain,(
  ~a=a),
  inference(backward_demodulation,[status(thm)],[f623,f12])).
fof(f654,plain,(
  $false),
  inference(trivial_equality_resolution,[status(esa)],[f653])).
% SZS output end CNFRefutation for BOO001-1.p

E 3.0

Sample solution for SET014^4

# SZS output start CNFRefutation
thf(thm, conjecture, ![X22:$i > $o, X23:$i > $o, X24:$i > $o]:(((subset @ X22 @ X24)&(subset @ X23 @ X24))=>(subset @ (union @ X22 @ X23) @ X24)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SET014^4.p', thm)).
thf(union, axiom, ((union)=(^[X5:$i > $o, X6:$i > $o, X4:$i]:(((X5 @ X4)|(X6 @ X4))))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/SET008^0.ax', union)).
thf(subset, axiom, ((subset)=(^[X16:$i > $o, X17:$i > $o]:(![X4:$i]:(((X16 @ X4)=>(X17 @ X4)))))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/SET008^0.ax', subset)).
thf(c_0_3, negated_conjecture, ~(![X22:$i > $o, X23:$i > $o, X24:$i > $o]:((![X29:$i]:((X22 @ X29)=>(X24 @ X29))&![X30:$i]:((X23 @ X30)=>(X24 @ X30)))=>![X32:$i]:(((X22 @ X32)|(X23 @ X32))=>(X24 @ X32)))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]), union]), subset])).
thf(c_0_4, negated_conjecture, ![X37:$i, X38:$i]:(((~(epred1_0 @ X37)|(epred3_0 @ X37))&(~(epred2_0 @ X38)|(epred3_0 @ X38)))&(((epred1_0 @ esk1_0)|(epred2_0 @ esk1_0))&~(epred3_0 @ esk1_0))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])).
thf(c_0_5, negated_conjecture, ![X1:$i]:((epred3_0 @ X1)|~(epred2_0 @ X1)), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_6, negated_conjecture, ((epred1_0 @ esk1_0)|(epred2_0 @ esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_7, negated_conjecture, ~(epred3_0 @ esk1_0), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_8, negated_conjecture, ![X1:$i]:((epred3_0 @ X1)|~(epred1_0 @ X1)), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_9, negated_conjecture, (epred1_0 @ esk1_0), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_5, c_0_6]), c_0_7])).
thf(c_0_10, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8, c_0_9]), c_0_7]), ['proof']).
# SZS output end CNFRefutation

Sample solution for SEU140+2

# SZS output start CNFRefutation
fof(t4_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~(in(X3,set_intersection2(X1,X2)))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t4_xboole_0)).
fof(t48_xboole_1, lemma, ![X1, X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t48_xboole_1)).
fof(t63_xboole_1, conjecture, ![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t63_xboole_1)).
fof(d1_xboole_0, axiom, ![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d1_xboole_0)).
fof(d4_xboole_0, axiom, ![X1, X2, X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2))))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d4_xboole_0)).
fof(t3_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(d3_xboole_0, axiom, ![X1, X2, X3]:(X3=set_intersection2(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&in(X4,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d3_xboole_0)).
fof(l32_xboole_1, lemma, ![X1, X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', l32_xboole_1)).
fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(subset(X1,X2)&subset(X2,X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d10_xboole_0)).
fof(t36_xboole_1, lemma, ![X1, X2]:subset(set_difference(X1,X2),X1), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t36_xboole_1)).
fof(t3_boole, axiom, ![X1]:set_difference(X1,empty_set)=X1, file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t3_boole)).
fof(c_0_11, lemma, ![X1, X2]:(~((~disjoint(X1,X2)&![X3]:~in(X3,set_intersection2(X1,X2))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2)))), inference(fof_simplification,[status(thm)],[t4_xboole_0])).
fof(c_0_12, lemma, ![X226, X227, X229, X230, X231]:((disjoint(X226,X227)|in(esk10_2(X226,X227),set_intersection2(X226,X227)))&(~in(X231,set_intersection2(X229,X230))|~disjoint(X229,X230))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])).
fof(c_0_13, lemma, ![X223, X224]:set_difference(X223,set_difference(X223,X224))=set_intersection2(X223,X224), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_14, negated_conjecture, ~(![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), inference(assume_negation,[status(cth)],[t63_xboole_1])).
cnf(c_0_15, lemma, (~in(X1,set_intersection2(X2,X3))|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_16, lemma, (set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_13])).
fof(c_0_17, negated_conjecture, ((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])).
fof(c_0_18, plain, ![X1]:(X1=empty_set<=>![X2]:~in(X2,X1)), inference(fof_simplification,[status(thm)],[d1_xboole_0])).
fof(c_0_19, plain, ![X1, X2, X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~in(X4,X2)))), inference(fof_simplification,[status(thm)],[d4_xboole_0])).
fof(c_0_20, lemma, ![X1, X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), inference(fof_simplification,[status(thm)],[t3_xboole_0])).
cnf(c_0_21, lemma, (~disjoint(X2,X3)|~in(X1,set_difference(X2,set_difference(X2,X3)))), inference(rw,[status(thm)],[c_0_15, c_0_16])).
cnf(c_0_22, negated_conjecture, (disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_17])).
fof(c_0_23, plain, ![X126, X127, X128]:((X126!=empty_set|~in(X127,X126))&(in(esk1_1(X128),X128)|X128=empty_set)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])])).
fof(c_0_24, plain, ![X145, X146, X147, X148, X149, X150, X151, X152]:((((in(X148,X145)|~in(X148,X147)|X147!=set_intersection2(X145,X146))&(in(X148,X146)|~in(X148,X147)|X147!=set_intersection2(X145,X146)))&(~in(X149,X145)|~in(X149,X146)|in(X149,X147)|X147!=set_intersection2(X145,X146)))&((~in(esk4_3(X150,X151,X152),X152)|(~in(esk4_3(X150,X151,X152),X150)|~in(esk4_3(X150,X151,X152),X151))|X152=set_intersection2(X150,X151))&((in(esk4_3(X150,X151,X152),X150)|in(esk4_3(X150,X151,X152),X152)|X152=set_intersection2(X150,X151))&(in(esk4_3(X150,X151,X152),X151)|in(esk4_3(X150,X151,X152),X152)|X152=set_intersection2(X150,X151))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])])).
fof(c_0_25, plain, ![X154, X155, X156, X157, X158, X159, X160, X161]:((((in(X157,X154)|~in(X157,X156)|X156!=set_difference(X154,X155))&(~in(X157,X155)|~in(X157,X156)|X156!=set_difference(X154,X155)))&(~in(X158,X154)|in(X158,X155)|in(X158,X156)|X156!=set_difference(X154,X155)))&((~in(esk5_3(X159,X160,X161),X161)|(~in(esk5_3(X159,X160,X161),X159)|in(esk5_3(X159,X160,X161),X160))|X161=set_difference(X159,X160))&((in(esk5_3(X159,X160,X161),X159)|in(esk5_3(X159,X160,X161),X161)|X161=set_difference(X159,X160))&(~in(esk5_3(X159,X160,X161),X160)|in(esk5_3(X159,X160,X161),X161)|X161=set_difference(X159,X160))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])])).
fof(c_0_26, lemma, ![X212, X213, X215, X216, X217]:(((in(esk9_2(X212,X213),X212)|disjoint(X212,X213))&(in(esk9_2(X212,X213),X213)|disjoint(X212,X213)))&(~in(X217,X215)|~in(X217,X216)|~disjoint(X215,X216))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])])])).
fof(c_0_27, lemma, ![X174, X175]:((set_difference(X174,X175)!=empty_set|subset(X174,X175))&(~subset(X174,X175)|set_difference(X174,X175)=empty_set)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])).
cnf(c_0_28, negated_conjecture, (~in(X1,set_difference(esk12_0,set_difference(esk12_0,esk13_0)))), inference(spm,[status(thm)],[c_0_21, c_0_22])).
cnf(c_0_29, plain, (in(esk1_1(X1),X1)|X1=empty_set), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_30, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_intersection2(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_31, plain, (~in(X1,X2)|~in(X1,X3)|X3!=set_difference(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_32, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_17])).
cnf(c_0_33, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_26])).
fof(c_0_34, plain, ![X124, X125]:(((subset(X124,X125)|X124!=X125)&(subset(X125,X124)|X124!=X125))&(~subset(X124,X125)|~subset(X125,X124)|X124=X125)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])).
cnf(c_0_35, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_27])).
cnf(c_0_36, negated_conjecture, (set_difference(esk12_0,set_difference(esk12_0,esk13_0))=empty_set), inference(spm,[status(thm)],[c_0_28, c_0_29])).
fof(c_0_37, lemma, ![X205, X206]:subset(set_difference(X205,X206),X205), inference(variable_rename,[status(thm)],[t36_xboole_1])).
cnf(c_0_38, plain, (in(X1,X2)|X3!=set_difference(X4,set_difference(X4,X2))|~in(X1,X3)), inference(rw,[status(thm)],[c_0_30, c_0_16])).
cnf(c_0_39, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_27])).
cnf(c_0_40, negated_conjecture, (subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_17])).
fof(c_0_41, plain, ![X211]:set_difference(X211,empty_set)=X211, inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_42, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3)), inference(er,[status(thm)],[c_0_31])).
cnf(c_0_43, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk13_0)), inference(spm,[status(thm)],[c_0_32, c_0_33])).
cnf(c_0_44, plain, (X1=X2|~subset(X1,X2)|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_34])).
cnf(c_0_45, lemma, (subset(esk12_0,set_difference(esk12_0,esk13_0))), inference(spm,[status(thm)],[c_0_35, c_0_36])).
cnf(c_0_46, lemma, (subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_37])).
cnf(c_0_47, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2)))), inference(er,[status(thm)],[c_0_38])).
cnf(c_0_48, negated_conjecture, (set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_39, c_0_40])).
cnf(c_0_49, plain, (set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_41])).
cnf(c_0_50, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_51, negated_conjecture, (~in(esk9_2(esk11_0,esk13_0),set_difference(X1,esk13_0))), inference(spm,[status(thm)],[c_0_42, c_0_43])).
cnf(c_0_52, lemma, (set_difference(esk12_0,esk13_0)=esk12_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_46])])).
cnf(c_0_53, negated_conjecture, (in(X1,esk12_0)|~in(X1,esk11_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_49])).
cnf(c_0_54, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk11_0)), inference(spm,[status(thm)],[c_0_32, c_0_50])).
cnf(c_0_55, lemma, (~in(esk9_2(esk11_0,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_51, c_0_52])).
cnf(c_0_56, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_55]), ['proof']).
# SZS output end CNFRefutation

Sample solution for NLP042+1

# SZS output start Saturation
fof(co1, conjecture, ~(?[X1]:(actual_world(X1)&?[X2, X3, X4, X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', co1)).
fof(ax27, axiom, ![X1, X2]:(shake_beverage(X1,X2)=>beverage(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax27)).
fof(ax15, axiom, ![X1, X2]:(relname(X1,X2)=>relation(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax15)).
fof(ax16, axiom, ![X1, X2]:(forename(X1,X2)=>relname(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax16)).
fof(ax26, axiom, ![X1, X2]:(beverage(X1,X2)=>food(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax26)).
fof(ax41, axiom, ![X1, X2]:(specific(X1,X2)=>~(general(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax41)).
fof(ax39, axiom, ![X1, X2]:(nonhuman(X1,X2)=>~(human(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax39)).
fof(ax14, axiom, ![X1, X2]:(relation(X1,X2)=>abstraction(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax14)).
fof(ax42, axiom, ![X1, X2]:(unisex(X1,X2)=>~(female(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax42)).
fof(ax38, axiom, ![X1, X2]:(existent(X1,X2)=>~(nonexistent(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax38)).
fof(ax40, axiom, ![X1, X2]:(nonliving(X1,X2)=>~(living(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax40)).
fof(ax25, axiom, ![X1, X2]:(food(X1,X2)=>substance_matter(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax25)).
fof(ax37, axiom, ![X1, X2]:(animate(X1,X2)=>~(nonliving(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax37)).
fof(ax6, axiom, ![X1, X2]:(organism(X1,X2)=>entity(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax6)).
fof(ax7, axiom, ![X1, X2]:(human_person(X1,X2)=>organism(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax7)).
fof(ax8, axiom, ![X1, X2]:(woman(X1,X2)=>human_person(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax8)).
fof(ax21, axiom, ![X1, X2]:(entity(X1,X2)=>specific(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax21)).
fof(ax12, axiom, ![X1, X2]:(abstraction(X1,X2)=>nonhuman(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax12)).
fof(ax10, axiom, ![X1, X2]:(abstraction(X1,X2)=>unisex(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax10)).
fof(ax30, axiom, ![X1, X2]:(eventuality(X1,X2)=>nonexistent(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax30)).
fof(ax34, axiom, ![X1, X2]:(event(X1,X2)=>eventuality(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax34)).
fof(ax31, axiom, ![X1, X2]:(eventuality(X1,X2)=>specific(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax31)).
fof(ax19, axiom, ![X1, X2]:(object(X1,X2)=>nonliving(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax19)).
fof(ax24, axiom, ![X1, X2]:(substance_matter(X1,X2)=>object(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax24)).
fof(ax17, axiom, ![X1, X2]:(object(X1,X2)=>unisex(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax17)).
fof(ax29, axiom, ![X1, X2]:(eventuality(X1,X2)=>unisex(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax29)).
fof(ax43, axiom, ![X1, X2, X3]:(((entity(X1,X2)&forename(X1,X3))&of(X1,X3,X2))=>~(?[X4]:((forename(X1,X4)&X4!=X3)&of(X1,X4,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax43)).
fof(ax11, axiom, ![X1, X2]:(abstraction(X1,X2)=>general(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax11)).
fof(ax44, axiom, ![X1, X2, X3, X4]:(((nonreflexive(X1,X2)&agent(X1,X2,X3))&patient(X1,X2,X4))=>X3!=X4), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax44)).
fof(ax3, axiom, ![X1, X2]:(human_person(X1,X2)=>human(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax3)).
fof(ax1, axiom, ![X1, X2]:(woman(X1,X2)=>female(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax1)).
fof(ax20, axiom, ![X1, X2]:(entity(X1,X2)=>existent(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax20)).
fof(ax4, axiom, ![X1, X2]:(organism(X1,X2)=>living(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax4)).
fof(ax2, axiom, ![X1, X2]:(human_person(X1,X2)=>animate(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax2)).
fof(ax23, axiom, ![X1, X2]:(object(X1,X2)=>entity(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax23)).
fof(ax32, axiom, ![X1, X2]:(thing(X1,X2)=>singleton(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax32)).
fof(ax33, axiom, ![X1, X2]:(eventuality(X1,X2)=>thing(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax33)).
fof(ax13, axiom, ![X1, X2]:(abstraction(X1,X2)=>thing(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax13)).
fof(ax22, axiom, ![X1, X2]:(entity(X1,X2)=>thing(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax22)).
fof(ax18, axiom, ![X1, X2]:(object(X1,X2)=>impartial(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax18)).
fof(ax5, axiom, ![X1, X2]:(organism(X1,X2)=>impartial(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax5)).
fof(ax36, axiom, ![X1, X2]:(order(X1,X2)=>act(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax36)).
fof(ax35, axiom, ![X1, X2]:(act(X1,X2)=>event(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax35)).
fof(ax28, axiom, ![X1, X2]:(order(X1,X2)=>event(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax28)).
fof(ax9, axiom, ![X1, X2]:(mia_forename(X1,X2)=>forename(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax9)).
fof(c_0_45, negated_conjecture, ~(~(?[X1]:(actual_world(X1)&?[X2, X3, X4, X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5))))), inference(assume_negation,[status(cth)],[co1])).
fof(c_0_46, plain, ![X155, X156]:(~shake_beverage(X155,X156)|beverage(X155,X156)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])).
fof(c_0_47, negated_conjecture, (actual_world(esk1_0)&((((((((((of(esk1_0,esk3_0,esk2_0)&woman(esk1_0,esk2_0))&mia_forename(esk1_0,esk3_0))&forename(esk1_0,esk3_0))&shake_beverage(esk1_0,esk4_0))&event(esk1_0,esk5_0))&agent(esk1_0,esk5_0,esk2_0))&patient(esk1_0,esk5_0,esk4_0))&past(esk1_0,esk5_0))&nonreflexive(esk1_0,esk5_0))&order(esk1_0,esk5_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])).
fof(c_0_48, plain, ![X131, X132]:(~relname(X131,X132)|relation(X131,X132)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])).
fof(c_0_49, plain, ![X133, X134]:(~forename(X133,X134)|relname(X133,X134)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])).
fof(c_0_50, plain, ![X153, X154]:(~beverage(X153,X154)|food(X153,X154)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])).
cnf(c_0_51, plain, (beverage(X1,X2)|~shake_beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46]), ['final']).
cnf(c_0_52, negated_conjecture, (shake_beverage(esk1_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
fof(c_0_53, plain, ![X1, X2]:(specific(X1,X2)=>~general(X1,X2)), inference(fof_simplification,[status(thm)],[ax41])).
fof(c_0_54, plain, ![X1, X2]:(nonhuman(X1,X2)=>~human(X1,X2)), inference(fof_simplification,[status(thm)],[ax39])).
fof(c_0_55, plain, ![X129, X130]:(~relation(X129,X130)|abstraction(X129,X130)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax14])])).
cnf(c_0_56, plain, (relation(X1,X2)|~relname(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48]), ['final']).
cnf(c_0_57, plain, (relname(X1,X2)|~forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_49]), ['final']).
fof(c_0_58, plain, ![X1, X2]:(unisex(X1,X2)=>~female(X1,X2)), inference(fof_simplification,[status(thm)],[ax42])).
fof(c_0_59, plain, ![X1, X2]:(existent(X1,X2)=>~nonexistent(X1,X2)), inference(fof_simplification,[status(thm)],[ax38])).
fof(c_0_60, plain, ![X1, X2]:(nonliving(X1,X2)=>~living(X1,X2)), inference(fof_simplification,[status(thm)],[ax40])).
fof(c_0_61, plain, ![X151, X152]:(~food(X151,X152)|substance_matter(X151,X152)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])).
cnf(c_0_62, plain, (food(X1,X2)|~beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_50]), ['final']).
cnf(c_0_63, negated_conjecture, (beverage(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_51, c_0_52]), ['final']).
fof(c_0_64, plain, ![X1, X2]:(animate(X1,X2)=>~nonliving(X1,X2)), inference(fof_simplification,[status(thm)],[ax37])).
fof(c_0_65, plain, ![X113, X114]:(~organism(X113,X114)|entity(X113,X114)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])).
fof(c_0_66, plain, ![X115, X116]:(~human_person(X115,X116)|organism(X115,X116)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])).
fof(c_0_67, plain, ![X117, X118]:(~woman(X117,X118)|human_person(X117,X118)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax8])])).
fof(c_0_68, plain, ![X183, X184]:(~specific(X183,X184)|~general(X183,X184)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])).
fof(c_0_69, plain, ![X143, X144]:(~entity(X143,X144)|specific(X143,X144)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])).
fof(c_0_70, plain, ![X179, X180]:(~nonhuman(X179,X180)|~human(X179,X180)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])).
fof(c_0_71, plain, ![X125, X126]:(~abstraction(X125,X126)|nonhuman(X125,X126)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])).
cnf(c_0_72, plain, (abstraction(X1,X2)|~relation(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_55]), ['final']).
cnf(c_0_73, plain, (relation(X1,X2)|~forename(X1,X2)), inference(spm,[status(thm)],[c_0_56, c_0_57]), ['final']).
fof(c_0_74, plain, ![X185, X186]:(~unisex(X185,X186)|~female(X185,X186)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])).
fof(c_0_75, plain, ![X121, X122]:(~abstraction(X121,X122)|unisex(X121,X122)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax10])])).
fof(c_0_76, plain, ![X177, X178]:(~existent(X177,X178)|~nonexistent(X177,X178)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])).
fof(c_0_77, plain, ![X161, X162]:(~eventuality(X161,X162)|nonexistent(X161,X162)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])])).
fof(c_0_78, plain, ![X169, X170]:(~event(X169,X170)|eventuality(X169,X170)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax34])])).
fof(c_0_79, plain, ![X163, X164]:(~eventuality(X163,X164)|specific(X163,X164)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax31])])).
fof(c_0_80, plain, ![X181, X182]:(~nonliving(X181,X182)|~living(X181,X182)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])).
fof(c_0_81, plain, ![X139, X140]:(~object(X139,X140)|nonliving(X139,X140)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])).
fof(c_0_82, plain, ![X149, X150]:(~substance_matter(X149,X150)|object(X149,X150)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])])).
cnf(c_0_83, plain, (substance_matter(X1,X2)|~food(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_61]), ['final']).
cnf(c_0_84, negated_conjecture, (food(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_62, c_0_63]), ['final']).
fof(c_0_85, plain, ![X175, X176]:(~animate(X175,X176)|~nonliving(X175,X176)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])).
fof(c_0_86, plain, ![X135, X136]:(~object(X135,X136)|unisex(X135,X136)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax17])])).
fof(c_0_87, plain, ![X159, X160]:(~eventuality(X159,X160)|unisex(X159,X160)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])])).
fof(c_0_88, plain, ![X187, X188, X189, X190]:(~entity(X187,X188)|~forename(X187,X189)|~of(X187,X189,X188)|(~forename(X187,X190)|X190=X189|~of(X187,X190,X188))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])])).
cnf(c_0_89, plain, (entity(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_65]), ['final']).
cnf(c_0_90, plain, (organism(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_66]), ['final']).
cnf(c_0_91, plain, (human_person(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_92, negated_conjecture, (woman(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_93, plain, (~specific(X1,X2)|~general(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_68]), ['final']).
cnf(c_0_94, plain, (specific(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_69]), ['final']).
fof(c_0_95, plain, ![X123, X124]:(~abstraction(X123,X124)|general(X123,X124)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11])])).
cnf(c_0_96, plain, (~nonhuman(X1,X2)|~human(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_70]), ['final']).
cnf(c_0_97, plain, (nonhuman(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_71]), ['final']).
cnf(c_0_98, plain, (abstraction(X1,X2)|~forename(X1,X2)), inference(spm,[status(thm)],[c_0_72, c_0_73]), ['final']).
cnf(c_0_99, negated_conjecture, (forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_100, plain, (~unisex(X1,X2)|~female(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_74]), ['final']).
cnf(c_0_101, plain, (unisex(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_75]), ['final']).
cnf(c_0_102, plain, (~existent(X1,X2)|~nonexistent(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_76]), ['final']).
cnf(c_0_103, plain, (nonexistent(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_77]), ['final']).
cnf(c_0_104, plain, (eventuality(X1,X2)|~event(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_78]), ['final']).
cnf(c_0_105, negated_conjecture, (event(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_106, plain, (specific(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_79]), ['final']).
cnf(c_0_107, plain, (~nonliving(X1,X2)|~living(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_80]), ['final']).
cnf(c_0_108, plain, (nonliving(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_81]), ['final']).
cnf(c_0_109, plain, (object(X1,X2)|~substance_matter(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_82]), ['final']).
cnf(c_0_110, negated_conjecture, (substance_matter(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_83, c_0_84]), ['final']).
cnf(c_0_111, plain, (~animate(X1,X2)|~nonliving(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_85]), ['final']).
cnf(c_0_112, plain, (unisex(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_86]), ['final']).
fof(c_0_113, plain, ![X191, X192, X193, X194]:(~nonreflexive(X191,X192)|~agent(X191,X192,X193)|~patient(X191,X192,X194)|X193!=X194), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])).
cnf(c_0_114, plain, (unisex(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_87]), ['final']).
cnf(c_0_115, plain, (X4=X3|~entity(X1,X2)|~forename(X1,X3)|~of(X1,X3,X2)|~forename(X1,X4)|~of(X1,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_88]), ['final']).
cnf(c_0_116, negated_conjecture, (of(esk1_0,esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_117, plain, (entity(X1,X2)|~human_person(X1,X2)), inference(spm,[status(thm)],[c_0_89, c_0_90]), ['final']).
cnf(c_0_118, negated_conjecture, (human_person(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_91, c_0_92]), ['final']).
cnf(c_0_119, plain, (~general(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_93, c_0_94]), ['final']).
cnf(c_0_120, plain, (general(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_95]), ['final']).
cnf(c_0_121, plain, (~abstraction(X1,X2)|~human(X1,X2)), inference(spm,[status(thm)],[c_0_96, c_0_97]), ['final']).
cnf(c_0_122, negated_conjecture, (abstraction(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_98, c_0_99]), ['final']).
fof(c_0_123, plain, ![X107, X108]:(~human_person(X107,X108)|human(X107,X108)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])).
cnf(c_0_124, plain, (~abstraction(X1,X2)|~female(X1,X2)), inference(spm,[status(thm)],[c_0_100, c_0_101]), ['final']).
fof(c_0_125, plain, ![X103, X104]:(~woman(X103,X104)|female(X103,X104)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])).
cnf(c_0_126, plain, (~eventuality(X1,X2)|~existent(X1,X2)), inference(spm,[status(thm)],[c_0_102, c_0_103]), ['final']).
cnf(c_0_127, negated_conjecture, (eventuality(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_104, c_0_105]), ['final']).
fof(c_0_128, plain, ![X141, X142]:(~entity(X141,X142)|existent(X141,X142)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])).
cnf(c_0_129, plain, (~eventuality(X1,X2)|~general(X1,X2)), inference(spm,[status(thm)],[c_0_93, c_0_106]), ['final']).
cnf(c_0_130, plain, (~object(X1,X2)|~living(X1,X2)), inference(spm,[status(thm)],[c_0_107, c_0_108]), ['final']).
cnf(c_0_131, negated_conjecture, (object(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_109, c_0_110]), ['final']).
fof(c_0_132, plain, ![X109, X110]:(~organism(X109,X110)|living(X109,X110)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])).
cnf(c_0_133, plain, (~object(X1,X2)|~animate(X1,X2)), inference(spm,[status(thm)],[c_0_111, c_0_108]), ['final']).
fof(c_0_134, plain, ![X105, X106]:(~human_person(X105,X106)|animate(X105,X106)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])).
cnf(c_0_135, plain, (~object(X1,X2)|~female(X1,X2)), inference(spm,[status(thm)],[c_0_100, c_0_112]), ['final']).
cnf(c_0_136, plain, (~nonreflexive(X1,X2)|~agent(X1,X2,X3)|~patient(X1,X2,X4)|X3!=X4), inference(split_conjunct,[status(thm)],[c_0_113])).
cnf(c_0_137, plain, (~eventuality(X1,X2)|~female(X1,X2)), inference(spm,[status(thm)],[c_0_100, c_0_114]), ['final']).
fof(c_0_138, plain, ![X147, X148]:(~object(X147,X148)|entity(X147,X148)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])).
cnf(c_0_139, negated_conjecture, (X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)|~entity(esk1_0,esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116]), c_0_99])])).
cnf(c_0_140, negated_conjecture, (entity(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_117, c_0_118]), ['final']).
fof(c_0_141, plain, ![X165, X166]:(~thing(X165,X166)|singleton(X165,X166)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax32])])).
fof(c_0_142, plain, ![X167, X168]:(~eventuality(X167,X168)|thing(X167,X168)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax33])])).
fof(c_0_143, plain, ![X127, X128]:(~abstraction(X127,X128)|thing(X127,X128)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax13])])).
fof(c_0_144, plain, ![X145, X146]:(~entity(X145,X146)|thing(X145,X146)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])])).
fof(c_0_145, plain, ![X137, X138]:(~object(X137,X138)|impartial(X137,X138)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])).
fof(c_0_146, plain, ![X111, X112]:(~organism(X111,X112)|impartial(X111,X112)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])).
fof(c_0_147, plain, ![X173, X174]:(~order(X173,X174)|act(X173,X174)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])).
fof(c_0_148, plain, ![X171, X172]:(~act(X171,X172)|event(X171,X172)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax35])])).
fof(c_0_149, plain, ![X157, X158]:(~order(X157,X158)|event(X157,X158)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])).
fof(c_0_150, plain, ![X119, X120]:(~mia_forename(X119,X120)|forename(X119,X120)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9])])).
cnf(c_0_151, plain, (~abstraction(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_119, c_0_120]), ['final']).
cnf(c_0_152, negated_conjecture, (~human(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_121, c_0_122]), ['final']).
cnf(c_0_153, plain, (human(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_123]), ['final']).
cnf(c_0_154, negated_conjecture, (~female(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_124, c_0_122]), ['final']).
cnf(c_0_155, plain, (female(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_125]), ['final']).
cnf(c_0_156, negated_conjecture, (~existent(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_126, c_0_127]), ['final']).
cnf(c_0_157, plain, (existent(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_128]), ['final']).
cnf(c_0_158, negated_conjecture, (~general(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_129, c_0_127]), ['final']).
cnf(c_0_159, negated_conjecture, (~living(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_130, c_0_131]), ['final']).
cnf(c_0_160, plain, (living(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_132]), ['final']).
cnf(c_0_161, negated_conjecture, (~animate(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_133, c_0_131]), ['final']).
cnf(c_0_162, plain, (animate(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_134]), ['final']).
cnf(c_0_163, negated_conjecture, (~female(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_135, c_0_131]), ['final']).
cnf(c_0_164, plain, (~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)), inference(er,[status(thm)],[c_0_136]), ['final']).
cnf(c_0_165, negated_conjecture, (patient(esk1_0,esk5_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_166, negated_conjecture, (nonreflexive(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_167, negated_conjecture, (~female(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_137, c_0_127]), ['final']).
cnf(c_0_168, plain, (entity(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_138]), ['final']).
cnf(c_0_169, negated_conjecture, (X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139, c_0_140])]), ['final']).
cnf(c_0_170, plain, (singleton(X1,X2)|~thing(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_141]), ['final']).
cnf(c_0_171, plain, (thing(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_142]), ['final']).
cnf(c_0_172, plain, (thing(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_143]), ['final']).
cnf(c_0_173, plain, (thing(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_144]), ['final']).
cnf(c_0_174, plain, (impartial(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_145]), ['final']).
cnf(c_0_175, plain, (impartial(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_146]), ['final']).
cnf(c_0_176, plain, (act(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_147]), ['final']).
cnf(c_0_177, plain, (event(X1,X2)|~act(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_148]), ['final']).
cnf(c_0_178, plain, (event(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_149]), ['final']).
cnf(c_0_179, plain, (forename(X1,X2)|~mia_forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_150]), ['final']).
cnf(c_0_180, negated_conjecture, (~entity(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_151, c_0_122]), ['final']).
cnf(c_0_181, negated_conjecture, (~human_person(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_152, c_0_153]), ['final']).
cnf(c_0_182, negated_conjecture, (~woman(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_154, c_0_155]), ['final']).
cnf(c_0_183, negated_conjecture, (~entity(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_156, c_0_157]), ['final']).
cnf(c_0_184, negated_conjecture, (~abstraction(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_158, c_0_120]), ['final']).
cnf(c_0_185, negated_conjecture, (~organism(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_159, c_0_160]), ['final']).
cnf(c_0_186, negated_conjecture, (~human_person(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_161, c_0_162]), ['final']).
cnf(c_0_187, negated_conjecture, (~woman(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_163, c_0_155]), ['final']).
cnf(c_0_188, negated_conjecture, (~agent(esk1_0,esk5_0,esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164, c_0_165]), c_0_166])]), ['final']).
cnf(c_0_189, negated_conjecture, (~woman(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_167, c_0_155]), ['final']).
cnf(c_0_190, negated_conjecture, (entity(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_168, c_0_131]), ['final']).
cnf(c_0_191, negated_conjecture, (agent(esk1_0,esk5_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_192, negated_conjecture, (past(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_193, negated_conjecture, (order(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_194, negated_conjecture, (mia_forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_195, negated_conjecture, (actual_world(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
# SZS output end Saturation

Sample solution for SWV017+1

# SZS output start Saturation
fof(server_t_generates_key, axiom, ![X1, X2, X3, X4, X5, X6, X7]:((((message(sent(X1,t,triple(X1,X2,encrypt(triple(X3,X4,X5),X6))))&t_holds(key(X6,X1)))&t_holds(key(X7,X3)))&a_nonce(X4))=>message(sent(t,X3,triple(encrypt(quadruple(X1,X4,generate_key(X4),X5),X7),encrypt(triple(X3,generate_key(X4),X5),X6),X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', server_t_generates_key)).
fof(b_creates_freash_nonces_in_time, axiom, ![X1, X2]:((message(sent(X1,b,pair(X1,X2)))&fresh_to_b(X2))=>(message(sent(b,t,triple(b,generate_b_nonce(X2),encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))))&b_stored(pair(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', b_creates_freash_nonces_in_time)).
fof(intruder_message_sent, axiom, ![X1, X2, X3]:(((intruder_message(X1)&party_of_protocol(X2))&party_of_protocol(X3))=>message(sent(X2,X3,X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_message_sent)).
fof(t_holds_key_at_for_a, axiom, t_holds(key(at,a)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', t_holds_key_at_for_a)).
fof(intruder_can_record, axiom, ![X1, X2, X3]:(message(sent(X1,X2,X3))=>intruder_message(X3)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_can_record)).
fof(a_sent_message_i_to_b, axiom, message(sent(a,b,pair(a,an_a_nonce))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', a_sent_message_i_to_b)).
fof(nonce_a_is_fresh_to_b, axiom, fresh_to_b(an_a_nonce), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', nonce_a_is_fresh_to_b)).
fof(b_is_party_of_protocol, axiom, party_of_protocol(b), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', b_is_party_of_protocol)).
fof(intruder_composes_pairs, axiom, ![X1, X2]:((intruder_message(X1)&intruder_message(X2))=>intruder_message(pair(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_composes_pairs)).
fof(a_forwards_secure, axiom, ![X1, X2, X3, X4, X5, X6]:((message(sent(t,a,triple(encrypt(quadruple(X5,X6,X3,X2),at),X4,X1)))&a_stored(pair(X5,X6)))=>(message(sent(a,X5,pair(X4,encrypt(X1,X3))))&a_holds(key(X3,X5)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', a_forwards_secure)).
fof(t_holds_key_bt_for_b, axiom, t_holds(key(bt,b)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', t_holds_key_bt_for_b)).
fof(intruder_decomposes_triples, axiom, ![X1, X2, X3]:(intruder_message(triple(X1,X2,X3))=>((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_decomposes_triples)).
fof(b_accepts_secure_session_key, axiom, ![X2, X4, X5]:(((message(sent(X4,b,pair(encrypt(triple(X4,X2,generate_expiration_time(X5)),bt),encrypt(generate_b_nonce(X5),X2))))&a_key(X2))&b_stored(pair(X4,X5)))=>b_holds(key(X2,X4))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', b_accepts_secure_session_key)).
fof(a_stored_message_i, axiom, a_stored(pair(b,an_a_nonce)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', a_stored_message_i)).
fof(an_a_nonce_is_a_nonce, axiom, a_nonce(an_a_nonce), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', an_a_nonce_is_a_nonce)).
fof(t_is_party_of_protocol, axiom, party_of_protocol(t), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', t_is_party_of_protocol)).
fof(intruder_composes_triples, axiom, ![X1, X2, X3]:(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))=>intruder_message(triple(X1,X2,X3))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_composes_triples)).
fof(intruder_key_encrypts, axiom, ![X1, X2, X3]:(((intruder_message(X1)&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(encrypt(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_key_encrypts)).
fof(intruder_holds_key, axiom, ![X2, X3]:((intruder_message(X2)&party_of_protocol(X3))=>intruder_holds(key(X2,X3))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_holds_key)).
fof(intruder_decomposes_pairs, axiom, ![X1, X2]:(intruder_message(pair(X1,X2))=>(intruder_message(X1)&intruder_message(X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_decomposes_pairs)).
fof(a_is_party_of_protocol, axiom, party_of_protocol(a), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', a_is_party_of_protocol)).
fof(generated_keys_are_keys, axiom, ![X1]:a_key(generate_key(X1)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', generated_keys_are_keys)).
fof(fresh_intruder_nonces_are_fresh_to_b, axiom, ![X1]:(fresh_intruder_nonce(X1)=>(fresh_to_b(X1)&intruder_message(X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', fresh_intruder_nonces_are_fresh_to_b)).
fof(can_generate_more_fresh_intruder_nonces, axiom, ![X1]:(fresh_intruder_nonce(X1)=>fresh_intruder_nonce(generate_intruder_nonce(X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', can_generate_more_fresh_intruder_nonces)).
fof(generated_keys_are_not_nonces, axiom, ![X1]:~(a_nonce(generate_key(X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', generated_keys_are_not_nonces)).
fof(intruder_composes_quadruples, axiom, ![X1, X2, X3, X4]:((((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))&intruder_message(X4))=>intruder_message(quadruple(X1,X2,X3,X4))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_composes_quadruples)).
fof(intruder_interception, axiom, ![X1, X2, X3]:(((intruder_message(encrypt(X1,X2))&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_interception)).
fof(intruder_decomposes_quadruples, axiom, ![X1, X2, X3, X4]:(intruder_message(quadruple(X1,X2,X3,X4))=>(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))&intruder_message(X4))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_decomposes_quadruples)).
fof(nothing_is_a_nonce_and_a_key, axiom, ![X1]:~((a_key(X1)&a_nonce(X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', nothing_is_a_nonce_and_a_key)).
fof(an_intruder_nonce_is_a_fresh_intruder_nonce, axiom, fresh_intruder_nonce(an_intruder_nonce), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', an_intruder_nonce_is_a_fresh_intruder_nonce)).
fof(generated_times_and_nonces_are_nonces, axiom, ![X1]:(a_nonce(generate_expiration_time(X1))&a_nonce(generate_b_nonce(X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', generated_times_and_nonces_are_nonces)).
fof(b_hold_key_bt_for_t, axiom, b_holds(key(bt,t)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', b_hold_key_bt_for_t)).
fof(a_holds_key_at_for_t, axiom, a_holds(key(at,t)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', a_holds_key_at_for_t)).
fof(c_0_33, plain, ![X75, X76, X77, X78, X79, X80, X81]:(~message(sent(X75,t,triple(X75,X76,encrypt(triple(X77,X78,X79),X80))))|~t_holds(key(X80,X75))|~t_holds(key(X81,X77))|~a_nonce(X78)|message(sent(t,X77,triple(encrypt(quadruple(X75,X78,generate_key(X78),X79),X81),encrypt(triple(X77,generate_key(X78),X79),X80),X76)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[server_t_generates_key])])).
fof(c_0_34, plain, ![X70, X71]:((message(sent(b,t,triple(b,generate_b_nonce(X71),encrypt(triple(X70,X71,generate_expiration_time(X71)),bt))))|(~message(sent(X70,b,pair(X70,X71)))|~fresh_to_b(X71)))&(b_stored(pair(X70,X71))|(~message(sent(X70,b,pair(X70,X71)))|~fresh_to_b(X71)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[b_creates_freash_nonces_in_time])])])).
fof(c_0_35, plain, ![X106, X107, X108]:(~intruder_message(X106)|~party_of_protocol(X107)|~party_of_protocol(X108)|message(sent(X107,X108,X106))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_message_sent])])).
cnf(c_0_36, plain, (message(sent(t,X3,triple(encrypt(quadruple(X1,X4,generate_key(X4),X5),X7),encrypt(triple(X3,generate_key(X4),X5),X6),X2)))|~message(sent(X1,t,triple(X1,X2,encrypt(triple(X3,X4,X5),X6))))|~t_holds(key(X6,X1))|~t_holds(key(X7,X3))|~a_nonce(X4)), inference(split_conjunct,[status(thm)],[c_0_33]), ['final']).
cnf(c_0_37, plain, (t_holds(key(at,a))), inference(split_conjunct,[status(thm)],[t_holds_key_at_for_a]), ['final']).
fof(c_0_38, plain, ![X82, X83, X84]:(~message(sent(X82,X83,X84))|intruder_message(X84)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_can_record])])).
cnf(c_0_39, plain, (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~message(sent(X2,b,pair(X2,X1)))|~fresh_to_b(X1)), inference(split_conjunct,[status(thm)],[c_0_34]), ['final']).
cnf(c_0_40, plain, (message(sent(a,b,pair(a,an_a_nonce)))), inference(split_conjunct,[status(thm)],[a_sent_message_i_to_b]), ['final']).
cnf(c_0_41, plain, (fresh_to_b(an_a_nonce)), inference(split_conjunct,[status(thm)],[nonce_a_is_fresh_to_b]), ['final']).
cnf(c_0_42, plain, (b_stored(pair(X1,X2))|~message(sent(X1,b,pair(X1,X2)))|~fresh_to_b(X2)), inference(split_conjunct,[status(thm)],[c_0_34]), ['final']).
cnf(c_0_43, plain, (message(sent(X2,X3,X1))|~intruder_message(X1)|~party_of_protocol(X2)|~party_of_protocol(X3)), inference(split_conjunct,[status(thm)],[c_0_35]), ['final']).
cnf(c_0_44, plain, (party_of_protocol(b)), inference(split_conjunct,[status(thm)],[b_is_party_of_protocol]), ['final']).
fof(c_0_45, plain, ![X94, X95]:(~intruder_message(X94)|~intruder_message(X95)|intruder_message(pair(X94,X95))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_composes_pairs])])).
fof(c_0_46, plain, ![X64, X65, X66, X67, X68, X69]:((message(sent(a,X68,pair(X67,encrypt(X64,X66))))|(~message(sent(t,a,triple(encrypt(quadruple(X68,X69,X66,X65),at),X67,X64)))|~a_stored(pair(X68,X69))))&(a_holds(key(X66,X68))|(~message(sent(t,a,triple(encrypt(quadruple(X68,X69,X66,X65),at),X67,X64)))|~a_stored(pair(X68,X69))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a_forwards_secure])])])).
cnf(c_0_47, plain, (message(sent(t,a,triple(encrypt(quadruple(X1,X2,generate_key(X2),X3),at),encrypt(triple(a,generate_key(X2),X3),X4),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(X1,t,triple(X1,X5,encrypt(triple(a,X2,X3),X4))))), inference(spm,[status(thm)],[c_0_36, c_0_37]), ['final']).
cnf(c_0_48, plain, (t_holds(key(bt,b))), inference(split_conjunct,[status(thm)],[t_holds_key_bt_for_b]), ['final']).
fof(c_0_49, plain, ![X87, X88, X89]:(((intruder_message(X87)|~intruder_message(triple(X87,X88,X89)))&(intruder_message(X88)|~intruder_message(triple(X87,X88,X89))))&(intruder_message(X89)|~intruder_message(triple(X87,X88,X89)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_decomposes_triples])])])).
cnf(c_0_50, plain, (intruder_message(X3)|~message(sent(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_38]), ['final']).
cnf(c_0_51, plain, (message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40]), c_0_41])]), ['final']).
fof(c_0_52, plain, ![X72, X73, X74]:(~message(sent(X73,b,pair(encrypt(triple(X73,X72,generate_expiration_time(X74)),bt),encrypt(generate_b_nonce(X74),X72))))|~a_key(X72)|~b_stored(pair(X73,X74))|b_holds(key(X72,X73))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[b_accepts_secure_session_key])])).
cnf(c_0_53, plain, (b_stored(pair(X1,X2))|~intruder_message(pair(X1,X2))|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_44])]), ['final']).
cnf(c_0_54, plain, (intruder_message(pair(X1,X2))|~intruder_message(X1)|~intruder_message(X2)), inference(split_conjunct,[status(thm)],[c_0_45]), ['final']).
cnf(c_0_55, plain, (message(sent(a,X1,pair(X2,encrypt(X3,X4))))|~message(sent(t,a,triple(encrypt(quadruple(X1,X5,X4,X6),at),X2,X3)))|~a_stored(pair(X1,X5))), inference(split_conjunct,[status(thm)],[c_0_46]), ['final']).
cnf(c_0_56, plain, (a_stored(pair(b,an_a_nonce))), inference(split_conjunct,[status(thm)],[a_stored_message_i]), ['final']).
cnf(c_0_57, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(a,X1,X2),bt))))), inference(spm,[status(thm)],[c_0_47, c_0_48]), ['final']).
cnf(c_0_58, plain, (a_nonce(an_a_nonce)), inference(split_conjunct,[status(thm)],[an_a_nonce_is_a_nonce]), ['final']).
cnf(c_0_59, plain, (party_of_protocol(t)), inference(split_conjunct,[status(thm)],[t_is_party_of_protocol]), ['final']).
fof(c_0_60, plain, ![X96, X97, X98]:(~intruder_message(X96)|~intruder_message(X97)|~intruder_message(X98)|intruder_message(triple(X96,X97,X98))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_composes_triples])])).
cnf(c_0_61, plain, (intruder_message(X1)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_49]), ['final']).
cnf(c_0_62, plain, (intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))), inference(spm,[status(thm)],[c_0_50, c_0_51]), ['final']).
cnf(c_0_63, plain, (b_holds(key(X2,X1))|~message(sent(X1,b,pair(encrypt(triple(X1,X2,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X2))))|~a_key(X2)|~b_stored(pair(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_52]), ['final']).
cnf(c_0_64, plain, (b_stored(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_53, c_0_54]), ['final']).
fof(c_0_65, plain, ![X111, X112, X113]:(~intruder_message(X111)|~intruder_holds(key(X112,X113))|~party_of_protocol(X113)|intruder_message(encrypt(X111,X112))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_key_encrypts])])).
fof(c_0_66, plain, ![X109, X110]:(~intruder_message(X109)|~party_of_protocol(X110)|intruder_holds(key(X109,X110))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_holds_key])])).
cnf(c_0_67, plain, (message(sent(t,b,triple(encrypt(quadruple(X1,X2,generate_key(X2),X3),bt),encrypt(triple(b,generate_key(X2),X3),X4),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(X1,t,triple(X1,X5,encrypt(triple(b,X2,X3),X4))))), inference(spm,[status(thm)],[c_0_36, c_0_48]), ['final']).
cnf(c_0_68, plain, (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(pair(X2,X1))|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_43]), c_0_44])]), ['final']).
fof(c_0_69, plain, ![X85, X86]:((intruder_message(X85)|~intruder_message(pair(X85,X86)))&(intruder_message(X86)|~intruder_message(pair(X85,X86)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_decomposes_pairs])])])).
cnf(c_0_70, plain, (message(sent(a,b,pair(X1,encrypt(X2,X3))))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2)))), inference(spm,[status(thm)],[c_0_55, c_0_56]), ['final']).
cnf(c_0_71, plain, (party_of_protocol(a)), inference(split_conjunct,[status(thm)],[a_is_party_of_protocol]), ['final']).
cnf(c_0_72, plain, (message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_51]), c_0_58])]), ['final']).
cnf(c_0_73, plain, (b_stored(pair(a,an_a_nonce))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_40]), c_0_41])]), ['final']).
cnf(c_0_74, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X3,encrypt(triple(a,X1,X2),bt)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_43]), c_0_59]), c_0_44])]), ['final']).
cnf(c_0_75, plain, (intruder_message(triple(X1,X2,X3))|~intruder_message(X1)|~intruder_message(X2)|~intruder_message(X3)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_76, plain, (intruder_message(b)), inference(spm,[status(thm)],[c_0_61, c_0_62]), ['final']).
cnf(c_0_77, plain, (intruder_message(X1)|~intruder_message(triple(X2,X3,X1))), inference(split_conjunct,[status(thm)],[c_0_49]), ['final']).
cnf(c_0_78, plain, (b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_63, c_0_64]), ['final']).
cnf(c_0_79, plain, (intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_holds(key(X2,X3))|~party_of_protocol(X3)), inference(split_conjunct,[status(thm)],[c_0_65]), ['final']).
cnf(c_0_80, plain, (intruder_holds(key(X1,X2))|~intruder_message(X1)|~party_of_protocol(X2)), inference(split_conjunct,[status(thm)],[c_0_66]), ['final']).
cnf(c_0_81, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(b,X1,X2),bt))))), inference(spm,[status(thm)],[c_0_67, c_0_48]), ['final']).
cnf(c_0_82, plain, (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_68, c_0_54]), ['final']).
cnf(c_0_83, plain, (intruder_message(X1)|~intruder_message(pair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_69]), ['final']).
cnf(c_0_84, plain, (intruder_message(pair(a,an_a_nonce))), inference(spm,[status(thm)],[c_0_50, c_0_40]), ['final']).
cnf(c_0_85, plain, (message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_43]), c_0_71]), c_0_59])]), ['final']).
cnf(c_0_86, plain, (intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce)))), inference(spm,[status(thm)],[c_0_50, c_0_72]), ['final']).
cnf(c_0_87, plain, (b_holds(key(X1,a))|~a_key(X1)|~message(sent(a,b,pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1))))), inference(spm,[status(thm)],[c_0_63, c_0_73]), ['final']).
cnf(c_0_88, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(encrypt(triple(a,X1,X2),bt))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75]), c_0_76])]), ['final']).
cnf(c_0_89, plain, (intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_77, c_0_62]), ['final']).
cnf(c_0_90, plain, (b_holds(key(X1,X2))|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_43]), c_0_44])]), ['final']).
cnf(c_0_91, plain, (intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X3)), inference(spm,[status(thm)],[c_0_79, c_0_80])).
cnf(c_0_92, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_76]), c_0_44])]), ['final']).
cnf(c_0_93, plain, (intruder_message(a)), inference(spm,[status(thm)],[c_0_83, c_0_84]), ['final']).
cnf(c_0_94, plain, (message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(encrypt(quadruple(b,an_a_nonce,X3,X4),at))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_85, c_0_75]), ['final']).
cnf(c_0_95, plain, (intruder_message(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at))), inference(spm,[status(thm)],[c_0_61, c_0_86]), ['final']).
cnf(c_0_96, plain, (message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))))), inference(spm,[status(thm)],[c_0_70, c_0_72]), ['final']).
cnf(c_0_97, plain, (b_holds(key(X1,a))|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|~a_key(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_43]), c_0_44]), c_0_71])]), ['final']).
cnf(c_0_98, plain, (a_holds(key(X1,X2))|~message(sent(t,a,triple(encrypt(quadruple(X2,X3,X1,X4),at),X5,X6)))|~a_stored(pair(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_46]), ['final']).
cnf(c_0_99, plain, (message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1)))|~intruder_message(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_58])]), ['final']).
cnf(c_0_100, plain, (intruder_message(triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt)))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_50, c_0_82]), ['final']).
cnf(c_0_101, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X3,encrypt(triple(b,X1,X2),bt)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_43]), c_0_59]), c_0_44])]), ['final']).
cnf(c_0_102, plain, (b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(encrypt(generate_b_nonce(X3),X1))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_90, c_0_54]), ['final']).
cnf(c_0_103, plain, (intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_91, c_0_44]), ['final']).
cnf(c_0_104, plain, (intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_50, c_0_92]), ['final']).
cnf(c_0_105, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_82]), c_0_93]), c_0_71])]), ['final']).
cnf(c_0_106, plain, (message(sent(a,b,pair(X1,encrypt(X2,generate_key(an_a_nonce)))))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_94, c_0_95]), ['final']).
cnf(c_0_107, plain, (message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(a,X1,X2),at))))), inference(spm,[status(thm)],[c_0_47, c_0_37]), ['final']).
fof(c_0_108, plain, ![X117]:a_key(generate_key(X117)), inference(variable_rename,[status(thm)],[generated_keys_are_keys])).
cnf(c_0_109, plain, (intruder_message(X1)|~intruder_message(triple(X2,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_49]), ['final']).
cnf(c_0_110, plain, (intruder_message(X1)|~intruder_message(pair(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_69]), ['final']).
cnf(c_0_111, plain, (intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))), inference(spm,[status(thm)],[c_0_50, c_0_96]), ['final']).
cnf(c_0_112, plain, (message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(b,X1,X2),at))))), inference(spm,[status(thm)],[c_0_67, c_0_37]), ['final']).
cnf(c_0_113, plain, (b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(encrypt(generate_b_nonce(an_a_nonce),X1))|~a_key(X1)), inference(spm,[status(thm)],[c_0_97, c_0_54]), ['final']).
cnf(c_0_114, plain, (a_holds(key(X1,b))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4)))), inference(spm,[status(thm)],[c_0_98, c_0_56]), ['final']).
fof(c_0_115, plain, ![X119]:((fresh_to_b(X119)|~fresh_intruder_nonce(X119))&(intruder_message(X119)|~fresh_intruder_nonce(X119))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fresh_intruder_nonces_are_fresh_to_b])])])).
cnf(c_0_116, plain, (message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)))))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_70, c_0_99]), ['final']).
cnf(c_0_117, plain, (intruder_message(encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_77, c_0_100]), ['final']).
cnf(c_0_118, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(encrypt(triple(b,X1,X2),bt))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_75]), c_0_76])]), ['final']).
cnf(c_0_119, plain, (b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(generate_b_nonce(X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_102, c_0_103]), ['final']).
cnf(c_0_120, plain, (intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_77, c_0_104]), ['final']).
cnf(c_0_121, plain, (intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_50, c_0_105]), ['final']).
cnf(c_0_122, plain, (intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_50, c_0_106]), ['final']).
cnf(c_0_123, plain, (message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X3,encrypt(triple(a,X1,X2),at)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_43]), c_0_59]), c_0_71])]), ['final']).
cnf(c_0_124, plain, (a_key(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_108]), ['final']).
cnf(c_0_125, plain, (intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_109, c_0_100]), ['final']).
cnf(c_0_126, plain, (intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))), inference(spm,[status(thm)],[c_0_110, c_0_111]), ['final']).
cnf(c_0_127, plain, (intruder_message(an_a_nonce)), inference(spm,[status(thm)],[c_0_110, c_0_84]), ['final']).
cnf(c_0_128, plain, (message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X3,encrypt(triple(b,X1,X2),at)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_43]), c_0_59]), c_0_71])]), ['final']).
cnf(c_0_129, plain, (intruder_message(generate_b_nonce(an_a_nonce))), inference(spm,[status(thm)],[c_0_109, c_0_62]), ['final']).
cnf(c_0_130, plain, (b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(generate_b_nonce(an_a_nonce))|~intruder_message(X1)|~a_key(X1)), inference(spm,[status(thm)],[c_0_113, c_0_103])).
cnf(c_0_131, plain, (a_holds(key(X1,b))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_43]), c_0_71]), c_0_59])]), ['final']).
fof(c_0_132, plain, ![X118]:(~fresh_intruder_nonce(X118)|fresh_intruder_nonce(generate_intruder_nonce(X118))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[can_generate_more_fresh_intruder_nonces])])).
fof(c_0_133, plain, ![X1]:~a_nonce(generate_key(X1)), inference(fof_simplification,[status(thm)],[generated_keys_are_not_nonces])).
cnf(c_0_134, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_68, c_0_111]), ['final']).
cnf(c_0_135, plain, (fresh_to_b(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_115]), ['final']).
cnf(c_0_136, plain, (intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_50, c_0_116]), ['final']).
cnf(c_0_137, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_117]), c_0_93]), c_0_71])]), ['final']).
cnf(c_0_138, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_117]), c_0_76]), c_0_44])]), ['final']).
cnf(c_0_139, plain, (b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_119, c_0_120]), ['final']).
cnf(c_0_140, plain, (intruder_message(encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_109, c_0_121]), ['final']).
cnf(c_0_141, plain, (intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_109, c_0_104]), ['final']).
cnf(c_0_142, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_68, c_0_122]), ['final']).
cnf(c_0_143, plain, (message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(encrypt(triple(a,X1,X2),at))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_75]), c_0_93])]), ['final']).
cnf(c_0_144, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_106]), c_0_93])]), ['final']).
cnf(c_0_145, plain, (b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_122]), c_0_124])]), c_0_125]), ['final']).
cnf(c_0_146, plain, (b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(encrypt(X2,generate_key(an_a_nonce)))|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_53, c_0_122]), ['final']).
cnf(c_0_147, plain, (b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_106]), c_0_93])]), ['final']).
cnf(c_0_148, plain, (intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_110, c_0_122])).
cnf(c_0_149, plain, (b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_53, c_0_111]), ['final']).
cnf(c_0_150, plain, (b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_126]), c_0_127]), c_0_124]), c_0_41])]), ['final']).
cnf(c_0_151, plain, (message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(encrypt(triple(b,X1,X2),at))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128, c_0_75]), c_0_93])]), ['final']).
cnf(c_0_152, plain, (b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~intruder_message(X4)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~party_of_protocol(X4)), inference(spm,[status(thm)],[c_0_119, c_0_125]), ['final']).
cnf(c_0_153, plain, (b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_129]), c_0_127]), c_0_41])]), ['final']).
cnf(c_0_154, plain, (b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~a_key(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130, c_0_129])]), ['final']).
cnf(c_0_155, plain, (a_holds(key(X1,b))|~intruder_message(encrypt(quadruple(b,an_a_nonce,X1,X2),at))|~intruder_message(X3)|~intruder_message(X4)), inference(spm,[status(thm)],[c_0_131, c_0_75]), ['final']).
cnf(c_0_156, plain, (intruder_message(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_115]), ['final']).
cnf(c_0_157, plain, (fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_132]), ['final']).
fof(c_0_158, plain, ![X99, X100, X101, X102]:(~intruder_message(X99)|~intruder_message(X100)|~intruder_message(X101)|~intruder_message(X102)|intruder_message(quadruple(X99,X100,X101,X102))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_composes_quadruples])])).
fof(c_0_159, plain, ![X103, X104, X105]:(~intruder_message(encrypt(X103,X104))|~intruder_holds(key(X104,X105))|~party_of_protocol(X105)|intruder_message(X104)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_interception])])).
fof(c_0_160, plain, ![X90, X91, X92, X93]:((((intruder_message(X90)|~intruder_message(quadruple(X90,X91,X92,X93)))&(intruder_message(X91)|~intruder_message(quadruple(X90,X91,X92,X93))))&(intruder_message(X92)|~intruder_message(quadruple(X90,X91,X92,X93))))&(intruder_message(X93)|~intruder_message(quadruple(X90,X91,X92,X93)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_decomposes_quadruples])])])).
fof(c_0_161, plain, ![X116]:(~a_key(X116)|~a_nonce(X116)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[nothing_is_a_nonce_and_a_key])])).
fof(c_0_162, plain, ![X114]:~a_nonce(generate_key(X114)), inference(variable_rename,[status(thm)],[c_0_133])).
cnf(c_0_163, plain, (fresh_intruder_nonce(an_intruder_nonce)), inference(split_conjunct,[status(thm)],[an_intruder_nonce_is_a_fresh_intruder_nonce]), ['final']).
fof(c_0_164, plain, ![X115]:(a_nonce(generate_expiration_time(X115))&a_nonce(generate_b_nonce(X115))), inference(variable_rename,[status(thm)],[generated_times_and_nonces_are_nonces])).
cnf(c_0_165, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_134, c_0_135]), ['final']).
cnf(c_0_166, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_68, c_0_136]), ['final']).
cnf(c_0_167, plain, (intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_50, c_0_137]), ['final']).
cnf(c_0_168, plain, (intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_50, c_0_138]), ['final']).
cnf(c_0_169, plain, (intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_61, c_0_121]), ['final']).
cnf(c_0_170, plain, (b_holds(key(generate_key(X1),a))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_140]), c_0_93]), c_0_124]), c_0_71])]), ['final']).
cnf(c_0_171, plain, (b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_103]), c_0_109]), c_0_61]), ['final']).
cnf(c_0_172, plain, (b_holds(key(generate_key(X1),b))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_141]), c_0_76]), c_0_124]), c_0_44])]), ['final']).
cnf(c_0_173, plain, (intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_61, c_0_104]), ['final']).
cnf(c_0_174, plain, (intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_50, c_0_99]), ['final']).
cnf(c_0_175, plain, (b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_53, c_0_136]), ['final']).
cnf(c_0_176, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_142, c_0_135]), ['final']).
cnf(c_0_177, plain, (message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_143, c_0_103]), ['final']).
cnf(c_0_178, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_144, c_0_135]), ['final']).
cnf(c_0_179, plain, (b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)|~intruder_message(X2)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_103]), c_0_61]), ['final']).
cnf(c_0_180, plain, (b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(generate_key(an_a_nonce))|~intruder_message(X1)|~fresh_to_b(generate_key(an_a_nonce))|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_145, c_0_117]), ['final']).
cnf(c_0_181, plain, (b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X2,generate_key(an_a_nonce)))|~intruder_message(X2)|~intruder_message(X1)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_146, c_0_135]), ['final']).
cnf(c_0_182, plain, (b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_147, c_0_135]), ['final']).
cnf(c_0_183, plain, (intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_148, c_0_86]), ['final']).
cnf(c_0_184, plain, (b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_149, c_0_135]), ['final']).
cnf(c_0_185, plain, (b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150, c_0_103]), c_0_61]), ['final']).
cnf(c_0_186, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(a,X1,X2))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_88, c_0_103]), ['final']).
cnf(c_0_187, plain, (message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(triple(b,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_151, c_0_103]), ['final']).
cnf(c_0_188, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X1,X2))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_118, c_0_103]), ['final']).
cnf(c_0_189, plain, (b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~intruder_message(X4)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~party_of_protocol(X4)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_103]), c_0_109]), c_0_61]), ['final']).
cnf(c_0_190, plain, (b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)|~party_of_protocol(X3)), inference(spm,[status(thm)],[c_0_152, c_0_117]), ['final']).
cnf(c_0_191, plain, (b_holds(key(an_a_nonce,X1))|~intruder_message(X1)|~a_key(an_a_nonce)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153, c_0_117]), c_0_127]), c_0_41])]), ['final']).
cnf(c_0_192, plain, (b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)|~party_of_protocol(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153, c_0_103]), c_0_109]), c_0_61]), ['final']).
cnf(c_0_193, plain, (message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(quadruple(b,an_a_nonce,X3,X4))|~intruder_message(at)|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_94, c_0_103]), ['final']).
cnf(c_0_194, plain, (b_holds(key(X1,a))|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154, c_0_103]), c_0_109]), ['final']).
cnf(c_0_195, plain, (b_holds(key(an_a_nonce,a))|~a_key(an_a_nonce)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154, c_0_89]), c_0_127])]), ['final']).
cnf(c_0_196, plain, (a_holds(key(X1,b))|~intruder_message(quadruple(b,an_a_nonce,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~intruder_message(X4)), inference(spm,[status(thm)],[c_0_155, c_0_103]), ['final']).
cnf(c_0_197, plain, (intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(spm,[status(thm)],[c_0_156, c_0_157]), ['final']).
cnf(c_0_198, plain, (intruder_message(quadruple(X1,X2,X3,X4))|~intruder_message(X1)|~intruder_message(X2)|~intruder_message(X3)|~intruder_message(X4)), inference(split_conjunct,[status(thm)],[c_0_158]), ['final']).
cnf(c_0_199, plain, (intruder_message(X2)|~intruder_message(encrypt(X1,X2))|~intruder_holds(key(X2,X3))|~party_of_protocol(X3)), inference(split_conjunct,[status(thm)],[c_0_159]), ['final']).
cnf(c_0_200, plain, (intruder_message(X1)|~intruder_message(quadruple(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_160]), ['final']).
cnf(c_0_201, plain, (intruder_message(X1)|~intruder_message(quadruple(X2,X1,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_160]), ['final']).
cnf(c_0_202, plain, (intruder_message(X1)|~intruder_message(quadruple(X2,X3,X1,X4))), inference(split_conjunct,[status(thm)],[c_0_160]), ['final']).
cnf(c_0_203, plain, (intruder_message(X1)|~intruder_message(quadruple(X2,X3,X4,X1))), inference(split_conjunct,[status(thm)],[c_0_160]), ['final']).
cnf(c_0_204, plain, (~a_key(X1)|~a_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_161]), ['final']).
cnf(c_0_205, plain, (~a_nonce(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_162]), ['final']).
cnf(c_0_206, plain, (b_holds(key(generate_key(an_a_nonce),b))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150, c_0_141]), c_0_76]), c_0_44]), c_0_127]), c_0_58]), c_0_41])]), ['final']).
cnf(c_0_207, plain, (intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_83, c_0_111]), ['final']).
cnf(c_0_208, plain, (b_holds(key(generate_key(an_a_nonce),a))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_96]), c_0_127]), c_0_93]), c_0_124]), c_0_41]), c_0_71])]), ['final']).
cnf(c_0_209, plain, (a_holds(key(generate_key(an_a_nonce),b))), inference(spm,[status(thm)],[c_0_114, c_0_72]), ['final']).
cnf(c_0_210, plain, (intruder_message(an_intruder_nonce)), inference(spm,[status(thm)],[c_0_156, c_0_163]), ['final']).
cnf(c_0_211, plain, (b_holds(key(bt,t))), inference(split_conjunct,[status(thm)],[b_hold_key_bt_for_t]), ['final']).
cnf(c_0_212, plain, (a_holds(key(at,t))), inference(split_conjunct,[status(thm)],[a_holds_key_at_for_t]), ['final']).
cnf(c_0_213, plain, (a_nonce(generate_expiration_time(X1))), inference(split_conjunct,[status(thm)],[c_0_164]), ['final']).
cnf(c_0_214, plain, (a_nonce(generate_b_nonce(X1))), inference(split_conjunct,[status(thm)],[c_0_164]), ['final']).
# SZS output end Saturation

Sample solution for BOO001-1

# SZS output start CNFRefutation
cnf(associativity, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', associativity)).
cnf(ternary_multiply_1, axiom, (multiply(X1,X2,X2)=X2), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', ternary_multiply_1)).
cnf(right_inverse, axiom, (multiply(X1,X2,inverse(X2))=X1), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', right_inverse)).
cnf(ternary_multiply_2, axiom, (multiply(X1,X1,X2)=X1), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', ternary_multiply_2)).
cnf(left_inverse, axiom, (multiply(inverse(X1),X1,X2)=X2), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', left_inverse)).
cnf(prove_inverse_is_self_cancelling, negated_conjecture, (inverse(inverse(a))!=a), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/BOO001-1.p', prove_inverse_is_self_cancelling)).
cnf(c_0_6, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), associativity).
cnf(c_0_7, axiom, (multiply(X1,X2,X2)=X2), ternary_multiply_1).
cnf(c_0_8, plain, (multiply(multiply(X1,X2,X3),X4,X2)=multiply(X1,X2,multiply(X3,X4,X2))), inference(spm,[status(thm)],[c_0_6, c_0_7])).
cnf(c_0_9, axiom, (multiply(X1,X2,inverse(X2))=X1), right_inverse).
cnf(c_0_10, plain, (multiply(X1,X2,X3)=multiply(X1,X3,multiply(inverse(X3),X2,X3))), inference(spm,[status(thm)],[c_0_8, c_0_9])).
cnf(c_0_11, axiom, (multiply(X1,X1,X2)=X1), ternary_multiply_2).
cnf(c_0_12, axiom, (multiply(inverse(X1),X1,X2)=X2), left_inverse).
cnf(c_0_13, plain, (multiply(X1,inverse(X2),X2)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10, c_0_11]), c_0_9])).
cnf(c_0_14, negated_conjecture, (inverse(inverse(a))!=a), prove_inverse_is_self_cancelling).
cnf(c_0_15, plain, (inverse(inverse(X1))=X1), inference(spm,[status(thm)],[c_0_12, c_0_13])).
cnf(c_0_16, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])]), ['proof']).
# SZS output end CNFRefutation

Ehoh 2.7

Sample solution for SET014^4

# No SInE strategy applied
# Trying AutoSched0 for 149 seconds
# AutoSched0-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S00A
# and selection function NoSelection.
#
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
thf(thm, conjecture, ![X22:$i > $o, X23:$i > $o, X24:$i > $o]:((subset @ X22 @ X24&subset @ X23 @ X24)=>subset @ (union @ X22 @ X23) @ X24), file('/home/petar/Documents/tptp/Problems/SET/SET014^4.p', thm)).
thf(union, axiom, (union)=(^[X5:$i > $o, X6:$i > $o, X4:$i]:(X5 @ X4|X6 @ X4)), file('/home/petar/Documents/tptp/Problems/SET/Axioms/SET008^0.ax', union)).
thf(subset, axiom, (subset)=(^[X16:$i > $o, X17:$i > $o]:![X4:$i]:(X16 @ X4=>X17 @ X4)), file('/home/petar/Documents/tptp/Problems/SET/Axioms/SET008^0.ax', subset)).
thf(c_0_3, negated_conjecture, ~(![X22:$i > $o, X23:$i > $o, X24:$i > $o]:((![X29:$i]:(X22 @ X29=>X24 @ X29)&![X30:$i]:(X23 @ X30=>X24 @ X30))=>![X32:$i]:((X22 @ X32|X23 @ X32)=>X24 @ X32))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]), union]), subset])).
thf(c_0_4, negated_conjecture, ![X37:$i, X38:$i]:(((~epred1_0 @ X37|epred3_0 @ X37)&(~epred2_0 @ X38|epred3_0 @ X38))&((epred1_0 @ esk1_0|epred2_0 @ esk1_0)&~epred3_0 @ esk1_0)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])).
thf(c_0_5, negated_conjecture, ![X1:$i]:(epred3_0 @ X1|~epred2_0 @ X1), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_6, negated_conjecture, (epred1_0 @ esk1_0|epred2_0 @ esk1_0), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_7, negated_conjecture, ~epred3_0 @ esk1_0, inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_8, negated_conjecture, ![X1:$i]:(epred3_0 @ X1|~epred1_0 @ X1), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_9, negated_conjecture, epred1_0 @ esk1_0, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_5, c_0_6]), c_0_7])).
thf(c_0_10, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8, c_0_9]), c_0_7]), ['proof']).
# SZS output end CNFRefutation
# Training examples: 0 positive, 0 negative

iProver 3.6

Sample solution for DAT013=1

% SZS output start CNFRefutation for DAT013=1.tptp

tff(f6,plain,(
  ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
  introduced(theory_axiom_143,[])).

tff(f8,plain,(
  ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
  introduced(theory_axiom_145,[])).

tff(f14,plain,(
  ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | $less($sum(X0,X2),$sum(X1,X2))) )),
  introduced(theory_axiom_153,[])).

tff(f13,plain,(
  ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
  introduced(theory_axiom_152,[])).

tff(f3,conjecture,(
  ! [X0 : array] : ! [X1 : $int] : ! [X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
  file('/tmp/SystemOnTPTP23709/DAT013=1.tptp',co1)).

tff(f4,negated_conjecture,(
  ~! [X0 : array] : ! [X1 : $int] : ! [X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
  inference(negated_conjecture,[],[f3])).

tff(f5,plain,(
  ~! [X0 : array] : ! [X1 : $int] : ! [X2 : $int] : (! [X3 : $int] : ((~$less(X2,X3) & ~$less(X3,X1)) => $less(0,read(X0,X3))) => ! [X4 : $int] : ((~$less(X2,X4) & ~$less(X4,$sum(X1,3))) => $less(0,read(X0,X4))))),
  inference(theory_normalization,[],[f4])).

tff(f19,plain,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : ((~$less(X2,X3) & ~$less(X3,X1)) => $less(0,read(X0,X3))) => ! [X4 : $int] : ((~$less(X2,X4) & ~$less(X4,$sum(X1,3))) => $less(0,read(X0,X4))))),
  inference(flattening,[],[f5])).

tff(f20,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & (~$less(X2,X4) & ~$less(X4,$sum(X1,3)))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | ($less(X2,X3) | $less(X3,X1))))),
  inference(ennf_transformation,[],[f19])).

tff(f21,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & ~$less(X2,X4) & ~$less(X4,$sum(X1,3))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | $less(X2,X3) | $less(X3,X1)))),
  inference(flattening,[],[f20])).

tff(f22,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1)))),
  inference(rectify,[],[f21])).

tff(f24,plain,(
  ? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) => (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3)))),
  introduced(choice_axiom,[])).

tff(f23,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1))) => (? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)))),
  introduced(choice_axiom,[])).

tff(f25,plain,(
  (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f22,f24,f23])).

tff(f29,plain,(
  ~$less(sK3,$sum(sK1,3))),
  inference(cnf_transformation,[],[f25])).

tff(f28,plain,(
  ( ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)) )),
  inference(cnf_transformation,[],[f25])).

tff(f31,plain,(
  ~$less(0,read(sK0,sK3))),
  inference(cnf_transformation,[],[f25])).

tff(f30,plain,(
  ~$less(sK2,sK3)),
  inference(cnf_transformation,[],[f25])).

tff(f12,plain,(
  ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,X2) | $less(X0,X2)) )),
  introduced(theory_axiom_151,[])).

tff(f15,plain,(
  ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,$sum(X0,1))) )),
  introduced(theory_axiom_155,[])).

tff(f11,plain,(
  ( ! [X0 : $int] : (~$less(X0,X0)) )),
  introduced(theory_axiom_150,[])).

tff(f17,plain,(
  ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,$sum(X0,1))) )),
  introduced(theory_axiom_169,[])).

cnf(c_60,plain,
    ( $sum_int(X0_3,X1_3) = $sum_int(X1_3,X0_3) ),
    inference(cnf_transformation,[],[f6]) ).

cnf(c_58,plain,
    ( $sum_int(X0_3,0) = X0_3 ),
    inference(cnf_transformation,[],[f8]) ).

cnf(c_9404,plain,
    ( $sum_int(0,X0_3) = X0_3 ),
    inference(superposition,[status(thm)],[c_58,c_60]) ).

cnf(c_52,plain,
    ( ~ $less_int(X0_3,X1_3)
    | $less_int($sum_int(X0_3,X2_3),$sum_int(X1_3,X2_3)) ),
    inference(cnf_transformation,[],[f14]) ).

cnf(c_9454,plain,
    ( ~ $less_int(0,X0_3) | $less_int(X1_3,$sum_int(X0_3,X1_3)) ),
    inference(superposition,[status(thm)],[c_9404,c_52]) ).

cnf(c_11457,plain,
    ( ~ $less_int(0,X0_3) | $less_int(X1_3,$sum_int(X1_3,X0_3)) ),
    inference(superposition,[status(thm)],[c_60,c_9454]) ).

cnf(c_53,plain,
    ( X0_3 = X1_3 | $less_int(X0_3,X1_3) | $less_int(X1_3,X0_3) ),
    inference(cnf_transformation,[],[f13]) ).

cnf(c_65,negated_conjecture,
    ( ~ $less_int(sK3,$sum_int(sK1,3)) ),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_762,plain,
    ( $sum_int(sK1,3) = sK3 | $less_int($sum_int(sK1,3),sK3) ),
    inference(superposition,[status(thm)],[c_53,c_65]) ).

cnf(c_66,negated_conjecture,
    ( $less_int(0,read(sK0,X0_3))
    | $less_int(X0_3,sK1)
    | $less_int(sK2,X0_3) ),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_63,negated_conjecture,
    ( ~ $less_int(0,read(sK0,sK3)) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_562,plain,
    ( $less_int(sK2,sK3) | $less_int(sK3,sK1) ),
    inference(superposition,[status(thm)],[c_66,c_63]) ).

cnf(c_64,negated_conjecture,
    ( ~ $less_int(sK2,sK3) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_517,plain,
    ( $less_int(0,read(sK0,sK3))
    | $less_int(sK2,sK3)
    | $less_int(sK3,sK1) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_563,plain,
    ( $less_int(sK3,sK1) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_562,c_64,c_63,c_517]) ).

cnf(c_54,plain,
    ( ~ $less_int(X0_3,X1_3)
    | ~ $less_int(X2_3,X0_3)
    | $less_int(X2_3,X1_3) ),
    inference(cnf_transformation,[],[f12]) ).

cnf(c_9563,plain,
    ( ~ $less_int(X0_3,sK3) | $less_int(X0_3,sK1) ),
    inference(superposition,[status(thm)],[c_563,c_54]) ).

cnf(c_9666,plain,
    ( $sum_int(sK1,3) = sK3 | $less_int($sum_int(sK1,3),sK1) ),
    inference(superposition,[status(thm)],[c_762,c_9563]) ).

cnf(c_2336,plain,
    ( ~ $less_int(X0_3,sK3) | $less_int(X0_3,sK1) ),
    inference(superposition,[status(thm)],[c_563,c_54]) ).

cnf(c_2467,plain,
    ( X0_3 = sK3 | $less_int(X0_3,sK1) | $less_int(sK3,X0_3) ),
    inference(superposition,[status(thm)],[c_53,c_2336]) ).

cnf(c_197,plain,
    ( X0_3 != X1_3
    | X2_3 != X3_3
    | ~ $less_int(X1_3,X3_3)
    | $less_int(X0_3,X2_3) ),
    theory(equality) ).

cnf(c_652,plain,
    ( X0_3 != sK3
    | X1_3 != sK1
    | ~ $less_int(sK3,sK1)
    | $less_int(X0_3,X1_3) ),
    inference(instantiation,[status(thm)],[c_197]) ).

cnf(c_932,plain,
    ( X0_3 != sK3
    | sK1 != sK1
    | ~ $less_int(sK3,sK1)
    | $less_int(X0_3,sK1) ),
    inference(instantiation,[status(thm)],[c_652]) ).

cnf(c_192,plain,( X0_3 = X0_3 ),theory(equality) ).

cnf(c_933,plain,
    ( sK1 = sK1 ),
    inference(instantiation,[status(thm)],[c_192]) ).

cnf(c_1431,plain,
    ( ~ $less_int(X0_3,sK3) | $less_int(X0_3,sK1) ),
    inference(superposition,[status(thm)],[c_563,c_54]) ).

cnf(c_1448,plain,
    ( X0_3 = sK3 | $less_int(X0_3,sK1) | $less_int(sK3,X0_3) ),
    inference(superposition,[status(thm)],[c_53,c_1431]) ).

cnf(c_3782,plain,
    ( $less_int(X0_3,sK1) | $less_int(sK3,X0_3) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_2467,c_64,c_63,c_517,c_932,c_933,c_1448]) ).

cnf(c_3789,plain,
    ( $less_int($sum_int(sK1,3),sK1) ),
    inference(superposition,[status(thm)],[c_3782,c_65]) ).

cnf(c_9676,plain,
    ( $less_int($sum_int(sK1,3),sK1) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_9666,c_3789]) ).

cnf(c_51,plain,
    ( $less_int(X0_3,$sum_int(X1_3,1)) | $less_int(X1_3,X0_3) ),
    inference(cnf_transformation,[],[f15]) ).

cnf(c_55,plain,
    ( ~ $less_int(X0_3,X0_3) ),
    inference(cnf_transformation,[],[f11]) ).

cnf(c_9426,plain,
    ( $less_int(X0_3,$sum_int(X0_3,1)) ),
    inference(superposition,[status(thm)],[c_51,c_55]) ).

cnf(c_9564,plain,
    ( ~ $less_int(X0_3,X1_3) | $less_int(X0_3,$sum_int(X1_3,1)) ),
    inference(superposition,[status(thm)],[c_9426,c_54]) ).

cnf(c_49,plain,
    ( ~ $less_int(X0_3,$sum_int(X1_3,1)) | ~ $less_int(X1_3,X0_3) ),
    inference(cnf_transformation,[],[f17]) ).

cnf(c_9755,plain,
    ( ~ $less_int(X0_3,X1_3) | ~ $less_int(X1_3,X0_3) ),
    inference(superposition,[status(thm)],[c_9564,c_49]) ).

cnf(c_10475,plain,
    ( ~ $less_int(sK1,$sum_int(sK1,3)) ),
    inference(superposition,[status(thm)],[c_9676,c_9755]) ).

cnf(c_18913,plain,
    ( ~ $less_int(0,3) ),
    inference(superposition,[status(thm)],[c_11457,c_10475]) ).

cnf(c_604,plain,
    ( ~ $less_int(1,X0_3) | ~ $less_int(0,1) | $less_int(0,X0_3) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_1084,plain,
    ( ~ $less_int(1,3) | ~ $less_int(0,1) | $less_int(0,3) ),
    inference(instantiation,[status(thm)],[c_604]) ).

cnf(c_79,plain,( $less_int(0,1) ),theory(arith) ).

cnf(c_80,plain,( $less_int(1,3) ),theory(arith) ).

cnf(contradiction,plain,
    ( $false ),
    inference(minisat,[status(thm)],[c_18913,c_1084,c_79,c_80]) ).

% SZS output end CNFRefutation for DAT013=1.tptp

Sample solution for SEU140+2

% SZS output start CNFRefutation for SEU140+2.tptp

fof(f8,axiom,(
  ! [X0] : ! [X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
  file('/tmp/SystemOnTPTP24033/SEU140+2.tptp',d3_tarski)).

fof(f64,plain,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
  inference(flattening,[],[f8])).

fof(f104,plain,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X1) | ~in(X2,X0)))),
  inference(ennf_transformation,[],[f64])).

fof(f142,plain,(
  ! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X2] : (in(X2,X1) | ~in(X2,X0)) | ~subset(X0,X1)))),
  inference(nnf_transformation,[],[f104])).

fof(f143,plain,(
  ! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
  inference(rectify,[],[f142])).

fof(f144,plain,(
  ! [X0,X1] : (? [X2] : (~in(X2,X1) & in(X2,X0)) => (~in(sK2(X0,X1),X1) & in(sK2(X0,X1),X0)))),
  introduced(choice_axiom,[])).

fof(f145,plain,(
  ! [X0,X1] : ((subset(X0,X1) | (~in(sK2(X0,X1),X1) & in(sK2(X0,X1),X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f143,f144])).

fof(f187,plain,(
  ( ! [X0,X3,X1] : (in(X3,X1) | ~in(X3,X0) | ~subset(X0,X1)) )),
  inference(cnf_transformation,[],[f145])).

fof(f43,axiom,(
  ! [X0] : ! [X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
  file('/tmp/SystemOnTPTP24033/SEU140+2.tptp',t3_xboole_0)).

fof(f88,plain,(
  ! [X0] : ! [X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
  inference(rectify,[],[f43])).

fof(f89,plain,(
  ! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
  inference(flattening,[],[f88])).

fof(f119,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
  inference(ennf_transformation,[],[f89])).

fof(f166,plain,(
  ! [X0,X1] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)))),
  introduced(choice_axiom,[])).

fof(f167,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)) | disjoint(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f119,f166])).

fof(f236,plain,(
  ( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
  inference(cnf_transformation,[],[f167])).

fof(f234,plain,(
  ( ! [X0,X1] : (in(sK8(X0,X1),X0) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f167])).

fof(f235,plain,(
  ( ! [X0,X1] : (in(sK8(X0,X1),X1) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f167])).

fof(f51,conjecture,(
  ! [X0] : ! [X1] : ! [X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  file('/tmp/SystemOnTPTP24033/SEU140+2.tptp',t63_xboole_1)).

fof(f52,negated_conjecture,(
  ~! [X0] : ! [X1] : ! [X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  inference(negated_conjecture,[],[f51])).

fof(f96,plain,(
  ~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  inference(flattening,[],[f52])).

fof(f124,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
  inference(ennf_transformation,[],[f96])).

fof(f125,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
  inference(flattening,[],[f124])).

fof(f170,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11))),
  introduced(choice_axiom,[])).

fof(f171,plain,(
  ~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f125,f170])).

fof(f247,plain,(
  ~disjoint(sK10,sK12)),
  inference(cnf_transformation,[],[f171])).

fof(f246,plain,(
  disjoint(sK11,sK12)),
  inference(cnf_transformation,[],[f171])).

fof(f245,plain,(
  subset(sK10,sK11)),
  inference(cnf_transformation,[],[f171])).

cnf(c_66,plain,
    ( ~ in(X0,X1) | ~ subset(X1,X2) | in(X0,X2) ),
    inference(cnf_transformation,[],[f187]) ).

cnf(c_3731,plain,
    ( ~ in(sK8(sK10,sK12),sK10)
    | ~ subset(sK10,X0)
    | in(sK8(sK10,sK12),X0) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_8290,plain,
    ( ~ in(sK8(sK10,sK12),sK10)
    | ~ subset(sK10,sK11)
    | in(sK8(sK10,sK12),sK11) ),
    inference(instantiation,[status(thm)],[c_3731]) ).

cnf(c_111,plain,
    ( ~ in(X0,X1) | ~ in(X0,X2) | ~ disjoint(X2,X1) ),
    inference(cnf_transformation,[],[f236]) ).

cnf(c_3649,plain,
    ( ~ in(sK8(sK10,sK12),X0)
    | ~ in(sK8(sK10,sK12),sK12)
    | ~ disjoint(X0,sK12) ),
    inference(instantiation,[status(thm)],[c_111]) ).

cnf(c_7873,plain,
    ( ~ in(sK8(sK10,sK12),sK12)
    | ~ in(sK8(sK10,sK12),sK11)
    | ~ disjoint(sK11,sK12) ),
    inference(instantiation,[status(thm)],[c_3649]) ).

cnf(c_113,plain,
    ( in(sK8(X0,X1),X0) | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f234]) ).

cnf(c_3362,plain,
    ( in(sK8(sK10,sK12),sK10) | disjoint(sK10,sK12) ),
    inference(instantiation,[status(thm)],[c_113]) ).

cnf(c_112,plain,
    ( in(sK8(X0,X1),X1) | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f235]) ).

cnf(c_3361,plain,
    ( in(sK8(sK10,sK12),sK12) | disjoint(sK10,sK12) ),
    inference(instantiation,[status(thm)],[c_112]) ).

cnf(c_121,negated_conjecture,
    ( ~ disjoint(sK10,sK12) ),
    inference(cnf_transformation,[],[f247]) ).

cnf(c_122,negated_conjecture,
    ( disjoint(sK11,sK12) ),
    inference(cnf_transformation,[],[f246]) ).

cnf(c_123,negated_conjecture,
    ( subset(sK10,sK11) ),
    inference(cnf_transformation,[],[f245]) ).

cnf(contradiction,plain,
    ( $false ),
    inference(minisat,
              [status(thm)],
              [c_8290,c_7873,c_3362,c_3361,c_121,c_122,c_123]) ).

% SZS output end CNFRefutation for SEU140+2.tptp

Sample solution for NLP042+1

% SZS output start Saturation for NLP042+1.tptp

fof(f45,conjecture,(
  ~? [X0] : (? [X1] : ? [X2] : ? [X3] : ? [X4] : (order(X0,X4) & nonreflexive(X0,X4) & past(X0,X4) & patient(X0,X4,X3) & agent(X0,X4,X1) & event(X0,X4) & shake_beverage(X0,X3) & forename(X0,X2) & mia_forename(X0,X2) & woman(X0,X1) & of(X0,X2,X1)) & actual_world(X0))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',co1)).

fof(f46,negated_conjecture,(
  ~~? [X0] : (? [X1] : ? [X2] : ? [X3] : ? [X4] : (order(X0,X4) & nonreflexive(X0,X4) & past(X0,X4) & patient(X0,X4,X3) & agent(X0,X4,X1) & event(X0,X4) & shake_beverage(X0,X3) & forename(X0,X2) & mia_forename(X0,X2) & woman(X0,X1) & of(X0,X2,X1)) & actual_world(X0))),
  inference(negated_conjecture,[],[f45])).

fof(f91,plain,(
  ? [X0] : (? [X1,X2,X3,X4] : (order(X0,X4) & nonreflexive(X0,X4) & past(X0,X4) & patient(X0,X4,X3) & agent(X0,X4,X1) & event(X0,X4) & shake_beverage(X0,X3) & forename(X0,X2) & mia_forename(X0,X2) & woman(X0,X1) & of(X0,X2,X1)) & actual_world(X0))),
  inference(flattening,[],[f46])).

fof(f92,plain,(
  ? [X0] : (? [X1,X2,X3,X4] : (order(X0,X4) & nonreflexive(X0,X4) & patient(X0,X4,X3) & agent(X0,X4,X1) & event(X0,X4) & shake_beverage(X0,X3) & forename(X0,X2) & mia_forename(X0,X2) & woman(X0,X1) & of(X0,X2,X1)) & actual_world(X0))),
  inference(pure_predicate_removal,[],[f91])).

fof(f93,plain,(
  ? [X0,X1,X2,X3,X4] : (order(X0,X4) & nonreflexive(X0,X4) & patient(X0,X4,X3) & agent(X0,X4,X1) & event(X0,X4) & shake_beverage(X0,X3) & forename(X0,X2) & mia_forename(X0,X2) & woman(X0,X1) & of(X0,X2,X1))),
  inference(pure_predicate_removal,[],[f92])).

fof(f140,plain,(
  ? [X0,X1,X2,X3,X4] : (order(X0,X4) & nonreflexive(X0,X4) & patient(X0,X4,X3) & agent(X0,X4,X1) & event(X0,X4) & shake_beverage(X0,X3) & forename(X0,X2) & mia_forename(X0,X2) & woman(X0,X1) & of(X0,X2,X1)) => (order(sK0,sK4) & nonreflexive(sK0,sK4) & patient(sK0,sK4,sK3) & agent(sK0,sK4,sK1) & event(sK0,sK4) & shake_beverage(sK0,sK3) & forename(sK0,sK2) & mia_forename(sK0,sK2) & woman(sK0,sK1) & of(sK0,sK2,sK1))),
  introduced(choice_axiom,[])).

fof(f141,plain,(
  order(sK0,sK4) & nonreflexive(sK0,sK4) & patient(sK0,sK4,sK3) & agent(sK0,sK4,sK1) & event(sK0,sK4) & shake_beverage(sK0,sK3) & forename(sK0,sK2) & mia_forename(sK0,sK2) & woman(sK0,sK1) & of(sK0,sK2,sK1)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f93,f140])).

fof(f180,plain,(
  of(sK0,sK2,sK1)),
  inference(cnf_transformation,[],[f141])).

fof(f43,axiom,(
  ! [X0] : ! [X1] : ! [X2] : ((of(X0,X2,X1) & forename(X0,X2) & entity(X0,X1)) => ~? [X3] : (of(X0,X3,X1) & X2 != X3 & forename(X0,X3)))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax43)).

fof(f89,plain,(
  ! [X0,X1,X2] : ((of(X0,X2,X1) & forename(X0,X2) & entity(X0,X1)) => ~? [X3] : (of(X0,X3,X1) & X2 != X3 & forename(X0,X3)))),
  inference(flattening,[],[f43])).

fof(f136,plain,(
  ! [X0,X1,X2] : (! [X3] : (~of(X0,X3,X1) | X2 = X3 | ~forename(X0,X3)) | (~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1)))),
  inference(ennf_transformation,[],[f89])).

fof(f137,plain,(
  ! [X0,X1,X2] : (! [X3] : (~of(X0,X3,X1) | X2 = X3 | ~forename(X0,X3)) | ~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1))),
  inference(flattening,[],[f136])).

fof(f178,plain,(
  ( ! [X2,X0,X3,X1] : (~of(X0,X3,X1) | X2 = X3 | ~forename(X0,X3) | ~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1)) )),
  inference(cnf_transformation,[],[f137])).

fof(f6,axiom,(
  ! [X0] : ! [X1] : (organism(X0,X1) => entity(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax6)).

fof(f52,plain,(
  ! [X0,X1] : (organism(X0,X1) => entity(X0,X1))),
  inference(flattening,[],[f6])).

fof(f104,plain,(
  ! [X0,X1] : (entity(X0,X1) | ~organism(X0,X1))),
  inference(ennf_transformation,[],[f52])).

fof(f146,plain,(
  ( ! [X0,X1] : (entity(X0,X1) | ~organism(X0,X1)) )),
  inference(cnf_transformation,[],[f104])).

fof(f7,axiom,(
  ! [X0] : ! [X1] : (human_person(X0,X1) => organism(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax7)).

fof(f53,plain,(
  ! [X0,X1] : (human_person(X0,X1) => organism(X0,X1))),
  inference(flattening,[],[f7])).

fof(f105,plain,(
  ! [X0,X1] : (organism(X0,X1) | ~human_person(X0,X1))),
  inference(ennf_transformation,[],[f53])).

fof(f147,plain,(
  ( ! [X0,X1] : (organism(X0,X1) | ~human_person(X0,X1)) )),
  inference(cnf_transformation,[],[f105])).

fof(f8,axiom,(
  ! [X0] : ! [X1] : (woman(X0,X1) => human_person(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax8)).

fof(f54,plain,(
  ! [X0,X1] : (woman(X0,X1) => human_person(X0,X1))),
  inference(flattening,[],[f8])).

fof(f106,plain,(
  ! [X0,X1] : (human_person(X0,X1) | ~woman(X0,X1))),
  inference(ennf_transformation,[],[f54])).

fof(f148,plain,(
  ( ! [X0,X1] : (human_person(X0,X1) | ~woman(X0,X1)) )),
  inference(cnf_transformation,[],[f106])).

fof(f181,plain,(
  woman(sK0,sK1)),
  inference(cnf_transformation,[],[f141])).

fof(f183,plain,(
  forename(sK0,sK2)),
  inference(cnf_transformation,[],[f141])).

fof(f24,axiom,(
  ! [X0] : ! [X1] : (substance_matter(X0,X1) => object(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax24)).

fof(f70,plain,(
  ! [X0,X1] : (substance_matter(X0,X1) => object(X0,X1))),
  inference(flattening,[],[f24])).

fof(f119,plain,(
  ! [X0,X1] : (object(X0,X1) | ~substance_matter(X0,X1))),
  inference(ennf_transformation,[],[f70])).

fof(f161,plain,(
  ( ! [X0,X1] : (object(X0,X1) | ~substance_matter(X0,X1)) )),
  inference(cnf_transformation,[],[f119])).

fof(f25,axiom,(
  ! [X0] : ! [X1] : (food(X0,X1) => substance_matter(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax25)).

fof(f71,plain,(
  ! [X0,X1] : (food(X0,X1) => substance_matter(X0,X1))),
  inference(flattening,[],[f25])).

fof(f120,plain,(
  ! [X0,X1] : (substance_matter(X0,X1) | ~food(X0,X1))),
  inference(ennf_transformation,[],[f71])).

fof(f162,plain,(
  ( ! [X0,X1] : (substance_matter(X0,X1) | ~food(X0,X1)) )),
  inference(cnf_transformation,[],[f120])).

fof(f26,axiom,(
  ! [X0] : ! [X1] : (beverage(X0,X1) => food(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax26)).

fof(f72,plain,(
  ! [X0,X1] : (beverage(X0,X1) => food(X0,X1))),
  inference(flattening,[],[f26])).

fof(f121,plain,(
  ! [X0,X1] : (food(X0,X1) | ~beverage(X0,X1))),
  inference(ennf_transformation,[],[f72])).

fof(f163,plain,(
  ( ! [X0,X1] : (food(X0,X1) | ~beverage(X0,X1)) )),
  inference(cnf_transformation,[],[f121])).

fof(f27,axiom,(
  ! [X0] : ! [X1] : (shake_beverage(X0,X1) => beverage(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax27)).

fof(f73,plain,(
  ! [X0,X1] : (shake_beverage(X0,X1) => beverage(X0,X1))),
  inference(flattening,[],[f27])).

fof(f122,plain,(
  ! [X0,X1] : (beverage(X0,X1) | ~shake_beverage(X0,X1))),
  inference(ennf_transformation,[],[f73])).

fof(f164,plain,(
  ( ! [X0,X1] : (beverage(X0,X1) | ~shake_beverage(X0,X1)) )),
  inference(cnf_transformation,[],[f122])).

fof(f184,plain,(
  shake_beverage(sK0,sK3)),
  inference(cnf_transformation,[],[f141])).

fof(f19,axiom,(
  ! [X0] : ! [X1] : (object(X0,X1) => nonliving(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax19)).

fof(f65,plain,(
  ! [X0,X1] : (object(X0,X1) => nonliving(X0,X1))),
  inference(flattening,[],[f19])).

fof(f115,plain,(
  ! [X0,X1] : (nonliving(X0,X1) | ~object(X0,X1))),
  inference(ennf_transformation,[],[f65])).

fof(f157,plain,(
  ( ! [X0,X1] : (nonliving(X0,X1) | ~object(X0,X1)) )),
  inference(cnf_transformation,[],[f115])).

fof(f2,axiom,(
  ! [X0] : ! [X1] : (human_person(X0,X1) => animate(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax2)).

fof(f48,plain,(
  ! [X0,X1] : (human_person(X0,X1) => animate(X0,X1))),
  inference(flattening,[],[f2])).

fof(f101,plain,(
  ! [X0,X1] : (animate(X0,X1) | ~human_person(X0,X1))),
  inference(ennf_transformation,[],[f48])).

fof(f143,plain,(
  ( ! [X0,X1] : (animate(X0,X1) | ~human_person(X0,X1)) )),
  inference(cnf_transformation,[],[f101])).

fof(f37,axiom,(
  ! [X0] : ! [X1] : (animate(X0,X1) => ~nonliving(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax37)).

fof(f83,plain,(
  ! [X0,X1] : (animate(X0,X1) => ~nonliving(X0,X1))),
  inference(flattening,[],[f37])).

fof(f130,plain,(
  ! [X0,X1] : (~nonliving(X0,X1) | ~animate(X0,X1))),
  inference(ennf_transformation,[],[f83])).

fof(f172,plain,(
  ( ! [X0,X1] : (~nonliving(X0,X1) | ~animate(X0,X1)) )),
  inference(cnf_transformation,[],[f130])).

fof(f34,axiom,(
  ! [X0] : ! [X1] : (event(X0,X1) => eventuality(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax34)).

fof(f80,plain,(
  ! [X0,X1] : (event(X0,X1) => eventuality(X0,X1))),
  inference(flattening,[],[f34])).

fof(f127,plain,(
  ! [X0,X1] : (eventuality(X0,X1) | ~event(X0,X1))),
  inference(ennf_transformation,[],[f80])).

fof(f169,plain,(
  ( ! [X0,X1] : (eventuality(X0,X1) | ~event(X0,X1)) )),
  inference(cnf_transformation,[],[f127])).

fof(f185,plain,(
  event(sK0,sK4)),
  inference(cnf_transformation,[],[f141])).

fof(f29,axiom,(
  ! [X0] : ! [X1] : (eventuality(X0,X1) => unisex(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax29)).

fof(f75,plain,(
  ! [X0,X1] : (eventuality(X0,X1) => unisex(X0,X1))),
  inference(flattening,[],[f29])).

fof(f124,plain,(
  ! [X0,X1] : (unisex(X0,X1) | ~eventuality(X0,X1))),
  inference(ennf_transformation,[],[f75])).

fof(f166,plain,(
  ( ! [X0,X1] : (unisex(X0,X1) | ~eventuality(X0,X1)) )),
  inference(cnf_transformation,[],[f124])).

fof(f1,axiom,(
  ! [X0] : ! [X1] : (woman(X0,X1) => female(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax1)).

fof(f47,plain,(
  ! [X0,X1] : (woman(X0,X1) => female(X0,X1))),
  inference(flattening,[],[f1])).

fof(f100,plain,(
  ! [X0,X1] : (female(X0,X1) | ~woman(X0,X1))),
  inference(ennf_transformation,[],[f47])).

fof(f142,plain,(
  ( ! [X0,X1] : (female(X0,X1) | ~woman(X0,X1)) )),
  inference(cnf_transformation,[],[f100])).

fof(f42,axiom,(
  ! [X0] : ! [X1] : (unisex(X0,X1) => ~female(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax42)).

fof(f88,plain,(
  ! [X0,X1] : (unisex(X0,X1) => ~female(X0,X1))),
  inference(flattening,[],[f42])).

fof(f135,plain,(
  ! [X0,X1] : (~female(X0,X1) | ~unisex(X0,X1))),
  inference(ennf_transformation,[],[f88])).

fof(f177,plain,(
  ( ! [X0,X1] : (~female(X0,X1) | ~unisex(X0,X1)) )),
  inference(cnf_transformation,[],[f135])).

fof(f23,axiom,(
  ! [X0] : ! [X1] : (object(X0,X1) => entity(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax23)).

fof(f69,plain,(
  ! [X0,X1] : (object(X0,X1) => entity(X0,X1))),
  inference(flattening,[],[f23])).

fof(f118,plain,(
  ! [X0,X1] : (entity(X0,X1) | ~object(X0,X1))),
  inference(ennf_transformation,[],[f69])).

fof(f160,plain,(
  ( ! [X0,X1] : (entity(X0,X1) | ~object(X0,X1)) )),
  inference(cnf_transformation,[],[f118])).

fof(f30,axiom,(
  ! [X0] : ! [X1] : (eventuality(X0,X1) => nonexistent(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax30)).

fof(f76,plain,(
  ! [X0,X1] : (eventuality(X0,X1) => nonexistent(X0,X1))),
  inference(flattening,[],[f30])).

fof(f125,plain,(
  ! [X0,X1] : (nonexistent(X0,X1) | ~eventuality(X0,X1))),
  inference(ennf_transformation,[],[f76])).

fof(f167,plain,(
  ( ! [X0,X1] : (nonexistent(X0,X1) | ~eventuality(X0,X1)) )),
  inference(cnf_transformation,[],[f125])).

fof(f20,axiom,(
  ! [X0] : ! [X1] : (entity(X0,X1) => existent(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax20)).

fof(f66,plain,(
  ! [X0,X1] : (entity(X0,X1) => existent(X0,X1))),
  inference(flattening,[],[f20])).

fof(f116,plain,(
  ! [X0,X1] : (existent(X0,X1) | ~entity(X0,X1))),
  inference(ennf_transformation,[],[f66])).

fof(f158,plain,(
  ( ! [X0,X1] : (existent(X0,X1) | ~entity(X0,X1)) )),
  inference(cnf_transformation,[],[f116])).

fof(f38,axiom,(
  ! [X0] : ! [X1] : (existent(X0,X1) => ~nonexistent(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax38)).

fof(f84,plain,(
  ! [X0,X1] : (existent(X0,X1) => ~nonexistent(X0,X1))),
  inference(flattening,[],[f38])).

fof(f131,plain,(
  ! [X0,X1] : (~nonexistent(X0,X1) | ~existent(X0,X1))),
  inference(ennf_transformation,[],[f84])).

fof(f173,plain,(
  ( ! [X0,X1] : (~nonexistent(X0,X1) | ~existent(X0,X1)) )),
  inference(cnf_transformation,[],[f131])).

fof(f21,axiom,(
  ! [X0] : ! [X1] : (entity(X0,X1) => specific(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax21)).

fof(f67,plain,(
  ! [X0,X1] : (entity(X0,X1) => specific(X0,X1))),
  inference(flattening,[],[f21])).

fof(f117,plain,(
  ! [X0,X1] : (specific(X0,X1) | ~entity(X0,X1))),
  inference(ennf_transformation,[],[f67])).

fof(f159,plain,(
  ( ! [X0,X1] : (specific(X0,X1) | ~entity(X0,X1)) )),
  inference(cnf_transformation,[],[f117])).

fof(f16,axiom,(
  ! [X0] : ! [X1] : (forename(X0,X1) => relname(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax16)).

fof(f62,plain,(
  ! [X0,X1] : (forename(X0,X1) => relname(X0,X1))),
  inference(flattening,[],[f16])).

fof(f113,plain,(
  ! [X0,X1] : (relname(X0,X1) | ~forename(X0,X1))),
  inference(ennf_transformation,[],[f62])).

fof(f155,plain,(
  ( ! [X0,X1] : (relname(X0,X1) | ~forename(X0,X1)) )),
  inference(cnf_transformation,[],[f113])).

fof(f15,axiom,(
  ! [X0] : ! [X1] : (relname(X0,X1) => relation(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax15)).

fof(f61,plain,(
  ! [X0,X1] : (relname(X0,X1) => relation(X0,X1))),
  inference(flattening,[],[f15])).

fof(f112,plain,(
  ! [X0,X1] : (relation(X0,X1) | ~relname(X0,X1))),
  inference(ennf_transformation,[],[f61])).

fof(f154,plain,(
  ( ! [X0,X1] : (relation(X0,X1) | ~relname(X0,X1)) )),
  inference(cnf_transformation,[],[f112])).

fof(f14,axiom,(
  ! [X0] : ! [X1] : (relation(X0,X1) => abstraction(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax14)).

fof(f60,plain,(
  ! [X0,X1] : (relation(X0,X1) => abstraction(X0,X1))),
  inference(flattening,[],[f14])).

fof(f111,plain,(
  ! [X0,X1] : (abstraction(X0,X1) | ~relation(X0,X1))),
  inference(ennf_transformation,[],[f60])).

fof(f153,plain,(
  ( ! [X0,X1] : (abstraction(X0,X1) | ~relation(X0,X1)) )),
  inference(cnf_transformation,[],[f111])).

fof(f11,axiom,(
  ! [X0] : ! [X1] : (abstraction(X0,X1) => general(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax11)).

fof(f57,plain,(
  ! [X0,X1] : (abstraction(X0,X1) => general(X0,X1))),
  inference(flattening,[],[f11])).

fof(f109,plain,(
  ! [X0,X1] : (general(X0,X1) | ~abstraction(X0,X1))),
  inference(ennf_transformation,[],[f57])).

fof(f151,plain,(
  ( ! [X0,X1] : (general(X0,X1) | ~abstraction(X0,X1)) )),
  inference(cnf_transformation,[],[f109])).

fof(f41,axiom,(
  ! [X0] : ! [X1] : (specific(X0,X1) => ~general(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax41)).

fof(f87,plain,(
  ! [X0,X1] : (specific(X0,X1) => ~general(X0,X1))),
  inference(flattening,[],[f41])).

fof(f134,plain,(
  ! [X0,X1] : (~general(X0,X1) | ~specific(X0,X1))),
  inference(ennf_transformation,[],[f87])).

fof(f176,plain,(
  ( ! [X0,X1] : (~general(X0,X1) | ~specific(X0,X1)) )),
  inference(cnf_transformation,[],[f134])).

fof(f31,axiom,(
  ! [X0] : ! [X1] : (eventuality(X0,X1) => specific(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax31)).

fof(f77,plain,(
  ! [X0,X1] : (eventuality(X0,X1) => specific(X0,X1))),
  inference(flattening,[],[f31])).

fof(f126,plain,(
  ! [X0,X1] : (specific(X0,X1) | ~eventuality(X0,X1))),
  inference(ennf_transformation,[],[f77])).

fof(f168,plain,(
  ( ! [X0,X1] : (specific(X0,X1) | ~eventuality(X0,X1)) )),
  inference(cnf_transformation,[],[f126])).

fof(f12,axiom,(
  ! [X0] : ! [X1] : (abstraction(X0,X1) => nonhuman(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax12)).

fof(f58,plain,(
  ! [X0,X1] : (abstraction(X0,X1) => nonhuman(X0,X1))),
  inference(flattening,[],[f12])).

fof(f110,plain,(
  ! [X0,X1] : (nonhuman(X0,X1) | ~abstraction(X0,X1))),
  inference(ennf_transformation,[],[f58])).

fof(f152,plain,(
  ( ! [X0,X1] : (nonhuman(X0,X1) | ~abstraction(X0,X1)) )),
  inference(cnf_transformation,[],[f110])).

fof(f3,axiom,(
  ! [X0] : ! [X1] : (human_person(X0,X1) => human(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax3)).

fof(f49,plain,(
  ! [X0,X1] : (human_person(X0,X1) => human(X0,X1))),
  inference(flattening,[],[f3])).

fof(f102,plain,(
  ! [X0,X1] : (human(X0,X1) | ~human_person(X0,X1))),
  inference(ennf_transformation,[],[f49])).

fof(f144,plain,(
  ( ! [X0,X1] : (human(X0,X1) | ~human_person(X0,X1)) )),
  inference(cnf_transformation,[],[f102])).

fof(f39,axiom,(
  ! [X0] : ! [X1] : (nonhuman(X0,X1) => ~human(X0,X1))),
  file('/tmp/SystemOnTPTP24503/NLP042+1.tptp',ax39)).

fof(f85,plain,(
  ! [X0,X1] : (nonhuman(X0,X1) => ~human(X0,X1))),
  inference(flattening,[],[f39])).

fof(f132,plain,(
  ! [X0,X1] : (~human(X0,X1) | ~nonhuman(X0,X1))),
  inference(ennf_transformation,[],[f85])).

fof(f174,plain,(
  ( ! [X0,X1] : (~human(X0,X1) | ~nonhuman(X0,X1)) )),
  inference(cnf_transformation,[],[f132])).

cnf(c_489,plain,
    ( X0 != X1 | X2 != X3 | ~ nonreflexive(X1,X3) | nonreflexive(X0,X2) ),
    theory(equality) ).

cnf(c_919,plain,
    ( X0 != X1 | X2 != X3 | X4 != X5 | ~ agent(X1,X3,X5) | agent(X0,X2,X4) ),
    theory(equality) ).

cnf(c_487,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | ~ patient(X1,X3,X5)
    | patient(X0,X2,X4) ),
    theory(equality) ).

cnf(c_485,plain,
    ( X0 != X1 | X2 != X3 | ~ order(X1,X3) | order(X0,X2) ),
    theory(equality) ).

cnf(c_484,plain,
    ( X0 != X1 | X2 != X3 | ~ event(X1,X3) | event(X0,X2) ),
    theory(equality) ).

cnf(c_483,plain,
    ( X0 != X1 | X2 != X3 | ~ shake_beverage(X1,X3) | shake_beverage(X0,X2) ),
    theory(equality) ).

cnf(c_482,plain,
    ( X0 != X1 | X2 != X3 | ~ mia_forename(X1,X3) | mia_forename(X0,X2) ),
    theory(equality) ).

cnf(c_480,plain,
    ( X0 != X1 | X2 != X3 | ~ woman(X1,X3) | woman(X0,X2) ),
    theory(equality) ).

cnf(c_978,plain,( X0_1 = X0_1 ),theory(equality) ).

cnf(c_96,negated_conjecture,
    ( of(sK0,sK2,sK1) ),
    inference(cnf_transformation,[],[f180]) ).

cnf(c_85,plain,
    ( ~ of(X0,X1,X2)
    | ~ of(X0,X3,X2)
    | ~ entity(X0,X2)
    | ~ forename(X0,X1)
    | ~ forename(X0,X3)
    | X1 = X3 ),
    inference(cnf_transformation,[],[f178]) ).

cnf(c_53,plain,
    ( ~ organism(X0,X1) | entity(X0,X1) ),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_54,plain,
    ( ~ human_person(X0,X1) | organism(X0,X1) ),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_55,plain,
    ( ~ woman(X0,X1) | human_person(X0,X1) ),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_95,negated_conjecture,
    ( woman(sK0,sK1) ),
    inference(cnf_transformation,[],[f181]) ).

cnf(c_532,plain,
    ( X0 != sK0 | X1 != sK1 | human_person(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_95]) ).

cnf(c_533,plain,
    ( human_person(sK0,sK1) ),
    inference(unflattening,[status(thm)],[c_532]) ).

cnf(c_685,plain,
    ( X0 != sK0 | X1 != sK1 | organism(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_533]) ).

cnf(c_686,plain,
    ( organism(sK0,sK1) ),
    inference(unflattening,[status(thm)],[c_685]) ).

cnf(c_695,plain,
    ( X0 != sK0 | X1 != sK1 | entity(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_53,c_686]) ).

cnf(c_696,plain,
    ( entity(sK0,sK1) ),
    inference(unflattening,[status(thm)],[c_695]) ).

cnf(c_799,plain,
    ( X0 != sK0
    | X1 != sK1
    | ~ of(X0,X2,X1)
    | ~ of(X0,X3,X1)
    | ~ forename(X0,X2)
    | ~ forename(X0,X3)
    | X2 = X3 ),
    inference(resolution_lifted,[status(thm)],[c_85,c_696]) ).

cnf(c_800,plain,
    ( ~ of(sK0,X0,sK1)
    | ~ of(sK0,X1,sK1)
    | ~ forename(sK0,X0)
    | ~ forename(sK0,X1)
    | X0 = X1 ),
    inference(unflattening,[status(thm)],[c_799]) ).

cnf(c_1115,plain,
    ( ~ of(sK0,X0,sK1)
    | ~ forename(sK0,X0)
    | ~ forename(sK0,sK2)
    | X0 = sK2 ),
    inference(superposition,[status(thm)],[c_96,c_800]) ).

cnf(c_93,negated_conjecture,
    ( forename(sK0,sK2) ),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_1116,plain,
    ( ~ of(sK0,X0,sK1) | ~ forename(sK0,X0) | X0 = sK2 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1115,c_93]) ).

cnf(c_68,plain,
    ( ~ substance_matter(X0,X1) | object(X0,X1) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_69,plain,
    ( ~ food(X0,X1) | substance_matter(X0,X1) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_70,plain,
    ( ~ beverage(X0,X1) | food(X0,X1) ),
    inference(cnf_transformation,[],[f163]) ).

cnf(c_71,plain,
    ( ~ shake_beverage(X0,X1) | beverage(X0,X1) ),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_92,negated_conjecture,
    ( shake_beverage(sK0,sK3) ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_492,plain,
    ( X0 != sK0 | X1 != sK3 | beverage(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_71,c_92]) ).

cnf(c_493,plain,
    ( beverage(sK0,sK3) ),
    inference(unflattening,[status(thm)],[c_492]) ).

cnf(c_498,plain,
    ( X0 != sK0 | X1 != sK3 | food(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_70,c_493]) ).

cnf(c_499,plain,
    ( food(sK0,sK3) ),
    inference(unflattening,[status(thm)],[c_498]) ).

cnf(c_504,plain,
    ( X0 != sK0 | X1 != sK3 | substance_matter(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_69,c_499]) ).

cnf(c_505,plain,
    ( substance_matter(sK0,sK3) ),
    inference(unflattening,[status(thm)],[c_504]) ).

cnf(c_510,plain,
    ( X0 != sK0 | X1 != sK3 | object(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_68,c_505]) ).

cnf(c_511,plain,
    ( object(sK0,sK3) ),
    inference(unflattening,[status(thm)],[c_510]) ).

cnf(c_64,plain,
    ( ~ object(X0,X1) | nonliving(X0,X1) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_50,plain,
    ( ~ human_person(X0,X1) | animate(X0,X1) ),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_79,plain,
    ( ~ animate(X0,X1) | ~ nonliving(X0,X1) ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_539,plain,
    ( X0 != X1 | X2 != X3 | ~ human_person(X0,X2) | ~ nonliving(X1,X3) ),
    inference(resolution_lifted,[status(thm)],[c_50,c_79]) ).

cnf(c_540,plain,
    ( ~ human_person(X0,X1) | ~ nonliving(X0,X1) ),
    inference(unflattening,[status(thm)],[c_539]) ).

cnf(c_680,plain,
    ( X0 != sK0 | X1 != sK1 | ~ nonliving(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_540,c_533]) ).

cnf(c_681,plain,
    ( ~ nonliving(sK0,sK1) ),
    inference(unflattening,[status(thm)],[c_680]) ).

cnf(c_701,plain,
    ( X0 != sK0 | X1 != sK1 | ~ object(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_64,c_681]) ).

cnf(c_702,plain,
    ( ~ object(sK0,sK1) ),
    inference(unflattening,[status(thm)],[c_701]) ).

cnf(c_717,plain,
    ( sK0 != sK0 | sK3 != sK1 ),
    inference(resolution_lifted,[status(thm)],[c_511,c_702]) ).

cnf(c_858,plain,
    ( sK3 != sK1 ),
    inference(equality_resolution_simp,[status(thm)],[c_717]) ).

cnf(c_76,plain,
    ( ~ event(X0,X1) | eventuality(X0,X1) ),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_91,negated_conjecture,
    ( event(sK0,sK4) ),
    inference(cnf_transformation,[],[f185]) ).

cnf(c_637,plain,
    ( X0 != sK0 | X1 != sK4 | eventuality(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_76,c_91]) ).

cnf(c_638,plain,
    ( eventuality(sK0,sK4) ),
    inference(unflattening,[status(thm)],[c_637]) ).

cnf(c_73,plain,
    ( ~ eventuality(X0,X1) | unisex(X0,X1) ),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_49,plain,
    ( ~ woman(X0,X1) | female(X0,X1) ),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_84,plain,
    ( ~ female(X0,X1) | ~ unisex(X0,X1) ),
    inference(cnf_transformation,[],[f177]) ).

cnf(c_516,plain,
    ( X0 != X1 | X2 != X3 | ~ woman(X0,X2) | ~ unisex(X1,X3) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_84]) ).

cnf(c_517,plain,
    ( ~ woman(X0,X1) | ~ unisex(X0,X1) ),
    inference(unflattening,[status(thm)],[c_516]) ).

cnf(c_527,plain,
    ( X0 != sK0 | X1 != sK1 | ~ unisex(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_517,c_95]) ).

cnf(c_528,plain,
    ( ~ unisex(sK0,sK1) ),
    inference(unflattening,[status(thm)],[c_527]) ).

cnf(c_728,plain,
    ( X0 != sK0 | X1 != sK1 | ~ eventuality(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_73,c_528]) ).

cnf(c_729,plain,
    ( ~ eventuality(sK0,sK1) ),
    inference(unflattening,[status(thm)],[c_728]) ).

cnf(c_747,plain,
    ( sK0 != sK0 | sK4 != sK1 ),
    inference(resolution_lifted,[status(thm)],[c_638,c_729]) ).

cnf(c_857,plain,
    ( sK4 != sK1 ),
    inference(equality_resolution_simp,[status(thm)],[c_747]) ).

cnf(c_67,plain,
    ( ~ object(X0,X1) | entity(X0,X1) ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_707,plain,
    ( X0 != sK0 | X1 != sK3 | entity(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_67,c_511]) ).

cnf(c_708,plain,
    ( entity(sK0,sK3) ),
    inference(unflattening,[status(thm)],[c_707]) ).

cnf(c_74,plain,
    ( ~ eventuality(X0,X1) | nonexistent(X0,X1) ),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_65,plain,
    ( ~ entity(X0,X1) | existent(X0,X1) ),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_80,plain,
    ( ~ existent(X0,X1) | ~ nonexistent(X0,X1) ),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_616,plain,
    ( X0 != X1 | X2 != X3 | ~ entity(X0,X2) | ~ nonexistent(X1,X3) ),
    inference(resolution_lifted,[status(thm)],[c_65,c_80]) ).

cnf(c_617,plain,
    ( ~ entity(X0,X1) | ~ nonexistent(X0,X1) ),
    inference(unflattening,[status(thm)],[c_616]) ).

cnf(c_643,plain,
    ( X0 != X1 | X2 != X3 | ~ entity(X1,X3) | ~ eventuality(X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_74,c_617]) ).

cnf(c_644,plain,
    ( ~ entity(X0,X1) | ~ eventuality(X0,X1) ),
    inference(unflattening,[status(thm)],[c_643]) ).

cnf(c_737,plain,
    ( X0 != sK0 | X1 != sK4 | ~ entity(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_644,c_638]) ).

cnf(c_738,plain,
    ( ~ entity(sK0,sK4) ),
    inference(unflattening,[status(thm)],[c_737]) ).

cnf(c_836,plain,
    ( sK0 != sK0 | sK4 != sK3 ),
    inference(resolution_lifted,[status(thm)],[c_708,c_738]) ).

cnf(c_856,plain,
    ( sK4 != sK3 ),
    inference(equality_resolution_simp,[status(thm)],[c_836]) ).

cnf(c_817,plain,
    ( X0 != sK0
    | X1 != sK3
    | ~ of(X0,X2,X1)
    | ~ of(X0,X3,X1)
    | ~ forename(X0,X2)
    | ~ forename(X0,X3)
    | X2 = X3 ),
    inference(resolution_lifted,[status(thm)],[c_85,c_708]) ).

cnf(c_818,plain,
    ( ~ of(sK0,X0,sK3)
    | ~ of(sK0,X1,sK3)
    | ~ forename(sK0,X0)
    | ~ forename(sK0,X1)
    | X0 = X1 ),
    inference(unflattening,[status(thm)],[c_817]) ).

cnf(c_66,plain,
    ( ~ entity(X0,X1) | specific(X0,X1) ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_62,plain,
    ( ~ forename(X0,X1) | relname(X0,X1) ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_61,plain,
    ( ~ relname(X0,X1) | relation(X0,X1) ),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_60,plain,
    ( ~ relation(X0,X1) | abstraction(X0,X1) ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_594,plain,
    ( X0 != X1 | X2 != X3 | ~ relname(X0,X2) | abstraction(X1,X3) ),
    inference(resolution_lifted,[status(thm)],[c_61,c_60]) ).

cnf(c_595,plain,
    ( ~ relname(X0,X1) | abstraction(X0,X1) ),
    inference(unflattening,[status(thm)],[c_594]) ).

cnf(c_605,plain,
    ( X0 != X1 | X2 != X3 | ~ forename(X0,X2) | abstraction(X1,X3) ),
    inference(resolution_lifted,[status(thm)],[c_62,c_595]) ).

cnf(c_606,plain,
    ( ~ forename(X0,X1) | abstraction(X0,X1) ),
    inference(unflattening,[status(thm)],[c_605]) ).

cnf(c_58,plain,
    ( ~ abstraction(X0,X1) | general(X0,X1) ),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_83,plain,
    ( ~ general(X0,X1) | ~ specific(X0,X1) ),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_572,plain,
    ( X0 != X1 | X2 != X3 | ~ abstraction(X0,X2) | ~ specific(X1,X3) ),
    inference(resolution_lifted,[status(thm)],[c_58,c_83]) ).

cnf(c_573,plain,
    ( ~ abstraction(X0,X1) | ~ specific(X0,X1) ),
    inference(unflattening,[status(thm)],[c_572]) ).

cnf(c_758,plain,
    ( X0 != X1 | X2 != X3 | ~ forename(X0,X2) | ~ specific(X1,X3) ),
    inference(resolution_lifted,[status(thm)],[c_606,c_573]) ).

cnf(c_759,plain,
    ( ~ forename(X0,X1) | ~ specific(X0,X1) ),
    inference(unflattening,[status(thm)],[c_758]) ).

cnf(c_775,plain,
    ( X0 != X1 | X2 != X3 | ~ entity(X0,X2) | ~ forename(X1,X3) ),
    inference(resolution_lifted,[status(thm)],[c_66,c_759]) ).

cnf(c_776,plain,
    ( ~ entity(X0,X1) | ~ forename(X0,X1) ),
    inference(unflattening,[status(thm)],[c_775]) ).

cnf(c_794,plain,
    ( X0 != sK0 | X1 != sK3 | ~ forename(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_776,c_708]) ).

cnf(c_795,plain,
    ( ~ forename(sK0,sK3) ),
    inference(unflattening,[status(thm)],[c_794]) ).

cnf(c_75,plain,
    ( ~ eventuality(X0,X1) | specific(X0,X1) ),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_742,plain,
    ( X0 != sK0 | X1 != sK4 | specific(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_75,c_638]) ).

cnf(c_743,plain,
    ( specific(sK0,sK4) ),
    inference(unflattening,[status(thm)],[c_742]) ).

cnf(c_784,plain,
    ( X0 != sK0 | X1 != sK4 | ~ forename(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_759,c_743]) ).

cnf(c_785,plain,
    ( ~ forename(sK0,sK4) ),
    inference(unflattening,[status(thm)],[c_784]) ).

cnf(c_59,plain,
    ( ~ abstraction(X0,X1) | nonhuman(X0,X1) ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_51,plain,
    ( ~ human_person(X0,X1) | human(X0,X1) ),
    inference(cnf_transformation,[],[f144]) ).

cnf(c_81,plain,
    ( ~ human(X0,X1) | ~ nonhuman(X0,X1) ),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_550,plain,
    ( X0 != X1 | X2 != X3 | ~ human_person(X0,X2) | ~ nonhuman(X1,X3) ),
    inference(resolution_lifted,[status(thm)],[c_51,c_81]) ).

cnf(c_551,plain,
    ( ~ human_person(X0,X1) | ~ nonhuman(X0,X1) ),
    inference(unflattening,[status(thm)],[c_550]) ).

cnf(c_583,plain,
    ( X0 != X1 | X2 != X3 | ~ human_person(X1,X3) | ~ abstraction(X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_59,c_551]) ).

cnf(c_584,plain,
    ( ~ human_person(X0,X1) | ~ abstraction(X0,X1) ),
    inference(unflattening,[status(thm)],[c_583]) ).

cnf(c_675,plain,
    ( X0 != sK0 | X1 != sK1 | ~ abstraction(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_584,c_533]) ).

cnf(c_676,plain,
    ( ~ abstraction(sK0,sK1) ),
    inference(unflattening,[status(thm)],[c_675]) ).

cnf(c_767,plain,
    ( X0 != sK0 | X1 != sK1 | ~ forename(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_606,c_676]) ).

cnf(c_768,plain,
    ( ~ forename(sK0,sK1) ),
    inference(unflattening,[status(thm)],[c_767]) ).

% SZS output end Saturation for NLP042+1.tptp

Sample solution for SWV017+1

% SZS output start Saturation for SWV017+1.tptp

fof(f33,axiom,(
  ! [X0] : (fresh_intruder_nonce(X0) => (intruder_message(X0) & fresh_to_b(X0)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',fresh_intruder_nonces_are_fresh_to_b)).

fof(f82,plain,(
  ! [X0] : ((intruder_message(X0) & fresh_to_b(X0)) | ~fresh_intruder_nonce(X0))),
  inference(ennf_transformation,[],[f33])).

fof(f119,plain,(
  ( ! [X0] : (fresh_to_b(X0) | ~fresh_intruder_nonce(X0)) )),
  inference(cnf_transformation,[],[f82])).

fof(f120,plain,(
  ( ! [X0] : (intruder_message(X0) | ~fresh_intruder_nonce(X0)) )),
  inference(cnf_transformation,[],[f82])).

fof(f32,axiom,(
  ! [X0] : (fresh_intruder_nonce(X0) => fresh_intruder_nonce(generate_intruder_nonce(X0)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',can_generate_more_fresh_intruder_nonces)).

fof(f81,plain,(
  ! [X0] : (fresh_intruder_nonce(generate_intruder_nonce(X0)) | ~fresh_intruder_nonce(X0))),
  inference(ennf_transformation,[],[f32])).

fof(f118,plain,(
  ( ! [X0] : (fresh_intruder_nonce(generate_intruder_nonce(X0)) | ~fresh_intruder_nonce(X0)) )),
  inference(cnf_transformation,[],[f81])).

fof(f31,axiom,(
  fresh_intruder_nonce(an_intruder_nonce)),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',an_intruder_nonce_is_a_fresh_intruder_nonce)).

fof(f117,plain,(
  fresh_intruder_nonce(an_intruder_nonce)),
  inference(cnf_transformation,[],[f31])).

fof(f27,axiom,(
  ! [X0] : ~a_nonce(generate_key(X0))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',generated_keys_are_not_nonces)).

fof(f112,plain,(
  ( ! [X0] : (~a_nonce(generate_key(X0))) )),
  inference(cnf_transformation,[],[f27])).

fof(f25,axiom,(
  ! [X0] : ! [X1] : ! [X2] : ((party_of_protocol(X2) & intruder_holds(key(X1,X2)) & intruder_message(X0)) => intruder_message(encrypt(X0,X1)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_key_encrypts)).

fof(f50,plain,(
  ! [X0,X1,X2] : ((party_of_protocol(X2) & intruder_holds(key(X1,X2)) & intruder_message(X0)) => intruder_message(encrypt(X0,X1)))),
  inference(flattening,[],[f25])).

fof(f78,plain,(
  ! [X0,X1,X2] : (intruder_message(encrypt(X0,X1)) | (~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(X0)))),
  inference(ennf_transformation,[],[f50])).

fof(f79,plain,(
  ! [X0,X1,X2] : (intruder_message(encrypt(X0,X1)) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(X0))),
  inference(flattening,[],[f78])).

fof(f110,plain,(
  ( ! [X2,X0,X1] : (intruder_message(encrypt(X0,X1)) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f79])).

fof(f24,axiom,(
  ! [X1] : ! [X2] : ((party_of_protocol(X2) & intruder_message(X1)) => intruder_holds(key(X1,X2)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_holds_key)).

fof(f48,plain,(
  ! [X0] : ! [X1] : ((party_of_protocol(X1) & intruder_message(X0)) => intruder_holds(key(X0,X1)))),
  inference(rectify,[],[f24])).

fof(f49,plain,(
  ! [X0,X1] : ((party_of_protocol(X1) & intruder_message(X0)) => intruder_holds(key(X0,X1)))),
  inference(flattening,[],[f48])).

fof(f76,plain,(
  ! [X0,X1] : (intruder_holds(key(X0,X1)) | (~party_of_protocol(X1) | ~intruder_message(X0)))),
  inference(ennf_transformation,[],[f49])).

fof(f77,plain,(
  ! [X0,X1] : (intruder_holds(key(X0,X1)) | ~party_of_protocol(X1) | ~intruder_message(X0))),
  inference(flattening,[],[f76])).

fof(f109,plain,(
  ( ! [X0,X1] : (intruder_holds(key(X0,X1)) | ~party_of_protocol(X1) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f77])).

fof(f23,axiom,(
  ! [X0] : ! [X1] : ! [X2] : ((party_of_protocol(X2) & party_of_protocol(X1) & intruder_message(X0)) => message(sent(X1,X2,X0)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_message_sent)).

fof(f47,plain,(
  ! [X0,X1,X2] : ((party_of_protocol(X2) & party_of_protocol(X1) & intruder_message(X0)) => message(sent(X1,X2,X0)))),
  inference(flattening,[],[f23])).

fof(f74,plain,(
  ! [X0,X1,X2] : (message(sent(X1,X2,X0)) | (~party_of_protocol(X2) | ~party_of_protocol(X1) | ~intruder_message(X0)))),
  inference(ennf_transformation,[],[f47])).

fof(f75,plain,(
  ! [X0,X1,X2] : (message(sent(X1,X2,X0)) | ~party_of_protocol(X2) | ~party_of_protocol(X1) | ~intruder_message(X0))),
  inference(flattening,[],[f74])).

fof(f108,plain,(
  ( ! [X2,X0,X1] : (message(sent(X1,X2,X0)) | ~party_of_protocol(X2) | ~party_of_protocol(X1) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f75])).

fof(f22,axiom,(
  ! [X0] : ! [X1] : ! [X2] : ((party_of_protocol(X2) & intruder_holds(key(X1,X2)) & intruder_message(encrypt(X0,X1))) => intruder_message(X1))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_interception)).

fof(f46,plain,(
  ! [X0,X1,X2] : ((party_of_protocol(X2) & intruder_holds(key(X1,X2)) & intruder_message(encrypt(X0,X1))) => intruder_message(X1))),
  inference(flattening,[],[f22])).

fof(f72,plain,(
  ! [X0,X1,X2] : (intruder_message(X1) | (~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(encrypt(X0,X1))))),
  inference(ennf_transformation,[],[f46])).

fof(f73,plain,(
  ! [X0,X1,X2] : (intruder_message(X1) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(encrypt(X0,X1)))),
  inference(flattening,[],[f72])).

fof(f107,plain,(
  ( ! [X2,X0,X1] : (intruder_message(X1) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(encrypt(X0,X1))) )),
  inference(cnf_transformation,[],[f73])).

fof(f21,axiom,(
  ! [X0] : ! [X1] : ! [X2] : ! [X3] : ((intruder_message(X3) & intruder_message(X2) & intruder_message(X1) & intruder_message(X0)) => intruder_message(quadruple(X0,X1,X2,X3)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_composes_quadruples)).

fof(f45,plain,(
  ! [X0,X1,X2,X3] : ((intruder_message(X3) & intruder_message(X2) & intruder_message(X1) & intruder_message(X0)) => intruder_message(quadruple(X0,X1,X2,X3)))),
  inference(flattening,[],[f21])).

fof(f70,plain,(
  ! [X0,X1,X2,X3] : (intruder_message(quadruple(X0,X1,X2,X3)) | (~intruder_message(X3) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)))),
  inference(ennf_transformation,[],[f45])).

fof(f71,plain,(
  ! [X0,X1,X2,X3] : (intruder_message(quadruple(X0,X1,X2,X3)) | ~intruder_message(X3) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0))),
  inference(flattening,[],[f70])).

fof(f106,plain,(
  ( ! [X2,X0,X3,X1] : (intruder_message(quadruple(X0,X1,X2,X3)) | ~intruder_message(X3) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f71])).

fof(f20,axiom,(
  ! [X0] : ! [X1] : ! [X2] : ((intruder_message(X2) & intruder_message(X1) & intruder_message(X0)) => intruder_message(triple(X0,X1,X2)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_composes_triples)).

fof(f44,plain,(
  ! [X0,X1,X2] : ((intruder_message(X2) & intruder_message(X1) & intruder_message(X0)) => intruder_message(triple(X0,X1,X2)))),
  inference(flattening,[],[f20])).

fof(f68,plain,(
  ! [X0,X1,X2] : (intruder_message(triple(X0,X1,X2)) | (~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)))),
  inference(ennf_transformation,[],[f44])).

fof(f69,plain,(
  ! [X0,X1,X2] : (intruder_message(triple(X0,X1,X2)) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0))),
  inference(flattening,[],[f68])).

fof(f105,plain,(
  ( ! [X2,X0,X1] : (intruder_message(triple(X0,X1,X2)) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f69])).

fof(f19,axiom,(
  ! [X0] : ! [X1] : ((intruder_message(X1) & intruder_message(X0)) => intruder_message(pair(X0,X1)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_composes_pairs)).

fof(f43,plain,(
  ! [X0,X1] : ((intruder_message(X1) & intruder_message(X0)) => intruder_message(pair(X0,X1)))),
  inference(flattening,[],[f19])).

fof(f66,plain,(
  ! [X0,X1] : (intruder_message(pair(X0,X1)) | (~intruder_message(X1) | ~intruder_message(X0)))),
  inference(ennf_transformation,[],[f43])).

fof(f67,plain,(
  ! [X0,X1] : (intruder_message(pair(X0,X1)) | ~intruder_message(X1) | ~intruder_message(X0))),
  inference(flattening,[],[f66])).

fof(f104,plain,(
  ( ! [X0,X1] : (intruder_message(pair(X0,X1)) | ~intruder_message(X1) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f67])).

fof(f18,axiom,(
  ! [X0] : ! [X1] : ! [X2] : ! [X3] : (intruder_message(quadruple(X0,X1,X2,X3)) => (intruder_message(X3) & intruder_message(X2) & intruder_message(X1) & intruder_message(X0)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_decomposes_quadruples)).

fof(f42,plain,(
  ! [X0,X1,X2,X3] : (intruder_message(quadruple(X0,X1,X2,X3)) => (intruder_message(X3) & intruder_message(X2) & intruder_message(X1) & intruder_message(X0)))),
  inference(flattening,[],[f18])).

fof(f65,plain,(
  ! [X0,X1,X2,X3] : ((intruder_message(X3) & intruder_message(X2) & intruder_message(X1) & intruder_message(X0)) | ~intruder_message(quadruple(X0,X1,X2,X3)))),
  inference(ennf_transformation,[],[f42])).

fof(f100,plain,(
  ( ! [X2,X0,X3,X1] : (intruder_message(X0) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
  inference(cnf_transformation,[],[f65])).

fof(f101,plain,(
  ( ! [X2,X0,X3,X1] : (intruder_message(X1) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
  inference(cnf_transformation,[],[f65])).

fof(f102,plain,(
  ( ! [X2,X0,X3,X1] : (intruder_message(X2) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
  inference(cnf_transformation,[],[f65])).

fof(f103,plain,(
  ( ! [X2,X0,X3,X1] : (intruder_message(X3) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
  inference(cnf_transformation,[],[f65])).

fof(f17,axiom,(
  ! [X0] : ! [X1] : ! [X2] : (intruder_message(triple(X0,X1,X2)) => (intruder_message(X2) & intruder_message(X1) & intruder_message(X0)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_decomposes_triples)).

fof(f41,plain,(
  ! [X0,X1,X2] : (intruder_message(triple(X0,X1,X2)) => (intruder_message(X2) & intruder_message(X1) & intruder_message(X0)))),
  inference(flattening,[],[f17])).

fof(f64,plain,(
  ! [X0,X1,X2] : ((intruder_message(X2) & intruder_message(X1) & intruder_message(X0)) | ~intruder_message(triple(X0,X1,X2)))),
  inference(ennf_transformation,[],[f41])).

fof(f97,plain,(
  ( ! [X2,X0,X1] : (intruder_message(X0) | ~intruder_message(triple(X0,X1,X2))) )),
  inference(cnf_transformation,[],[f64])).

fof(f98,plain,(
  ( ! [X2,X0,X1] : (intruder_message(X1) | ~intruder_message(triple(X0,X1,X2))) )),
  inference(cnf_transformation,[],[f64])).

fof(f99,plain,(
  ( ! [X2,X0,X1] : (intruder_message(X2) | ~intruder_message(triple(X0,X1,X2))) )),
  inference(cnf_transformation,[],[f64])).

fof(f16,axiom,(
  ! [X0] : ! [X1] : (intruder_message(pair(X0,X1)) => (intruder_message(X1) & intruder_message(X0)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_decomposes_pairs)).

fof(f40,plain,(
  ! [X0,X1] : (intruder_message(pair(X0,X1)) => (intruder_message(X1) & intruder_message(X0)))),
  inference(flattening,[],[f16])).

fof(f63,plain,(
  ! [X0,X1] : ((intruder_message(X1) & intruder_message(X0)) | ~intruder_message(pair(X0,X1)))),
  inference(ennf_transformation,[],[f40])).

fof(f95,plain,(
  ( ! [X0,X1] : (intruder_message(X0) | ~intruder_message(pair(X0,X1))) )),
  inference(cnf_transformation,[],[f63])).

fof(f96,plain,(
  ( ! [X0,X1] : (intruder_message(X1) | ~intruder_message(pair(X0,X1))) )),
  inference(cnf_transformation,[],[f63])).

fof(f15,axiom,(
  ! [X0] : ! [X1] : ! [X2] : (message(sent(X0,X1,X2)) => intruder_message(X2))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',intruder_can_record)).

fof(f39,plain,(
  ! [X0,X1,X2] : (message(sent(X0,X1,X2)) => intruder_message(X2))),
  inference(flattening,[],[f15])).

fof(f62,plain,(
  ! [X0,X1,X2] : (intruder_message(X2) | ~message(sent(X0,X1,X2)))),
  inference(ennf_transformation,[],[f39])).

fof(f94,plain,(
  ( ! [X2,X0,X1] : (intruder_message(X2) | ~message(sent(X0,X1,X2))) )),
  inference(cnf_transformation,[],[f62])).

fof(f14,axiom,(
  ! [X0] : ! [X1] : ! [X2] : ! [X3] : ! [X4] : ! [X5] : ! [X6] : ((a_nonce(X3) & t_holds(key(X6,X2)) & t_holds(key(X5,X0)) & message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5))))) => message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',server_t_generates_key)).

fof(f38,plain,(
  ! [X0,X1,X2,X3,X4,X5,X6] : ((a_nonce(X3) & t_holds(key(X6,X2)) & t_holds(key(X5,X0)) & message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5))))) => message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))))),
  inference(flattening,[],[f14])).

fof(f60,plain,(
  ! [X0,X1,X2,X3,X4,X5,X6] : (message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))) | (~a_nonce(X3) | ~t_holds(key(X6,X2)) | ~t_holds(key(X5,X0)) | ~message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5))))))),
  inference(ennf_transformation,[],[f38])).

fof(f61,plain,(
  ! [X0,X1,X2,X3,X4,X5,X6] : (message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))) | ~a_nonce(X3) | ~t_holds(key(X6,X2)) | ~t_holds(key(X5,X0)) | ~message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5)))))),
  inference(flattening,[],[f60])).

fof(f93,plain,(
  ( ! [X6,X4,X2,X0,X5,X3,X1] : (message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))) | ~a_nonce(X3) | ~t_holds(key(X6,X2)) | ~t_holds(key(X5,X0)) | ~message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5))))) )),
  inference(cnf_transformation,[],[f61])).

fof(f13,axiom,(
  party_of_protocol(t)),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',t_is_party_of_protocol)).

fof(f92,plain,(
  party_of_protocol(t)),
  inference(cnf_transformation,[],[f13])).

fof(f12,axiom,(
  t_holds(key(bt,b))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',t_holds_key_bt_for_b)).

fof(f91,plain,(
  t_holds(key(bt,b))),
  inference(cnf_transformation,[],[f12])).

fof(f11,axiom,(
  t_holds(key(at,a))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',t_holds_key_at_for_a)).

fof(f90,plain,(
  t_holds(key(at,a))),
  inference(cnf_transformation,[],[f11])).

fof(f9,axiom,(
  ! [X0] : ! [X1] : ((fresh_to_b(X1) & message(sent(X0,b,pair(X0,X1)))) => (b_stored(pair(X0,X1)) & message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt))))))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',b_creates_freash_nonces_in_time)).

fof(f35,plain,(
  ! [X0,X1] : ((fresh_to_b(X1) & message(sent(X0,b,pair(X0,X1)))) => (b_stored(pair(X0,X1)) & message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt))))))),
  inference(flattening,[],[f9])).

fof(f53,plain,(
  ! [X0,X1] : ((fresh_to_b(X1) & message(sent(X0,b,pair(X0,X1)))) => message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))))),
  inference(pure_predicate_removal,[],[f35])).

fof(f58,plain,(
  ! [X0,X1] : (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))) | (~fresh_to_b(X1) | ~message(sent(X0,b,pair(X0,X1)))))),
  inference(ennf_transformation,[],[f53])).

fof(f59,plain,(
  ! [X0,X1] : (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))) | ~fresh_to_b(X1) | ~message(sent(X0,b,pair(X0,X1))))),
  inference(flattening,[],[f58])).

fof(f89,plain,(
  ( ! [X0,X1] : (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))) | ~fresh_to_b(X1) | ~message(sent(X0,b,pair(X0,X1)))) )),
  inference(cnf_transformation,[],[f59])).

fof(f8,axiom,(
  fresh_to_b(an_a_nonce)),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',nonce_a_is_fresh_to_b)).

fof(f88,plain,(
  fresh_to_b(an_a_nonce)),
  inference(cnf_transformation,[],[f8])).

fof(f7,axiom,(
  party_of_protocol(b)),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',b_is_party_of_protocol)).

fof(f87,plain,(
  party_of_protocol(b)),
  inference(cnf_transformation,[],[f7])).

fof(f5,axiom,(
  ! [X0] : ! [X1] : ! [X2] : ! [X3] : ! [X4] : ! [X5] : ((a_stored(pair(X4,X5)) & message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0)))) => (a_holds(key(X2,X4)) & message(sent(a,X4,pair(X3,encrypt(X0,X2))))))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',a_forwards_secure)).

fof(f34,plain,(
  ! [X0,X1,X2,X3,X4,X5] : ((a_stored(pair(X4,X5)) & message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0)))) => (a_holds(key(X2,X4)) & message(sent(a,X4,pair(X3,encrypt(X0,X2))))))),
  inference(flattening,[],[f5])).

fof(f54,plain,(
  ! [X0,X1,X2,X3,X4,X5] : ((a_stored(pair(X4,X5)) & message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0)))) => message(sent(a,X4,pair(X3,encrypt(X0,X2)))))),
  inference(pure_predicate_removal,[],[f34])).

fof(f56,plain,(
  ! [X0,X1,X2,X3,X4,X5] : (message(sent(a,X4,pair(X3,encrypt(X0,X2)))) | (~a_stored(pair(X4,X5)) | ~message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0)))))),
  inference(ennf_transformation,[],[f54])).

fof(f57,plain,(
  ! [X0,X1,X2,X3,X4,X5] : (message(sent(a,X4,pair(X3,encrypt(X0,X2)))) | ~a_stored(pair(X4,X5)) | ~message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0))))),
  inference(flattening,[],[f56])).

fof(f86,plain,(
  ( ! [X4,X2,X0,X5,X3,X1] : (message(sent(a,X4,pair(X3,encrypt(X0,X2)))) | ~a_stored(pair(X4,X5)) | ~message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0)))) )),
  inference(cnf_transformation,[],[f57])).

fof(f4,axiom,(
  a_stored(pair(b,an_a_nonce))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',a_stored_message_i)).

fof(f85,plain,(
  a_stored(pair(b,an_a_nonce))),
  inference(cnf_transformation,[],[f4])).

fof(f3,axiom,(
  message(sent(a,b,pair(a,an_a_nonce)))),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',a_sent_message_i_to_b)).

fof(f84,plain,(
  message(sent(a,b,pair(a,an_a_nonce)))),
  inference(cnf_transformation,[],[f3])).

fof(f2,axiom,(
  party_of_protocol(a)),
  file('/tmp/SystemOnTPTP26063/SWV017+1.tptp',a_is_party_of_protocol)).

fof(f83,plain,(
  party_of_protocol(a)),
  inference(cnf_transformation,[],[f2])).

cnf(c_86,plain,
    ( ~ fresh_intruder_nonce(X0) | fresh_to_b(X0) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_85,plain,
    ( ~ fresh_intruder_nonce(X0) | intruder_message(X0) ),
    inference(cnf_transformation,[],[f120]) ).

cnf(c_84,plain,
    ( ~ fresh_intruder_nonce(X0)
    | fresh_intruder_nonce(generate_intruder_nonce(X0)) ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_83,plain,
    ( fresh_intruder_nonce(an_intruder_nonce) ),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_78,plain,
    ( ~ a_nonce(generate_key(X0)) ),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_76,plain,
    ( ~ intruder_holds(key(X0,X1))
    | ~ party_of_protocol(X1)
    | ~ intruder_message(X2)
    | intruder_message(encrypt(X2,X0)) ),
    inference(cnf_transformation,[],[f110]) ).

cnf(c_75,plain,
    ( ~ party_of_protocol(X0)
    | ~ intruder_message(X1)
    | intruder_holds(key(X1,X0)) ),
    inference(cnf_transformation,[],[f109]) ).

cnf(c_74,plain,
    ( ~ party_of_protocol(X0)
    | ~ party_of_protocol(X1)
    | ~ intruder_message(X2)
    | message(sent(X1,X0,X2)) ),
    inference(cnf_transformation,[],[f108]) ).

cnf(c_73,plain,
    ( ~ intruder_message(encrypt(X0,X1))
    | ~ intruder_holds(key(X1,X2))
    | ~ party_of_protocol(X2)
    | intruder_message(X1) ),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_72,plain,
    ( ~ intruder_message(X0)
    | ~ intruder_message(X1)
    | ~ intruder_message(X2)
    | ~ intruder_message(X3)
    | intruder_message(quadruple(X1,X3,X2,X0)) ),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_71,plain,
    ( ~ intruder_message(X0)
    | ~ intruder_message(X1)
    | ~ intruder_message(X2)
    | intruder_message(triple(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_70,plain,
    ( ~ intruder_message(X0)
    | ~ intruder_message(X1)
    | intruder_message(pair(X0,X1)) ),
    inference(cnf_transformation,[],[f104]) ).

cnf(c_69,plain,
    ( ~ intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X0) ),
    inference(cnf_transformation,[],[f100]) ).

cnf(c_68,plain,
    ( ~ intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X1) ),
    inference(cnf_transformation,[],[f101]) ).

cnf(c_67,plain,
    ( ~ intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X2) ),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_66,plain,
    ( ~ intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X3) ),
    inference(cnf_transformation,[],[f103]) ).

cnf(c_65,plain,
    ( ~ intruder_message(triple(X0,X1,X2)) | intruder_message(X0) ),
    inference(cnf_transformation,[],[f97]) ).

cnf(c_64,plain,
    ( ~ intruder_message(triple(X0,X1,X2)) | intruder_message(X1) ),
    inference(cnf_transformation,[],[f98]) ).

cnf(c_63,plain,
    ( ~ intruder_message(triple(X0,X1,X2)) | intruder_message(X2) ),
    inference(cnf_transformation,[],[f99]) ).

cnf(c_62,plain,
    ( ~ intruder_message(pair(X0,X1)) | intruder_message(X0) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_61,plain,
    ( ~ intruder_message(pair(X0,X1)) | intruder_message(X1) ),
    inference(cnf_transformation,[],[f96]) ).

cnf(c_60,plain,
    ( ~ message(sent(X0,X1,X2)) | intruder_message(X2) ),
    inference(cnf_transformation,[],[f94]) ).

cnf(c_59,plain,
    ( ~ message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5))))
    | ~ t_holds(key(X5,X0))
    | ~ t_holds(key(X6,X2))
    | ~ a_nonce(X3)
    | message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))) ),
    inference(cnf_transformation,[],[f93]) ).

cnf(c_58,plain,
    ( party_of_protocol(t) ),
    inference(cnf_transformation,[],[f92]) ).

cnf(c_57,plain,
    ( t_holds(key(bt,b)) ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_56,plain,
    ( t_holds(key(at,a)) ),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_55,plain,
    ( ~ message(sent(X0,b,pair(X0,X1)))
    | ~ fresh_to_b(X1)
    | message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))) ),
    inference(cnf_transformation,[],[f89]) ).

cnf(c_54,plain,
    ( fresh_to_b(an_a_nonce) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_53,plain,
    ( party_of_protocol(b) ),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_52,plain,
    ( ~ message(sent(t,a,triple(encrypt(quadruple(X0,X1,X2,X3),at),X4,X5)))
    | ~ a_stored(pair(X0,X1))
    | message(sent(a,X0,pair(X4,encrypt(X5,X2)))) ),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_51,plain,
    ( a_stored(pair(b,an_a_nonce)) ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_50,plain,
    ( message(sent(a,b,pair(a,an_a_nonce))) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_49,plain,
    ( party_of_protocol(a) ),
    inference(cnf_transformation,[],[f83]) ).

% SZS output end Saturation for SWV017+1.tptp

Sample solution for BOO001-1

% SZS output start CNFRefutation for BOO001-1.tptp

cnf(c_49,negated_conjecture,
    ( inverse(inverse(a)) != a ),
    file('/tmp/SystemOnTPTP27206/BOO001-1.tptp', prove_inverse_is_self_cancelling) ).

cnf(c_54,plain,
    ( multiply(X0,X1,inverse(X1)) = X0 ),
    file('/exp/home/tptp/TPTP/Axioms/BOO001-0.ax', right_inverse) ).

cnf(c_51,plain,
    ( multiply(X0,X1,X1) = X1 ),
    file('/exp/home/tptp/TPTP/Axioms/BOO001-0.ax', ternary_multiply_1) ).

cnf(c_50,plain,
    ( multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)) ),
    file('/exp/home/tptp/TPTP/Axioms/BOO001-0.ax', associativity) ).

cnf(c_115,plain,
    ( multiply(X0,X1,multiply(X1,X2,X3)) = multiply(X1,X2,multiply(X0,X1,X3)) ),
    inference(superposition,[status(thm)],[c_51,c_50]) ).

cnf(c_143,plain,
    ( multiply(X0,X1,multiply(X2,X0,X1)) = multiply(X2,X0,X1) ),
    inference(superposition,[status(thm)],[c_51,c_115]) ).

cnf(c_184,plain,
    ( multiply(X0,inverse(X0),X1) = X1 ),
    inference(superposition,[status(thm)],[c_54,c_143]) ).

cnf(c_205,plain,
    ( inverse(inverse(X0)) = X0 ),
    inference(superposition,[status(thm)],[c_184,c_54]) ).

cnf(c_211,plain,
    ( $false ),
    inference(backward_subsumption_resolution,[status(thm)],[c_49,c_205]) ).

% SZS output end CNFRefutation for BOO001-1.tptp

Lash 1.12

Sample solution for SET014^4

% SZS output start Proof
thf(ty_eigen__2, type, eigen__2 : ($i>$o)).
thf(ty_eigen__1, type, eigen__1 : ($i>$o)).
thf(ty_eigen__0, type, eigen__0 : ($i>$o)).
thf(ty_eigen__3, type, eigen__3 : $i).
thf(sP1,plain,sP1 <=> ((~((eigen__0 @ eigen__3))) => (eigen__1 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP1])])).
thf(sP2,plain,sP2 <=> ((eigen__0 @ eigen__3) => (eigen__2 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP2])])).
thf(sP3,plain,sP3 <=> (eigen__0 @ eigen__3),introduced(definition,[new_symbols(definition,[sP3])])).
thf(sP4,plain,sP4 <=> (eigen__1 @ eigen__3),introduced(definition,[new_symbols(definition,[sP4])])).
thf(sP5,plain,sP5 <=> (![X1:$i]:((eigen__1 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP5])])).
thf(sP6,plain,sP6 <=> (eigen__2 @ eigen__3),introduced(definition,[new_symbols(definition,[sP6])])).
thf(sP7,plain,sP7 <=> (sP4 => sP6),introduced(definition,[new_symbols(definition,[sP7])])).
thf(sP8,plain,sP8 <=> (![X1:$i]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP8])])).
thf(def_in,definition,(in = (^[X1:$i]:(^[X2:$i>$o]:(X2 @ X1))))).
thf(def_is_a,definition,(is_a = (^[X1:$i]:(^[X2:$i>$o]:(X2 @ X1))))).
thf(def_emptyset,definition,(emptyset = (^[X1:$i]:$false))).
thf(def_unord_pair,definition,(unord_pair = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((X3 = X1) | (X3 = X2))))))).
thf(def_singleton,definition,(singleton = (^[X1:$i]:(^[X2:$i]:(X2 = X1))))).
thf(def_union,definition,(union = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
thf(def_excl_union,definition,(excl_union = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(((X1 @ X3) & ((~) @ (X2 @ X3))) | (((~) @ (X1 @ X3)) & (X2 @ X3)))))))).
thf(def_intersection,definition,(intersection = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) & (X2 @ X3))))))).
thf(def_setminus,definition,(setminus = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) & ((~) @ (X2 @ X3)))))))).
thf(def_complement,definition,(complement = (^[X1:$i>$o]:(^[X2:$i]:((~) @ (X1 @ X2)))))).
thf(def_disjoint,definition,(disjoint = (^[X1:$i>$o]:(^[X2:$i>$o]:(((intersection @ X1) @ X2) = emptyset))))).
thf(def_subset,definition,(subset = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ (X1 @ X3)) @ (X2 @ X3))))))).
thf(def_meets,definition,(meets = (^[X1:$i>$o]:(^[X2:$i>$o]:(?[X3:$i]:((X1 @ X3) & (X2 @ X3))))))).
thf(def_misses,definition,(misses = (^[X1:$i>$o]:(^[X2:$i>$o]:((~) @ (?[X3:$i]:((X1 @ X3) & (X2 @ X3)))))))).
thf(thm,conjecture,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:((~(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4)))))))).
thf(h0,negated_conjecture,(~((![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:((~(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4))))))))),inference(assume_negation,[status(cth)],[thm])).
thf(h1,assumption,(~((![X1:$i>$o]:(![X2:$i>$o]:((~(((![X3:$i]:((eigen__0 @ X3) => (X2 @ X3))) => (~((![X3:$i]:((X1 @ X3) => (X2 @ X3)))))))) => (![X3:$i]:(((~((eigen__0 @ X3))) => (X1 @ X3)) => (X2 @ X3)))))))),introduced(assumption,[])).
thf(h2,assumption,(~((![X1:$i>$o]:((~(((![X2:$i]:((eigen__0 @ X2) => (X1 @ X2))) => (~((![X2:$i]:((eigen__1 @ X2) => (X1 @ X2)))))))) => (![X2:$i]:(((~((eigen__0 @ X2))) => (eigen__1 @ X2)) => (X1 @ X2))))))),introduced(assumption,[])).
thf(h3,assumption,(~(((~((sP8 => (~(sP5))))) => (![X1:$i]:(((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (eigen__2 @ X1)))))),introduced(assumption,[])).
thf(h4,assumption,(~((sP8 => (~(sP5))))),introduced(assumption,[])).
thf(h5,assumption,(~((![X1:$i]:(((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (eigen__2 @ X1))))),introduced(assumption,[])).
thf(h6,assumption,sP8,introduced(assumption,[])).
thf(h7,assumption,sP5,introduced(assumption,[])).
thf(h8,assumption,(~((sP1 => sP6))),introduced(assumption,[])).
thf(h9,assumption,sP1,introduced(assumption,[])).
thf(h10,assumption,(~(sP6)),introduced(assumption,[])).
thf(1,plain,((~(sP7) | ~(sP4)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(2,plain,((~(sP2) | ~(sP3)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(3,plain,(~(sP5) | sP7),inference(all_rule,[status(thm)],[])).
thf(4,plain,(~(sP8) | sP2),inference(all_rule,[status(thm)],[])).
thf(5,plain,((~(sP1) | sP3) | sP4),inference(prop_rule,[status(thm)],[])).
thf(6,plain,$false,inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,h6,h7,h9,h10])).
thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,6,h9,h10])).
thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,7,h8])).
thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,8,h6,h7])).
thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,9,h4,h5])).
thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,10,h3])).
thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,11,h2])).
thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,12,h1])).
thf(0,theorem,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:((~(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4))))))),inference(contra,[status(thm),contra(discharge,[h0])],[13,h0])).
% SZS output end Proof

Etableau 0.67

Sample solution for SEU140+2

# SZS status Theorem for /home/hesterj/Projects/Testing/FOL/SEU140+2.p
# SZS output start for /home/hesterj/Projects/Testing/FOL/SEU140+2.p
# Begin clausification derivation

# End clausification derivation
# Begin listing active clauses obtained from FOF to CNF conversion
cnf(i_0_82, negated_conjecture, (subset(esk11_0,esk12_0))).
cnf(i_0_81, negated_conjecture, (disjoint(esk12_0,esk13_0))).
cnf(i_0_40, plain, (empty(empty_set))).
cnf(i_0_48, plain, (empty(esk6_0))).
cnf(i_0_62, lemma, (subset(empty_set,X1))).
cnf(i_0_50, plain, (subset(X1,X1))).
cnf(i_0_76, plain, (set_difference(empty_set,X1)=empty_set)).
cnf(i_0_55, plain, (set_union2(X1,empty_set)=X1)).
cnf(i_0_68, plain, (set_difference(X1,empty_set)=X1)).
cnf(i_0_43, plain, (set_union2(X1,X1)=X1)).
cnf(i_0_85, lemma, (subset(X1,set_union2(X1,X2)))).
cnf(i_0_64, lemma, (subset(set_difference(X1,X2),X1))).
cnf(i_0_59, plain, (set_difference(X1,X1)=empty_set)).
cnf(i_0_67, lemma, (set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2))).
cnf(i_0_73, lemma, (set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2))).
cnf(i_0_3, plain, (set_union2(X1,X2)=set_union2(X2,X1))).
cnf(i_0_4, plain, (set_difference(X1,set_difference(X1,X2))=set_difference(X2,set_difference(X2,X1)))).
cnf(i_0_80, negated_conjecture, (~disjoint(esk11_0,esk13_0))).
cnf(i_0_49, plain, (~empty(esk7_0))).
cnf(i_0_45, plain, (~proper_subset(X1,X1))).
cnf(i_0_9, plain, (~in(X1,empty_set))).
cnf(i_0_84, plain, (~empty(X1)|~in(X2,X1))).
cnf(i_0_83, plain, (X1=empty_set|~empty(X1))).
cnf(i_0_72, lemma, (X1=empty_set|~subset(X1,empty_set))).
cnf(i_0_79, lemma, (~subset(X1,X2)|~proper_subset(X2,X1))).
cnf(i_0_1, plain, (~in(X1,X2)|~in(X2,X1))).
cnf(i_0_2, plain, (~proper_subset(X1,X2)|~proper_subset(X2,X1))).
cnf(i_0_35, plain, (subset(X1,X2)|~proper_subset(X1,X2))).
cnf(i_0_51, plain, (disjoint(X1,X2)|~disjoint(X2,X1))).
cnf(i_0_86, plain, (X1=X2|~empty(X2)|~empty(X1))).
cnf(i_0_69, lemma, (~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1))).
cnf(i_0_42, plain, (empty(X1)|~empty(set_union2(X2,X1)))).
cnf(i_0_41, plain, (empty(X1)|~empty(set_union2(X1,X2)))).
cnf(i_0_77, lemma, (~disjoint(X1,X2)|~in(X3,set_difference(X1,set_difference(X1,X2))))).
cnf(i_0_47, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set)).
cnf(i_0_46, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2))).
cnf(i_0_8, plain, (X1=empty_set|in(esk1_1(X1),X1))).
cnf(i_0_52, lemma, (set_union2(X1,X2)=X2|~subset(X1,X2))).
cnf(i_0_18, plain, (in(X1,X2)|~subset(X3,X2)|~in(X1,X3))).
cnf(i_0_29, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3))).
cnf(i_0_5, plain, (X1=X2|~subset(X2,X1)|~subset(X1,X2))).
cnf(i_0_16, plain, (subset(X1,X2)|~in(esk3_2(X1,X2),X2))).
cnf(i_0_31, plain, (disjoint(X1,X2)|set_difference(X1,set_difference(X1,X2))!=empty_set)).
cnf(i_0_56, lemma, (subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3))).
cnf(i_0_32, plain, (set_difference(X1,set_difference(X1,X2))=empty_set|~disjoint(X1,X2))).
cnf(i_0_33, plain, (X1=X2|proper_subset(X1,X2)|~subset(X1,X2))).
cnf(i_0_58, lemma, (set_difference(X1,set_difference(X1,X2))=X1|~subset(X1,X2))).
cnf(i_0_17, plain, (subset(X1,X2)|in(esk3_2(X1,X2),X1))).
cnf(i_0_70, lemma, (disjoint(X1,X2)|in(esk9_2(X1,X2),X2))).
cnf(i_0_71, lemma, (disjoint(X1,X2)|in(esk9_2(X1,X2),X1))).
cnf(i_0_87, lemma, (subset(set_union2(X1,X2),X3)|~subset(X2,X3)|~subset(X1,X3))).
cnf(i_0_13, plain, (in(X1,set_union2(X2,X3))|~in(X1,X3))).
cnf(i_0_30, plain, (in(X1,X2)|~in(X1,set_difference(X2,X3)))).
cnf(i_0_14, plain, (in(X1,set_union2(X2,X3))|~in(X1,X2))).
cnf(i_0_63, lemma, (subset(set_difference(X1,X2),set_difference(X3,X2))|~subset(X1,X3))).
cnf(i_0_23, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2))))).
cnf(i_0_78, lemma, (disjoint(X1,X2)|in(esk10_2(X1,X2),set_difference(X1,set_difference(X1,X2))))).
cnf(i_0_61, plain, (X1=X2|~in(esk8_2(X1,X2),X2)|~in(esk8_2(X1,X2),X1))).
cnf(i_0_28, plain, (in(X1,set_difference(X2,X3))|in(X1,X3)|~in(X1,X2))).
cnf(i_0_54, lemma, (subset(X1,set_difference(X2,set_difference(X2,X3)))|~subset(X1,X3)|~subset(X1,X2))).
cnf(i_0_22, plain, (in(X1,set_difference(X2,set_difference(X2,X3)))|~in(X1,X3)|~in(X1,X2))).
cnf(i_0_15, plain, (in(X1,X2)|in(X1,X3)|~in(X1,set_union2(X3,X2)))).
cnf(i_0_60, plain, (X1=X2|in(esk8_2(X1,X2),X1)|in(esk8_2(X1,X2),X2))).
cnf(i_0_11, plain, (X1=set_union2(X2,X3)|~in(esk2_3(X2,X3,X1),X1)|~in(esk2_3(X2,X3,X1),X3))).
cnf(i_0_12, plain, (X1=set_union2(X2,X3)|~in(esk2_3(X2,X3,X1),X1)|~in(esk2_3(X2,X3,X1),X2))).
cnf(i_0_25, plain, (X1=set_difference(X2,X3)|in(esk5_3(X2,X3,X1),X1)|~in(esk5_3(X2,X3,X1),X3))).
cnf(i_0_57, lemma, (subset(set_difference(X1,set_difference(X1,X2)),set_difference(X3,set_difference(X3,X2)))|~subset(X1,X3))).
cnf(i_0_26, plain, (X1=set_difference(X2,X3)|in(esk5_3(X2,X3,X1),X2)|in(esk5_3(X2,X3,X1),X1))).
cnf(i_0_19, plain, (X1=set_difference(X2,set_difference(X2,X3))|in(esk4_3(X2,X3,X1),X3)|in(esk4_3(X2,X3,X1),X1))).
cnf(i_0_20, plain, (X1=set_difference(X2,set_difference(X2,X3))|in(esk4_3(X2,X3,X1),X2)|in(esk4_3(X2,X3,X1),X1))).
cnf(i_0_21, plain, (X1=set_difference(X2,set_difference(X2,X3))|~in(esk4_3(X2,X3,X1),X1)|~in(esk4_3(X2,X3,X1),X3)|~in(esk4_3(X2,X3,X1),X2))).
cnf(i_0_27, plain, (X1=set_difference(X2,X3)|in(esk5_3(X2,X3,X1),X3)|~in(esk5_3(X2,X3,X1),X1)|~in(esk5_3(X2,X3,X1),X2))).
cnf(i_0_10, plain, (X1=set_union2(X2,X3)|in(esk2_3(X2,X3,X1),X2)|in(esk2_3(X2,X3,X1),X3)|in(esk2_3(X2,X3,X1),X1))).
# End listing active clauses.  There is an equivalent clause to each of these in the clausification!
# Begin printing tableau
# Found 4 steps
cnf(i_0_80, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(start_rule)).
cnf(i_0_101, plain, (~disjoint(esk11_0,esk13_0)), inference(extension_rule, [i_0_51])).
cnf(i_0_119, plain, (~disjoint(esk13_0,esk11_0)), inference(extension_rule, [i_0_31])).
cnf(i_0_165, plain, (set_difference(esk13_0,set_difference(esk13_0,esk11_0))!=empty_set), inference(etableau_closure_rule, [i_0_165, ...])).
# End printing tableau
# SZS output end

GKC 0.7

Sample solution for SEU140+2

% SZS status Theorem for /opt/TPTP/Problems/SEU/SEU140+2.p

% SZS output start CNFRefutation for /opt/TPTP/Problems/SEU/SEU140+2.p
fof('t3_xboole_0_$sk', plain, ((~disjoint(X2,X1) | (~in(X3,X1) | 
~in(X3,X2))) & ((in($sk5(X4,X5),X5) & in($sk5(X4,X5),X4)) | 
disjoint(X4,X5))),
   inference(negpush_and_skolemize,[],['t3_xboole_0'])).
fof('t3_xboole_0', lemma, (! [A,B] : (~(~disjoint(A,B) & (! [C] : 
~(in(C,A) & in(C,B)))) & ~((? [C] : (in(C,A) & in(C,B))) & disjoint(A,B)))),
   input).
fof('symmetry_r1_xboole_0_$sk', plain, (disjoint(X2,X1) | ~disjoint(X1,X2)),
   inference(negpush_and_skolemize,[],['symmetry_r1_xboole_0'])).
fof('symmetry_r1_xboole_0', axiom, (! [A,B] : (disjoint(A,B) => 
disjoint(B,A))),
   input).
fof('t63_xboole_1_$sk', plain, (~disjoint($sk3,$sk2) & 
(disjoint($sk1,$sk2) & subset($sk3,$sk1))),
   inference(negpush_and_skolemize,[],['t63_xboole_1'])).
fof('t63_xboole_1', conjecture, (! [A,B,C] : ((subset(A,B) & 
disjoint(B,C)) => disjoint(A,C))),
   input).
fof('d3_tarski_$sk', plain, ((~subset(X2,X1) | (in(X3,X1) | ~in(X3,X2))) 
& (subset(X5,X4) | (~in($sk14(X4,X5),X4) & in($sk14(X4,X5),X5)))),
   inference(negpush_and_skolemize,[],['d3_tarski'])).
fof('d3_tarski', axiom, (! [A,B] : (subset(A,B) <=> (! [C] : (in(C,A) => 
in(C,B))))),
   input).
cnf('1', plain, (~disjoint(X,Y) | ~in(Z,Y) | ~in(Z,X)),
   inference(cnf_transformation,[],['t3_xboole_0_$sk'])).
cnf('2', plain, (~disjoint(X,Y) | disjoint(Y,X)),
   inference(cnf_transformation,[],['symmetry_r1_xboole_0_$sk'])).
cnf('3', plain, (disjoint($sk1,$sk2)),
   inference(cnf_transformation,[],['t63_xboole_1_$sk'])).
cnf('4', plain, (disjoint($sk2,$sk1)),
   inference(resolution,[],['2','3'])).
cnf('5', plain, (~in(X,$sk1) | ~in(X,$sk2)),
   inference(resolution,[],['1','4'])).
cnf('6', plain, (~subset(X,Y) | ~in(Z,X) | in(Z,Y)),
   inference(cnf_transformation,[],['d3_tarski_$sk'])).
cnf('7', plain, (subset($sk3,$sk1)),
   inference(cnf_transformation,[],['t63_xboole_1_$sk'])).
cnf('8', plain, (~in(X,$sk3) | in(X,$sk1)),
   inference(resolution,[],['6','7'])).
cnf('9', plain, (in($sk5(X,Y),Y) | disjoint(X,Y)),
   inference(cnf_transformation,[],['t3_xboole_0_$sk'])).
cnf('10', plain, (in($sk5(X,$sk3),$sk1) | disjoint(X,$sk3)),
   inference(resolution,[],['8','9'])).
cnf('11', plain, (~in($sk5(X,$sk3),$sk2) | disjoint(X,$sk3)),
   inference(resolution,[],['5','10'])).
cnf('12', plain, (in($sk5(X,Y),X) | disjoint(X,Y)),
   inference(cnf_transformation,[],['t3_xboole_0_$sk'])).
cnf('13', plain, (disjoint($sk2,$sk3)),
   inference(resolution,[],['11','12'])).
cnf('14', plain, (~disjoint($sk3,$sk2)),
   inference(cnf_transformation,[],['t63_xboole_1_$sk'])).
cnf('15', plain, ($false),
   inference(resolution,[then_simplify],['13','2','14'])).

% SZS output end CNFRefutation for /opt/TPTP/Problems/SEU/SEU140+2.p

Sample solution for BOO001-1

% SZS status Unsatisfiable for /opt/TPTP/Problems/BOO/BOO001-1.p

% SZS output start CNFRefutation for /opt/TPTP/Problems/BOO/BOO001-1.p
cnf('1', plain, (multiply(X,Y,inverse(Y)) = X),
   inference(cnf_transformation,[],['$inc_right_inverse'])).
cnf('2', plain, (multiply(X,Y,Y) = Y),
   inference(cnf_transformation,[],['$inc_ternary_multiply_1'])).
cnf('3', plain, (multiply(multiply(X,Y,Z),U,multiply(X,Y,V)) = 
multiply(X,Y,multiply(Z,U,V))),
   inference(cnf_transformation,[],['$inc_associativity'])).
cnf('4', plain, (multiply(X,Y,multiply(Z,X,U)) = 
multiply(Z,X,multiply(X,Y,U))),
   inference(paramodulation,[],['2','3'])).
cnf('5', plain, (multiply(X,X,Y) = X),
   inference(cnf_transformation,[],['$inc_ternary_multiply_2'])).
cnf('6', plain, (multiply(X,Y,multiply(Z,multiply(X,Y,Z),U)) = 
multiply(X,Y,Z)),
   inference(paramodulation,[],['3','5'])).
cnf('7', plain, (multiply(X3,Y3,multiply(inverse(Y3),X3,Z3)) = 
multiply(X3,Y3,inverse(Y3))),
   inference(paramodulation,[],['1','6'])).
cnf('8', plain, (multiply(X,Y,multiply(inverse(Y),X,Z)) = X),
   inference(simplify,[],['7','1'])).
cnf('9', plain, (multiply(inverse(X),Y,multiply(Y,X,Z)) = Y),
   inference(paramodulation,[],['4','8'])).
cnf('10', plain, (multiply(inverse(X),Y,X) = Y),
   inference(paramodulation,[],['2','9'])).
cnf('11', plain, (inverse(inverse(a)) != a),
inference(cnf_transformation,[],['prove_inverse_is_self_cancelling'])).
cnf('12', plain, ($false),
   inference(paramodulation,[then_simplify],['1','10','11'])).

% SZS output end CNFRefutation for /opt/TPTP/Problems/BOO/BOO001-1.p

Goéland 1.0.0

Sample solution for SYN036+1

% SZS output start Proof for SYN036+1.tptp
[0] (β¬⇔) BETA_NOT_EQUIV : ¬((∃ X (∀ Y ((big_p(X) ⇔ big_p(Y)))) ⇔ (∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))) ⇔ (∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))) ⇔ (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))))
    -> [1] ¬(∃ X (∀ Y ((big_p(X) ⇔ big_p(Y)))) ⇔ (∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))), (∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))) ⇔ (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1))))
    -> [2] (∃ X (∀ Y ((big_p(X) ⇔ big_p(Y)))) ⇔ (∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))), ¬(∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))) ⇔ (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1))))

[1] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ X (∀ Y ((big_p(X) ⇔ big_p(Y)))) ⇔ (∃ U (big_q(U)) ⇔ ∀ W (big_q(W))))
    -> [5] ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y)))), (∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))
    -> [6] ∃ X (∀ Y ((big_p(X) ⇔ big_p(Y)))), ¬(∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))

[5] (β⇔) BETA_EQUIV : (∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))) ⇔ (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1))))
    -> [11] ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))), ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [12] ∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))), (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))

[12] (δ∃) DELTA_EXISTS : ∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [23] ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))

[23] (β⇔) BETA_EQUIV : (∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))
    -> [31] ¬∃ U (big_q(U)), ¬∀ W (big_q(W))
    -> [32] ∃ U (big_q(U)), ∀ W (big_q(W))

[32] (δ∃) DELTA_EXISTS : ∃ U (big_q(U))
    -> [48] big_q(skolem_U2)

[48] (β⇔) BETA_EQUIV : (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [52] ¬∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))
    -> [53] ∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))

[53] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [61] big_p(skolem_U16)

[61] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [184] ¬∀ Y ((big_p(skolem_U16) ⇔ big_p(Y)))

[184] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_U16) ⇔ big_p(Y)))
    -> [189] ¬(big_p(skolem_U16) ⇔ big_p(skolem_Y1(skolem_U16)))

[189] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_U16) ⇔ big_p(skolem_Y1(skolem_U16)))
    -> [192] ¬big_p(skolem_U16), big_p(skolem_Y1(skolem_U16))
    -> [193] big_p(skolem_U16), ¬big_p(skolem_Y1(skolem_U16))

[193] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [241] (big_q(skolem_X14) ⇔ big_q(skolem_U2))

[241] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_U2))
    -> [244] ¬big_q(skolem_X14), ¬big_q(skolem_U2)
    -> [245] big_q(skolem_X14), big_q(skolem_U2)

[245] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [267] big_q(W)

[267] (γ∀) GAMMA_FORALL : ∀ W1 (big_p(W1))
    -> [277] big_p(skolem_Y1(skolem_U16))

[277] (⊙ / {(W1, skolem_Y1(X))}) CLOSURE : big_p(skolem_Y1(skolem_U16))

[52] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [76] ¬big_p(skolem_W17)

[76] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [86] ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))

[86] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))
    -> [88] ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))

[88] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))
    -> [90] ¬big_p(skolem_W17), big_p(skolem_Y1(skolem_W17))
    -> [91] big_p(skolem_W17), ¬big_p(skolem_Y1(skolem_W17))

[90] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [405] (big_q(skolem_X14) ⇔ big_q(skolem_U2))

[405] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_U2))
    -> [406] ¬big_q(skolem_X14), ¬big_q(skolem_U2)
    -> [407] big_q(skolem_X14), big_q(skolem_U2)

[407] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [418] big_q(W)

[418] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [428] ¬big_p(skolem_Y1(skolem_W17))

[428] (⊙ / {(U1, skolem_Y1(X))}) CLOSURE : ¬big_p(skolem_Y1(skolem_W17))

[31] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W (big_q(W))
    -> [63] ¬big_q(skolem_W3)

[63] (β⇔) BETA_EQUIV : (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [69] ¬∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))
    -> [70] ∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))

[69] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [133] ¬big_p(skolem_W17)

[133] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [136] ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))

[136] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))
    -> [137] ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))

[137] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))
    -> [138] ¬big_p(skolem_W17), big_p(skolem_Y1(skolem_W17))
    -> [139] big_p(skolem_W17), ¬big_p(skolem_Y1(skolem_W17))

[138] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [324] (big_q(skolem_X14) ⇔ big_q(skolem_W3))

[324] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_W3))
    -> [325] ¬big_q(skolem_X14), ¬big_q(skolem_W3)
    -> [326] big_q(skolem_X14), big_q(skolem_W3)

[325] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [332] ¬big_q(U)

[332] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [333] ¬big_p(skolem_Y1(skolem_W17))

[333] (⊙ / {(U1, skolem_Y1(X))}) CLOSURE : ¬big_p(skolem_Y1(skolem_W17))

[70] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [99] big_p(skolem_U16)

[99] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [101] ¬∀ Y ((big_p(skolem_U16) ⇔ big_p(Y)))

[101] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_U16) ⇔ big_p(Y)))
    -> [103] ¬(big_p(skolem_U16) ⇔ big_p(skolem_Y1(skolem_U16)))

[103] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_U16) ⇔ big_p(skolem_Y1(skolem_U16)))
    -> [104] ¬big_p(skolem_U16), big_p(skolem_Y1(skolem_U16))
    -> [105] big_p(skolem_U16), ¬big_p(skolem_Y1(skolem_U16))

[105] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [125] (big_q(skolem_X14) ⇔ big_q(skolem_W3))

[125] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_W3))
    -> [127] ¬big_q(skolem_X14), ¬big_q(skolem_W3)
    -> [128] big_q(skolem_X14), big_q(skolem_W3)

[127] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [147] ¬big_q(U)

[147] (γ∀) GAMMA_FORALL : ∀ W1 (big_p(W1))
    -> [148] big_p(skolem_Y1(skolem_U16))

[148] (⊙ / {(W1, skolem_Y1(X))}) CLOSURE : big_p(skolem_Y1(skolem_U16))

[11] (β⇔) BETA_EQUIV : (∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))
    -> [25] ¬∃ U (big_q(U)), ¬∀ W (big_q(W))
    -> [26] ∃ U (big_q(U)), ∀ W (big_q(W))

[26] (δ∃) DELTA_EXISTS : ∃ U (big_q(U))
    -> [35] big_q(skolem_U2)

[35] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [39] ¬∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))
    -> [40] ∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))

[39] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [328] ¬∀ Y ((big_p(X) ⇔ big_p(Y)))

[328] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(X) ⇔ big_p(Y)))
    -> [329] ¬(big_p(X) ⇔ big_p(skolem_Y1(X)))

[329] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(X) ⇔ big_p(skolem_Y1(X)))
    -> [330] ¬big_p(X), big_p(skolem_Y1(X))
    -> [331] big_p(X), ¬big_p(skolem_Y1(X))

[331] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [334] ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))

[334] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))
    -> [336] ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))

[336] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))
    -> [339] ¬big_q(skolem_U2), big_q(skolem_Y15(skolem_U2))
    -> [340] big_q(skolem_U2), ¬big_q(skolem_Y15(skolem_U2))

[340] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [361] big_q(skolem_Y15(skolem_U2))

[361] (⊙ / {(W, skolem_Y15(X1))}) CLOSURE : big_q(skolem_Y15(skolem_U2))

[330] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [349] ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))

[349] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))
    -> [350] ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))

[350] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))
    -> [351] ¬big_q(skolem_U2), big_q(skolem_Y15(skolem_U2))
    -> [352] big_q(skolem_U2), ¬big_q(skolem_Y15(skolem_U2))

[352] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [363] big_q(skolem_Y15(skolem_U2))

[363] (⊙ / {(W, skolem_Y15(X1))}) CLOSURE : big_q(skolem_Y15(skolem_U2))

[40] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [49] big_p(skolem_U16)

[49] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [195] ¬big_p(skolem_W17)

[195] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [231] ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))

[231] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))
    -> [232] ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))

[232] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))
    -> [233] ¬big_p(skolem_W17), big_p(skolem_Y1(skolem_W17))
    -> [234] big_p(skolem_W17), ¬big_p(skolem_Y1(skolem_W17))

[234] (⊙ / {(X, skolem_W17)}) CLOSURE : big_p(skolem_W17)

[233] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [282] ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))

[282] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))
    -> [283] ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))

[283] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))
    -> [286] ¬big_q(skolem_U2), big_q(skolem_Y15(skolem_U2))
    -> [287] big_q(skolem_U2), ¬big_q(skolem_Y15(skolem_U2))

[287] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [432] big_q(skolem_Y15(skolem_U2))

[432] (⊙ / {(W, skolem_Y15(X1))}) CLOSURE : big_q(skolem_Y15(skolem_U2))

[25] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W (big_q(W))
    -> [72] ¬big_q(skolem_W3)

[72] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [77] ¬∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))
    -> [78] ∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))

[77] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [198] ¬∀ Y ((big_p(X) ⇔ big_p(Y)))

[198] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(X) ⇔ big_p(Y)))
    -> [199] ¬(big_p(X) ⇔ big_p(skolem_Y1(X)))

[199] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(X) ⇔ big_p(skolem_Y1(X)))
    -> [200] ¬big_p(X), big_p(skolem_Y1(X))
    -> [201] big_p(X), ¬big_p(skolem_Y1(X))

[201] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [217] ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))

[217] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))
    -> [218] ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))

[218] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))
    -> [221] ¬big_q(skolem_W3), big_q(skolem_Y15(skolem_W3))
    -> [222] big_q(skolem_W3), ¬big_q(skolem_Y15(skolem_W3))

[221] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [281] ¬big_q(skolem_Y15(skolem_W3))

[281] (⊙ / {(U, skolem_Y15(X1))}) CLOSURE : ¬big_q(skolem_Y15(skolem_W3))

[200] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [235] ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))

[235] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))
    -> [236] ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))

[236] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))
    -> [237] ¬big_q(skolem_W3), big_q(skolem_Y15(skolem_W3))
    -> [238] big_q(skolem_W3), ¬big_q(skolem_Y15(skolem_W3))

[237] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [284] ¬big_q(skolem_Y15(skolem_W3))

[284] (⊙ / {(U, skolem_Y15(X1))}) CLOSURE : ¬big_q(skolem_Y15(skolem_W3))

[78] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [98] big_p(skolem_U16)

[98] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [100] ¬big_p(skolem_W17)

[100] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [110] ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))

[110] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))
    -> [113] ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))

[113] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))
    -> [114] ¬big_p(skolem_W17), big_p(skolem_Y1(skolem_W17))
    -> [115] big_p(skolem_W17), ¬big_p(skolem_Y1(skolem_W17))

[115] (⊙ / {(X, skolem_W17)}) CLOSURE : big_p(skolem_W17)

[114] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [341] ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))

[341] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))
    -> [342] ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))

[342] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))
    -> [346] ¬big_q(skolem_W3), big_q(skolem_Y15(skolem_W3))
    -> [347] big_q(skolem_W3), ¬big_q(skolem_Y15(skolem_W3))

[346] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [376] ¬big_q(skolem_Y15(skolem_W3))

[376] (⊙ / {(U, skolem_Y15(X1))}) CLOSURE : ¬big_q(skolem_Y15(skolem_W3))

[6] (δ∃) DELTA_EXISTS : ∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [10] ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))

[10] (β⇔) BETA_EQUIV : (∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))) ⇔ (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1))))
    -> [15] ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))), ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [16] ∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))), (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))

[16] (δ∃) DELTA_EXISTS : ∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [24] ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))

[24] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))
    -> [33] ¬∃ U (big_q(U)), ∀ W (big_q(W))
    -> [34] ∃ U (big_q(U)), ¬∀ W (big_q(W))

[33] (β⇔) BETA_EQUIV : (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [268] ¬∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))
    -> [269] ∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))

[268] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [300] ¬big_p(skolem_W17)

[300] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [302] (big_p(skolem_X0) ⇔ big_p(skolem_W17))

[302] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_W17))
    -> [305] ¬big_p(skolem_X0), ¬big_p(skolem_W17)
    -> [306] big_p(skolem_X0), big_p(skolem_W17)

[305] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [313] (big_q(skolem_X14) ⇔ big_q(Y1))

[313] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(Y1))
    -> [314] ¬big_q(skolem_X14), ¬big_q(Y1)
    -> [315] big_q(skolem_X14), big_q(Y1)

[315] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [321] ¬big_q(U)

[321] (⊙ / {(Y1, U)}) CLOSURE : ¬big_q(U)

[314] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [322] ¬big_q(U)

[322] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [323] big_q(W)

[323] (⊙ / {(Y1, W)}) CLOSURE : big_q(W)

[269] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [273] big_p(skolem_U16)

[273] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [274] (big_p(skolem_X0) ⇔ big_p(skolem_U16))

[274] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_U16))
    -> [275] ¬big_p(skolem_X0), ¬big_p(skolem_U16)
    -> [276] big_p(skolem_X0), big_p(skolem_U16)

[276] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [278] (big_q(skolem_X14) ⇔ big_q(Y1))

[278] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(Y1))
    -> [279] ¬big_q(skolem_X14), ¬big_q(Y1)
    -> [280] big_q(skolem_X14), big_q(Y1)

[280] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [427] ¬big_q(U)

[427] (⊙ / {(Y1, U)}) CLOSURE : ¬big_q(U)

[279] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [429] ¬big_q(U)

[429] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [430] big_q(skolem_X14)

[430] (⊙ / {(W, skolem_X14)}) CLOSURE : big_q(skolem_X14)

[34] (δ∃) DELTA_EXISTS : ∃ U (big_q(U))
    -> [44] big_q(skolem_U2)

[44] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W (big_q(W))
    -> [51] ¬big_q(skolem_W3)

[51] (β⇔) BETA_EQUIV : (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [57] ¬∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))
    -> [58] ∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))

[58] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [62] big_p(skolem_U16)

[62] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [116] (big_p(skolem_X0) ⇔ big_p(skolem_U16))

[116] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_U16))
    -> [117] ¬big_p(skolem_X0), ¬big_p(skolem_U16)
    -> [118] big_p(skolem_X0), big_p(skolem_U16)

[118] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [156] (big_q(skolem_X14) ⇔ big_q(skolem_W3))

[156] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_W3))
    -> [158] ¬big_q(skolem_X14), ¬big_q(skolem_W3)
    -> [159] big_q(skolem_X14), big_q(skolem_W3)

[159] (⊙ / {(Y1, skolem_W3)}) CLOSURE : big_q(skolem_W3)

[158] (γ∀) GAMMA_FORALL : ∀ W1 (big_p(W1))
    -> [379] big_p(W1)

[379] (Reintroduction) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [397] ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))

[397] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [398] (big_p(skolem_X0) ⇔ big_p(Y))

[398] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(Y))
    -> [399] ¬big_p(skolem_X0), ¬big_p(Y)
    -> [400] big_p(skolem_X0), big_p(Y)

[399] (⊙ / {}) CLOSURE : ¬big_p(skolem_X0)

[400] (Reintroduction)  : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [412] ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))

[412] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [413] (big_q(skolem_X14) ⇔ big_q(skolem_U2))

[413] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_U2))
    -> [414] ¬big_q(skolem_X14), ¬big_q(skolem_U2)
    -> [415] big_q(skolem_X14), big_q(skolem_U2)

[415] (⊙ / {}) CLOSURE : big_q(skolem_X14)

[57] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [102] ¬big_p(skolem_W17)

[102] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [402] (big_p(skolem_X0) ⇔ big_p(skolem_W17))

[402] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_W17))
    -> [403] ¬big_p(skolem_X0), ¬big_p(skolem_W17)
    -> [404] big_p(skolem_X0), big_p(skolem_W17)

[403] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [419] (big_q(skolem_X14) ⇔ big_q(skolem_U2))

[419] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_U2))
    -> [420] ¬big_q(skolem_X14), ¬big_q(skolem_U2)
    -> [421] big_q(skolem_X14), big_q(skolem_U2)

[420] (⊙ / {(Y1, skolem_U2)}) CLOSURE : ¬big_q(skolem_U2)

[421] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [433] ¬big_p(U1)

[433] (Reintroduction) GAMMA_NOT_EXISTS : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [434] ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))

[434] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [435] (big_p(skolem_X0) ⇔ big_p(Y))

[435] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(Y))
    -> [436] ¬big_p(skolem_X0), ¬big_p(Y)
    -> [437] big_p(skolem_X0), big_p(Y)

[437] (⊙ / {}) CLOSURE : big_p(skolem_X0)

[436] (Reintroduction)  : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [438] ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))

[438] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [439] (big_q(skolem_X14) ⇔ big_q(skolem_W3))

[439] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_W3))
    -> [440] ¬big_q(skolem_X14), ¬big_q(skolem_W3)
    -> [441] big_q(skolem_X14), big_q(skolem_W3)

[440] (⊙ / {}) CLOSURE : ¬big_q(skolem_X14)

[15] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))
    -> [82] ¬∃ U (big_q(U)), ∀ W (big_q(W))
    -> [83] ∃ U (big_q(U)), ¬∀ W (big_q(W))

[82] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [111] ¬∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))
    -> [112] ∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))

[112] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [120] big_p(skolem_U16)

[120] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [122] ¬big_p(skolem_W17)

[122] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [126] (big_p(skolem_X0) ⇔ big_p(skolem_W17))

[126] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_W17))
    -> [129] ¬big_p(skolem_X0), ¬big_p(skolem_W17)
    -> [130] big_p(skolem_X0), big_p(skolem_W17)

[130] (⊙ / {(Y, skolem_W17)}) CLOSURE : big_p(skolem_W17)

[129] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [393] ¬∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))

[393] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))
    -> [394] ¬(big_q(X1) ⇔ big_q(skolem_Y15(X1)))

[394] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(X1) ⇔ big_q(skolem_Y15(X1)))
    -> [395] ¬big_q(X1), big_q(skolem_Y15(X1))
    -> [396] big_q(X1), ¬big_q(skolem_Y15(X1))

[395] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [417] ¬big_q(skolem_Y15(X1))

[417] (⊙ / {(U, skolem_Y15(X1))}) CLOSURE : ¬big_q(skolem_Y15(X1))

[396] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [416] ¬big_q(U)

[416] (⊙ / {(X1, U)}) CLOSURE : ¬big_q(U)

[111] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [163] (big_p(skolem_X0) ⇔ big_p(Y))

[163] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(Y))
    -> [164] ¬big_p(skolem_X0), ¬big_p(Y)
    -> [165] big_p(skolem_X0), big_p(Y)

[164] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [368] ¬∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))

[368] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))
    -> [369] ¬(big_q(X1) ⇔ big_q(skolem_Y15(X1)))

[369] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(X1) ⇔ big_q(skolem_Y15(X1)))
    -> [370] ¬big_q(X1), big_q(skolem_Y15(X1))
    -> [371] big_q(X1), ¬big_q(skolem_Y15(X1))

[371] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [375] ¬big_q(U)

[375] (⊙ / {(X1, U)}) CLOSURE : ¬big_q(U)

[370] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [377] ¬big_q(skolem_Y15(X1))

[377] (⊙ / {(U, skolem_Y15(X1))}) CLOSURE : ¬big_q(skolem_Y15(X1))

[165] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [170] ¬∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))

[170] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))
    -> [171] ¬(big_q(X1) ⇔ big_q(skolem_Y15(X1)))

[171] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(X1) ⇔ big_q(skolem_Y15(X1)))
    -> [172] ¬big_q(X1), big_q(skolem_Y15(X1))
    -> [173] big_q(X1), ¬big_q(skolem_Y15(X1))

[173] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [408] ¬big_q(U)

[408] (⊙ / {(X1, U)}) CLOSURE : ¬big_q(U)

[172] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [450] ¬big_q(skolem_Y15(X1))

[450] (⊙ / {(U, skolem_Y15(X1))}) CLOSURE : ¬big_q(skolem_Y15(X1))

[83] (δ∃) DELTA_EXISTS : ∃ U (big_q(U))
    -> [94] big_q(skolem_U2)

[94] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W (big_q(W))
    -> [95] ¬big_q(skolem_W3)

[95] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [96] ¬∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))
    -> [97] ∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))

[96] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [153] (big_p(skolem_X0) ⇔ big_p(Y))

[153] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(Y))
    -> [154] ¬big_p(skolem_X0), ¬big_p(Y)
    -> [155] big_p(skolem_X0), big_p(Y)

[155] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [389] ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))

[389] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))
    -> [390] ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))

[390] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))
    -> [391] ¬big_q(skolem_W3), big_q(skolem_Y15(skolem_W3))
    -> [392] big_q(skolem_W3), ¬big_q(skolem_Y15(skolem_W3))

[392] (⊙ / {(X1, skolem_W3)}) CLOSURE : big_q(skolem_W3)

[391] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [426] ¬big_p(U1)

[426] (⊙ / {(Y, U1)}) CLOSURE : ¬big_p(U1)

[154] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [177] ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))

[177] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))
    -> [180] ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))

[180] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))
    -> [181] ¬big_q(skolem_W3), big_q(skolem_Y15(skolem_W3))
    -> [182] big_q(skolem_W3), ¬big_q(skolem_Y15(skolem_W3))

[182] (⊙ / {(X1, skolem_W3)}) CLOSURE : big_q(skolem_W3)

[181] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [455] ¬big_p(U1)

[455] (γ∀) GAMMA_FORALL : ∀ W1 (big_p(W1))
    -> [456] big_p(W1)

[456] (⊙ / {(Y, W1)}) CLOSURE : big_p(W1)

[97] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [320] big_p(skolem_U16)

[320] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [327] ¬big_p(skolem_W17)

[327] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [335] (big_p(skolem_X0) ⇔ big_p(skolem_W17))

[335] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_W17))
    -> [337] ¬big_p(skolem_X0), ¬big_p(skolem_W17)
    -> [338] big_p(skolem_X0), big_p(skolem_W17)

[338] (⊙ / {(Y, skolem_W17)}) CLOSURE : big_p(skolem_W17)

[337] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [380] ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))

[380] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))
    -> [381] ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))

[381] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))
    -> [386] ¬big_q(skolem_U2), big_q(skolem_Y15(skolem_U2))
    -> [387] big_q(skolem_U2), ¬big_q(skolem_Y15(skolem_U2))

[386] (⊙ / {(X1, skolem_U2)}) CLOSURE : ¬big_q(skolem_U2)

[387] (Reintroduction)  : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [457] ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))

[457] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [458] (big_p(skolem_X0) ⇔ big_p(skolem_U16))

[458] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_U16))
    -> [459] ¬big_p(skolem_X0), ¬big_p(skolem_U16)
    -> [460] big_p(skolem_X0), big_p(skolem_U16)

[460] (⊙ / {}) CLOSURE : big_p(skolem_X0)

[2] (β⇔) BETA_EQUIV : (∃ X (∀ Y ((big_p(X) ⇔ big_p(Y)))) ⇔ (∃ U (big_q(U)) ⇔ ∀ W (big_q(W))))
    -> [3] ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y)))), ¬(∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))
    -> [4] ∃ X (∀ Y ((big_p(X) ⇔ big_p(Y)))), (∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))

[4] (δ∃) DELTA_EXISTS : ∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [9] ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))

[9] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))) ⇔ (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1))))
    -> [13] ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))), (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [14] ∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))), ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))

[14] (δ∃) DELTA_EXISTS : ∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [22] ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))

[22] (β⇔) BETA_EQUIV : (∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))
    -> [29] ¬∃ U (big_q(U)), ¬∀ W (big_q(W))
    -> [30] ∃ U (big_q(U)), ∀ W (big_q(W))

[29] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W (big_q(W))
    -> [183] ¬big_q(skolem_W3)

[183] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [186] ¬∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))
    -> [187] ∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))

[186] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [225] (big_p(skolem_X0) ⇔ big_p(Y))

[225] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(Y))
    -> [226] ¬big_p(skolem_X0), ¬big_p(Y)
    -> [227] big_p(skolem_X0), big_p(Y)

[227] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [228] (big_q(skolem_X14) ⇔ big_q(skolem_W3))

[228] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_W3))
    -> [229] ¬big_q(skolem_X14), ¬big_q(skolem_W3)
    -> [230] big_q(skolem_X14), big_q(skolem_W3)

[229] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [261] ¬big_q(U)

[261] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [265] ¬big_p(U1)

[265] (⊙ / {(Y, U1)}) CLOSURE : ¬big_p(U1)

[226] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [246] (big_q(skolem_X14) ⇔ big_q(skolem_W3))

[246] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_W3))
    -> [248] ¬big_q(skolem_X14), ¬big_q(skolem_W3)
    -> [249] big_q(skolem_X14), big_q(skolem_W3)

[248] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [270] ¬big_q(U)

[270] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [271] ¬big_p(U1)

[271] (γ∀) GAMMA_FORALL : ∀ W1 (big_p(W1))
    -> [272] big_p(W1)

[272] (⊙ / {(Y, W1)}) CLOSURE : big_p(W1)

[187] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [203] big_p(skolem_U16)

[203] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [206] ¬big_p(skolem_W17)

[206] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [212] (big_p(skolem_X0) ⇔ big_p(skolem_U16))

[212] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_U16))
    -> [213] ¬big_p(skolem_X0), ¬big_p(skolem_U16)
    -> [214] big_p(skolem_X0), big_p(skolem_U16)

[213] (⊙ / {(Y, skolem_U16)}) CLOSURE : ¬big_p(skolem_U16)

[214] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [301] (big_q(skolem_X14) ⇔ big_q(skolem_W3))

[301] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_W3))
    -> [303] ¬big_q(skolem_X14), ¬big_q(skolem_W3)
    -> [304] big_q(skolem_X14), big_q(skolem_W3)

[303] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [308] ¬big_q(U)

[308] (Reintroduction) GAMMA_NOT_EXISTS : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [309] ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))

[309] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [310] (big_p(skolem_X0) ⇔ big_p(skolem_W17))

[310] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_W17))
    -> [311] ¬big_p(skolem_X0), ¬big_p(skolem_W17)
    -> [312] big_p(skolem_X0), big_p(skolem_W17)

[311] (⊙ / {}) CLOSURE : ¬big_p(skolem_X0)

[30] (δ∃) DELTA_EXISTS : ∃ U (big_q(U))
    -> [41] big_q(skolem_U2)

[41] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [46] ¬∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))
    -> [47] ∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))

[47] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [59] big_p(skolem_U16)

[59] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [266] ¬big_p(skolem_W17)

[266] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [316] (big_p(skolem_X0) ⇔ big_p(skolem_W17))

[316] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_W17))
    -> [317] ¬big_p(skolem_X0), ¬big_p(skolem_W17)
    -> [318] big_p(skolem_X0), big_p(skolem_W17)

[318] (⊙ / {(Y, skolem_W17)}) CLOSURE : big_p(skolem_W17)

[317] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [343] (big_q(skolem_X14) ⇔ big_q(skolem_U2))

[343] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_U2))
    -> [344] ¬big_q(skolem_X14), ¬big_q(skolem_U2)
    -> [345] big_q(skolem_X14), big_q(skolem_U2)

[345] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [356] big_q(W)

[356] (Reintroduction) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [364] ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))

[364] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [365] (big_p(skolem_X0) ⇔ big_p(skolem_U16))

[365] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_U16))
    -> [366] ¬big_p(skolem_X0), ¬big_p(skolem_U16)
    -> [367] big_p(skolem_X0), big_p(skolem_U16)

[367] (⊙ / {}) CLOSURE : big_p(skolem_X0)

[46] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [167] (big_p(skolem_X0) ⇔ big_p(Y))

[167] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(Y))
    -> [168] ¬big_p(skolem_X0), ¬big_p(Y)
    -> [169] big_p(skolem_X0), big_p(Y)

[168] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [353] (big_q(skolem_X14) ⇔ big_q(skolem_U2))

[353] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_U2))
    -> [354] ¬big_q(skolem_X14), ¬big_q(skolem_U2)
    -> [355] big_q(skolem_X14), big_q(skolem_U2)

[355] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [357] big_q(W)

[357] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [358] ¬big_p(U1)

[358] (γ∀) GAMMA_FORALL : ∀ W1 (big_p(W1))
    -> [359] big_p(W1)

[359] (⊙ / {(Y, W1)}) CLOSURE : big_p(W1)

[169] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [372] (big_q(skolem_X14) ⇔ big_q(skolem_U2))

[372] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_U2))
    -> [373] ¬big_q(skolem_X14), ¬big_q(skolem_U2)
    -> [374] big_q(skolem_X14), big_q(skolem_U2)

[374] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [378] big_q(W)

[378] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [443] ¬big_p(U1)

[443] (⊙ / {(Y, U1)}) CLOSURE : ¬big_p(U1)

[13] (β⇔) BETA_EQUIV : (∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))
    -> [64] ¬∃ U (big_q(U)), ¬∀ W (big_q(W))
    -> [65] ∃ U (big_q(U)), ∀ W (big_q(W))

[64] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W (big_q(W))
    -> [107] ¬big_q(skolem_W3)

[107] (β⇔) BETA_EQUIV : (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [108] ¬∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))
    -> [109] ∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))

[109] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [119] big_p(skolem_U16)

[119] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [121] (big_p(skolem_X0) ⇔ big_p(skolem_U16))

[121] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_U16))
    -> [123] ¬big_p(skolem_X0), ¬big_p(skolem_U16)
    -> [124] big_p(skolem_X0), big_p(skolem_U16)

[124] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [140] ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))

[140] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))
    -> [141] ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))

[141] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))
    -> [142] ¬big_q(skolem_W3), big_q(skolem_Y15(skolem_W3))
    -> [143] big_q(skolem_W3), ¬big_q(skolem_Y15(skolem_W3))

[142] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [174] ¬big_q(skolem_Y15(skolem_W3))

[174] (⊙ / {(U, skolem_Y15(X1))}) CLOSURE : ¬big_q(skolem_Y15(skolem_W3))

[108] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [131] ¬big_p(skolem_W17)

[131] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [132] (big_p(skolem_X0) ⇔ big_p(skolem_W17))

[132] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_W17))
    -> [134] ¬big_p(skolem_X0), ¬big_p(skolem_W17)
    -> [135] big_p(skolem_X0), big_p(skolem_W17)

[134] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [149] ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))

[149] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))
    -> [150] ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))

[150] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))
    -> [151] ¬big_q(skolem_W3), big_q(skolem_Y15(skolem_W3))
    -> [152] big_q(skolem_W3), ¬big_q(skolem_Y15(skolem_W3))

[151] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [166] ¬big_q(skolem_Y15(skolem_W3))

[166] (⊙ / {(U, skolem_Y15(X1))}) CLOSURE : ¬big_q(skolem_Y15(skolem_W3))

[65] (δ∃) DELTA_EXISTS : ∃ U (big_q(U))
    -> [74] big_q(skolem_U2)

[74] (β⇔) BETA_EQUIV : (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [84] ¬∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))
    -> [85] ∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))

[85] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [106] big_p(skolem_U16)

[106] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [144] (big_p(skolem_X0) ⇔ big_p(skolem_U16))

[144] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_U16))
    -> [145] ¬big_p(skolem_X0), ¬big_p(skolem_U16)
    -> [146] big_p(skolem_X0), big_p(skolem_U16)

[146] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [157] ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))

[157] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))
    -> [160] ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))

[160] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))
    -> [161] ¬big_q(skolem_U2), big_q(skolem_Y15(skolem_U2))
    -> [162] big_q(skolem_U2), ¬big_q(skolem_Y15(skolem_U2))

[162] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [388] big_q(skolem_Y15(skolem_U2))

[388] (⊙ / {(W, skolem_Y15(X1))}) CLOSURE : big_q(skolem_Y15(skolem_U2))

[84] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [175] ¬big_p(skolem_W17)

[175] (γ∀) GAMMA_FORALL : ∀ Y ((big_p(skolem_X0) ⇔ big_p(Y)))
    -> [176] (big_p(skolem_X0) ⇔ big_p(skolem_W17))

[176] (β⇔) BETA_EQUIV : (big_p(skolem_X0) ⇔ big_p(skolem_W17))
    -> [178] ¬big_p(skolem_X0), ¬big_p(skolem_W17)
    -> [179] big_p(skolem_X0), big_p(skolem_W17)

[178] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [382] ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))

[382] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_U2) ⇔ big_q(Y1)))
    -> [383] ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))

[383] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_U2) ⇔ big_q(skolem_Y15(skolem_U2)))
    -> [384] ¬big_q(skolem_U2), big_q(skolem_Y15(skolem_U2))
    -> [385] big_q(skolem_U2), ¬big_q(skolem_Y15(skolem_U2))

[385] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [453] big_q(skolem_Y15(skolem_U2))

[453] (⊙ / {(W, skolem_Y15(X1))}) CLOSURE : big_q(skolem_Y15(skolem_U2))

[3] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))) ⇔ (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1))))
    -> [7] ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))), (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [8] ∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))), ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))

[7] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))
    -> [20] ¬∃ U (big_q(U)), ∀ W (big_q(W))
    -> [21] ∃ U (big_q(U)), ¬∀ W (big_q(W))

[21] (δ∃) DELTA_EXISTS : ∃ U (big_q(U))
    -> [28] big_q(skolem_U2)

[28] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W (big_q(W))
    -> [194] ¬big_q(skolem_W3)

[194] (β⇔) BETA_EQUIV : (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [196] ¬∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))
    -> [197] ∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))

[196] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [216] ¬big_p(skolem_W17)

[216] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [219] ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))

[219] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))
    -> [220] ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))

[220] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))
    -> [223] ¬big_p(skolem_W17), big_p(skolem_Y1(skolem_W17))
    -> [224] big_p(skolem_W17), ¬big_p(skolem_Y1(skolem_W17))

[223] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [285] ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))

[285] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))
    -> [288] ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))

[288] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))
    -> [290] ¬big_q(skolem_W3), big_q(skolem_Y15(skolem_W3))
    -> [291] big_q(skolem_W3), ¬big_q(skolem_Y15(skolem_W3))

[291] (⊙ / {(X1, skolem_W3)}) CLOSURE : big_q(skolem_W3)

[290] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [360] ¬big_p(skolem_Y1(skolem_W17))

[360] (⊙ / {(U1, skolem_Y1(X))}) CLOSURE : ¬big_p(skolem_Y1(skolem_W17))

[197] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [215] big_p(skolem_U16)

[215] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [253] ¬∀ Y ((big_p(skolem_U16) ⇔ big_p(Y)))

[253] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_U16) ⇔ big_p(Y)))
    -> [255] ¬(big_p(skolem_U16) ⇔ big_p(skolem_Y1(skolem_U16)))

[255] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_U16) ⇔ big_p(skolem_Y1(skolem_U16)))
    -> [256] ¬big_p(skolem_U16), big_p(skolem_Y1(skolem_U16))
    -> [257] big_p(skolem_U16), ¬big_p(skolem_Y1(skolem_U16))

[257] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [296] ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))

[296] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(skolem_W3) ⇔ big_q(Y1)))
    -> [297] ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))

[297] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(skolem_W3) ⇔ big_q(skolem_Y15(skolem_W3)))
    -> [298] ¬big_q(skolem_W3), big_q(skolem_Y15(skolem_W3))
    -> [299] big_q(skolem_W3), ¬big_q(skolem_Y15(skolem_W3))

[299] (⊙ / {(X1, skolem_W3)}) CLOSURE : big_q(skolem_W3)

[298] (γ∀) GAMMA_FORALL : ∀ W1 (big_p(W1))
    -> [362] big_p(skolem_Y1(skolem_U16))

[362] (⊙ / {(W1, skolem_Y1(X))}) CLOSURE : big_p(skolem_Y1(skolem_U16))

[20] (β⇔) BETA_EQUIV : (∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [36] ¬∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))
    -> [37] ∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))

[36] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [68] ¬big_p(skolem_W17)

[68] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [71] ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))

[71] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))
    -> [75] ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))

[75] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))
    -> [79] ¬big_p(skolem_W17), big_p(skolem_Y1(skolem_W17))
    -> [80] big_p(skolem_W17), ¬big_p(skolem_Y1(skolem_W17))

[79] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [202] ¬∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))

[202] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))
    -> [204] ¬(big_q(X1) ⇔ big_q(skolem_Y15(X1)))

[204] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(X1) ⇔ big_q(skolem_Y15(X1)))
    -> [207] ¬big_q(X1), big_q(skolem_Y15(X1))
    -> [208] big_q(X1), ¬big_q(skolem_Y15(X1))

[208] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [252] ¬big_q(U)

[252] (⊙ / {(X1, U)}) CLOSURE : ¬big_q(U)

[207] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [260] ¬big_q(skolem_Y15(X1))

[260] (⊙ / {(U, skolem_Y15(X1))}) CLOSURE : ¬big_q(skolem_Y15(X1))

[37] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [45] big_p(skolem_U16)

[45] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [50] ¬∀ Y ((big_p(skolem_U16) ⇔ big_p(Y)))

[50] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_U16) ⇔ big_p(Y)))
    -> [54] ¬(big_p(skolem_U16) ⇔ big_p(skolem_Y1(skolem_U16)))

[54] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_U16) ⇔ big_p(skolem_Y1(skolem_U16)))
    -> [55] ¬big_p(skolem_U16), big_p(skolem_Y1(skolem_U16))
    -> [56] big_p(skolem_U16), ¬big_p(skolem_Y1(skolem_U16))

[56] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [205] ¬∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))

[205] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y1 ((big_q(X1) ⇔ big_q(Y1)))
    -> [209] ¬(big_q(X1) ⇔ big_q(skolem_Y15(X1)))

[209] (β¬⇔) BETA_NOT_EQUIV : ¬(big_q(X1) ⇔ big_q(skolem_Y15(X1)))
    -> [210] ¬big_q(X1), big_q(skolem_Y15(X1))
    -> [211] big_q(X1), ¬big_q(skolem_Y15(X1))

[211] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [319] ¬big_q(U)

[319] (⊙ / {(X1, U)}) CLOSURE : ¬big_q(U)

[210] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [401] ¬big_q(skolem_Y15(X1))

[401] (⊙ / {(U, skolem_Y15(X1))}) CLOSURE : ¬big_q(skolem_Y15(X1))

[8] (δ∃) DELTA_EXISTS : ∃ X1 (∀ Y1 ((big_q(X1) ⇔ big_q(Y1))))
    -> [17] ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))

[17] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U (big_q(U)) ⇔ ∀ W (big_q(W)))
    -> [18] ¬∃ U (big_q(U)), ∀ W (big_q(W))
    -> [19] ∃ U (big_q(U)), ¬∀ W (big_q(W))

[18] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [66] ¬∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))
    -> [67] ∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))

[66] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [239] ¬∀ Y ((big_p(X) ⇔ big_p(Y)))

[239] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(X) ⇔ big_p(Y)))
    -> [240] ¬(big_p(X) ⇔ big_p(skolem_Y1(X)))

[240] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(X) ⇔ big_p(skolem_Y1(X)))
    -> [242] ¬big_p(X), big_p(skolem_Y1(X))
    -> [243] big_p(X), ¬big_p(skolem_Y1(X))

[243] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [254] (big_q(skolem_X14) ⇔ big_q(Y1))

[254] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(Y1))
    -> [258] ¬big_q(skolem_X14), ¬big_q(Y1)
    -> [259] big_q(skolem_X14), big_q(Y1)

[258] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [294] ¬big_q(U)

[294] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [295] big_q(W)

[295] (⊙ / {(Y1, W)}) CLOSURE : big_q(W)

[259] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [307] ¬big_q(U)

[307] (⊙ / {(Y1, U)}) CLOSURE : ¬big_q(U)

[242] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [289] (big_q(skolem_X14) ⇔ big_q(Y1))

[289] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(Y1))
    -> [292] ¬big_q(skolem_X14), ¬big_q(Y1)
    -> [293] big_q(skolem_X14), big_q(Y1)

[292] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [410] ¬big_q(U)

[410] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [411] big_q(W)

[411] (⊙ / {(Y1, W)}) CLOSURE : big_q(W)

[293] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [431] ¬big_q(U)

[431] (⊙ / {(Y1, U)}) CLOSURE : ¬big_q(U)

[67] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [73] big_p(skolem_U16)

[73] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [81] ¬big_p(skolem_W17)

[81] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [87] ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))

[87] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))
    -> [89] ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))

[89] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))
    -> [92] ¬big_p(skolem_W17), big_p(skolem_Y1(skolem_W17))
    -> [93] big_p(skolem_W17), ¬big_p(skolem_Y1(skolem_W17))

[93] (⊙ / {(X, skolem_W17)}) CLOSURE : big_p(skolem_W17)

[92] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [444] (big_q(skolem_X14) ⇔ big_q(Y1))

[444] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(Y1))
    -> [445] ¬big_q(skolem_X14), ¬big_q(Y1)
    -> [446] big_q(skolem_X14), big_q(Y1)

[445] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [451] ¬big_q(U)

[451] (γ∀) GAMMA_FORALL : ∀ W (big_q(W))
    -> [452] big_q(W)

[452] (⊙ / {(Y1, W)}) CLOSURE : big_q(W)

[446] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U (big_q(U))
    -> [454] ¬big_q(U)

[454] (⊙ / {(Y1, U)}) CLOSURE : ¬big_q(U)

[19] (δ∃) DELTA_EXISTS : ∃ U (big_q(U))
    -> [27] big_q(skolem_U2)

[27] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W (big_q(W))
    -> [38] ¬big_q(skolem_W3)

[38] (β¬⇔) BETA_NOT_EQUIV : ¬(∃ U1 (big_p(U1)) ⇔ ∀ W1 (big_p(W1)))
    -> [42] ¬∃ U1 (big_p(U1)), ∀ W1 (big_p(W1))
    -> [43] ∃ U1 (big_p(U1)), ¬∀ W1 (big_p(W1))

[42] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [185] ¬∀ Y ((big_p(X) ⇔ big_p(Y)))

[185] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(X) ⇔ big_p(Y)))
    -> [188] ¬(big_p(X) ⇔ big_p(skolem_Y1(X)))

[188] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(X) ⇔ big_p(skolem_Y1(X)))
    -> [190] ¬big_p(X), big_p(skolem_Y1(X))
    -> [191] big_p(X), ¬big_p(skolem_Y1(X))

[190] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [262] (big_q(skolem_X14) ⇔ big_q(skolem_W3))

[262] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_W3))
    -> [263] ¬big_q(skolem_X14), ¬big_q(skolem_W3)
    -> [264] big_q(skolem_X14), big_q(skolem_W3)

[264] (⊙ / {(Y1, skolem_W3)}) CLOSURE : big_q(skolem_W3)

[263] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [348] ¬big_p(skolem_Y1(X))

[348] (⊙ / {(U1, skolem_Y1(X))}) CLOSURE : ¬big_p(skolem_Y1(X))

[191] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [247] (big_q(skolem_X14) ⇔ big_q(skolem_W3))

[247] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_W3))
    -> [250] ¬big_q(skolem_X14), ¬big_q(skolem_W3)
    -> [251] big_q(skolem_X14), big_q(skolem_W3)

[251] (⊙ / {(Y1, skolem_W3)}) CLOSURE : big_q(skolem_W3)

[250] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ U1 (big_p(U1))
    -> [442] ¬big_p(U1)

[442] (⊙ / {(X, U1)}) CLOSURE : ¬big_p(U1)

[43] (δ∃) DELTA_EXISTS : ∃ U1 (big_p(U1))
    -> [60] big_p(skolem_U16)

[60] (δ¬∀) DELTA_NOT_FORALL : ¬∀ W1 (big_p(W1))
    -> [409] ¬big_p(skolem_W17)

[409] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [422] ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))

[422] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_W17) ⇔ big_p(Y)))
    -> [423] ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))

[423] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_W17) ⇔ big_p(skolem_Y1(skolem_W17)))
    -> [424] ¬big_p(skolem_W17), big_p(skolem_Y1(skolem_W17))
    -> [425] big_p(skolem_W17), ¬big_p(skolem_Y1(skolem_W17))

[425] (⊙ / {(X, skolem_W17)}) CLOSURE : big_p(skolem_W17)

[424] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [447] (big_q(skolem_X14) ⇔ big_q(skolem_U2))

[447] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_U2))
    -> [448] ¬big_q(skolem_X14), ¬big_q(skolem_U2)
    -> [449] big_q(skolem_X14), big_q(skolem_U2)

[448] (⊙ / {(Y1, skolem_U2)}) CLOSURE : ¬big_q(skolem_U2)

[449] (Reintroduction)  : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [461] ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))

[461] (γ¬∃) GAMMA_NOT_EXISTS : ¬∃ X (∀ Y ((big_p(X) ⇔ big_p(Y))))
    -> [462] ¬∀ Y ((big_p(skolem_U16) ⇔ big_p(Y)))

[462] (δ¬∀) DELTA_NOT_FORALL : ¬∀ Y ((big_p(skolem_U16) ⇔ big_p(Y)))
    -> [463] ¬(big_p(skolem_U16) ⇔ big_p(skolem_Y1(skolem_U16)))

[463] (β¬⇔) BETA_NOT_EQUIV : ¬(big_p(skolem_U16) ⇔ big_p(skolem_Y1(skolem_U16)))
    -> [464] ¬big_p(skolem_U16), big_p(skolem_Y1(skolem_U16))
    -> [465] big_p(skolem_U16), ¬big_p(skolem_Y1(skolem_U16))

[464] (⊙ / {(X, skolem_U16)}) CLOSURE : ¬big_p(skolem_U16)

[465] (Reintroduction)  : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [466] ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))

[466] (γ∀) GAMMA_FORALL : ∀ Y1 ((big_q(skolem_X14) ⇔ big_q(Y1)))
    -> [467] (big_q(skolem_X14) ⇔ big_q(skolem_W3))

[467] (β⇔) BETA_EQUIV : (big_q(skolem_X14) ⇔ big_q(skolem_W3))
    -> [468] ¬big_q(skolem_X14), ¬big_q(skolem_W3)
    -> [469] big_q(skolem_X14), big_q(skolem_W3)

[468] (⊙ / {}) CLOSURE : ¬big_q(skolem_X14)

% SZS output end Proof for SYN036+1.tptp

LEO-II 1.7.0

Sample solution for SET014^4

% SZS output start CNFRefutation
thf(tp_complement,type,(complement: (($i>$o)>($i>$o)))).
thf(tp_disjoint,type,(disjoint: (($i>$o)>(($i>$o)>$o)))).
thf(tp_emptyset,type,(emptyset: ($i>$o))).
thf(tp_excl_union,type,(excl_union: (($i>$o)>(($i>$o)>($i>$o))))).
thf(tp_in,type,(in: ($i>(($i>$o)>$o)))).
thf(tp_intersection,type,(intersection: (($i>$o)>(($i>$o)>($i>$o))))).
thf(tp_is_a,type,(is_a: ($i>(($i>$o)>$o)))).
thf(tp_meets,type,(meets: (($i>$o)>(($i>$o)>$o)))).
thf(tp_misses,type,(misses: (($i>$o)>(($i>$o)>$o)))).
thf(tp_sK1_X,type,(sK1_X: ($i>$o))).
thf(tp_sK2_SY0,type,(sK2_SY0: ($i>$o))).
thf(tp_sK3_SY2,type,(sK3_SY2: ($i>$o))).
thf(tp_sK4_SX0,type,(sK4_SX0: $i)).
thf(tp_setminus,type,(setminus: (($i>$o)>(($i>$o)>($i>$o))))).
thf(tp_singleton,type,(singleton: ($i>($i>$o)))).
thf(tp_subset,type,(subset: (($i>$o)>(($i>$o)>$o)))).
thf(tp_union,type,(union: (($i>$o)>(($i>$o)>($i>$o))))).
thf(tp_unord_pair,type,(unord_pair: ($i>($i>($i>$o))))).
thf(complement,definition,(complement = (^[X:($i>$o),U:$i]: (~ (X@U)))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',complement)).
thf(disjoint,definition,(disjoint = (^[X:($i>$o),Y:($i>$o)]: (((intersection@X)@Y) = emptyset))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',disjoint)).
thf(emptyset,definition,(emptyset = (^[X:$i]: $false)), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',emptyset)).
thf(excl_union,definition,(excl_union = (^[X:($i>$o),Y:($i>$o),U:$i]: (((X@U) & (~ (Y@U))) | ((~ (X@U)) & (Y@U))))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',excl_union)).
thf(in,definition,(in = (^[X:$i,M:($i>$o)]: (M@X))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',in)).
thf(intersection,definition,(intersection = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) & (Y@U)))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',intersection)).
thf(is_a,definition,(is_a = (^[X:$i,M:($i>$o)]: (M@X))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',is_a)).
thf(meets,definition,(meets = (^[X:($i>$o),Y:($i>$o)]: (?[U:$i]: ((X@U) & (Y@U))))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',meets)).
thf(misses,definition,(misses = (^[X:($i>$o),Y:($i>$o)]: (~ (?[U:$i]: ((X@U) & (Y@U)))))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',misses)).
thf(setminus,definition,(setminus = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) & (~ (Y@U))))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',setminus)).
thf(singleton,definition,(singleton = (^[X:$i,U:$i]: (U = X))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',singleton)).
thf(subset,definition,(subset = (^[X:($i>$o),Y:($i>$o)]: (![U:$i]: ((X@U) => (Y@U))))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',subset)).
thf(union,definition,(union = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) | (Y@U)))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',union)).
thf(unord_pair,definition,(unord_pair = (^[X:$i,Y:$i,U:$i]: ((U = X) | (U = Y)))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',unord_pair)).
thf(1,conjecture,(![X:($i>$o),Y:($i>$o),A:($i>$o)]: ((((subset@X)@A) & ((subset@Y)@A)) => ((subset@((union@X)@Y))@A))), file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',thm)).
thf(2,negated_conjecture,(((![X:($i>$o),Y:($i>$o),A:($i>$o)]: ((((subset@X)@A) & ((subset@Y)@A)) => ((subset@((union@X)@Y))@A)))=$false)), inference(negate_conjecture,[status(cth)],[1])).
thf(3,plain,(((![SY0:($i>$o),SY1:($i>$o)]: ((((subset@sK1_X)@SY1) & ((subset@SY0)@SY1)) => ((subset@((union@sK1_X)@SY0))@SY1)))=$false)), inference(extcnf_forall_neg,[status(esa)],[2])).
thf(4,plain,(((![SY2:($i>$o)]: ((((subset@sK1_X)@SY2) & ((subset@sK2_SY0)@SY2)) => ((subset@((union@sK1_X)@sK2_SY0))@SY2)))=$false)), inference(extcnf_forall_neg,[status(esa)],[3])).
thf(5,plain,((((((subset@sK1_X)@sK3_SY2) & ((subset@sK2_SY0)@sK3_SY2)) => ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=$false)), inference(extcnf_forall_neg,[status(esa)],[4])).
thf(6,plain,((((subset@sK1_X)@sK3_SY2)=$true)), inference(standard_cnf,[status(thm)],[5])).
thf(7,plain,((((subset@sK2_SY0)@sK3_SY2)=$true)), inference(standard_cnf,[status(thm)],[5])).
thf(8,plain,((((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2)=$false)), inference(standard_cnf,[status(thm)],[5])).
thf(9,plain,(((~ ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=$true)), inference(polarity_switch,[status(thm)],[8])).
thf(10,plain,((((subset@sK2_SY0)@sK3_SY2)=$true)), inference(copy,[status(thm)],[7])).
thf(11,plain,((((subset@sK1_X)@sK3_SY2)=$true)), inference(copy,[status(thm)],[6])).
thf(12,plain,(((~ ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=$true)), inference(copy,[status(thm)],[9])).
thf(13,plain,(((~ (![SX0:$i]: ((~ ((sK1_X@SX0) | (sK2_SY0@SX0))) | (sK3_SY2@SX0))))=$true)), inference(unfold_def,[status(thm)],[12,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
thf(14,plain,(((![SX0:$i]: ((~ (sK1_X@SX0)) | (sK3_SY2@SX0)))=$true)), inference(unfold_def,[status(thm)],[11,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
thf(15,plain,(((![SX0:$i]: ((~ (sK2_SY0@SX0)) | (sK3_SY2@SX0)))=$true)), inference(unfold_def,[status(thm)],[10,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
thf(16,plain,(((![SX0:$i]: ((~ ((sK1_X@SX0) | (sK2_SY0@SX0))) | (sK3_SY2@SX0)))=$false)), inference(extcnf_not_pos,[status(thm)],[13])).
thf(17,plain,(![SV1:$i]: ((((~ (sK1_X@SV1)) | (sK3_SY2@SV1))=$true))), inference(extcnf_forall_pos,[status(thm)],[14])).
thf(18,plain,(![SV2:$i]: ((((~ (sK2_SY0@SV2)) | (sK3_SY2@SV2))=$true))), inference(extcnf_forall_pos,[status(thm)],[15])).
thf(19,plain,((((~ ((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0))) | (sK3_SY2@sK4_SX0))=$false)), inference(extcnf_forall_neg,[status(esa)],[16])).
thf(20,plain,(![SV1:$i]: (((~ (sK1_X@SV1))=$true) | ((sK3_SY2@SV1)=$true))), inference(extcnf_or_pos,[status(thm)],[17])).
thf(21,plain,(![SV2:$i]: (((~ (sK2_SY0@SV2))=$true) | ((sK3_SY2@SV2)=$true))), inference(extcnf_or_pos,[status(thm)],[18])).
thf(22,plain,(((~ ((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0)))=$false)), inference(extcnf_or_neg,[status(thm)],[19])).
thf(23,plain,(((sK3_SY2@sK4_SX0)=$false)), inference(extcnf_or_neg,[status(thm)],[19])).
thf(24,plain,(![SV1:$i]: (((sK1_X@SV1)=$false) | ((sK3_SY2@SV1)=$true))), inference(extcnf_not_pos,[status(thm)],[20])).
thf(25,plain,(![SV2:$i]: (((sK2_SY0@SV2)=$false) | ((sK3_SY2@SV2)=$true))), inference(extcnf_not_pos,[status(thm)],[21])).
thf(26,plain,((((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0))=$true)), inference(extcnf_not_neg,[status(thm)],[22])).
thf(27,plain,(((sK1_X@sK4_SX0)=$true) | ((sK2_SY0@sK4_SX0)=$true)), inference(extcnf_or_pos,[status(thm)],[26])).
thf(28,plain,((($false)=$true)), inference(fo_atp_e,[status(thm)],[23,27,25,24])).
thf(29,plain,($false), inference(solved_all_splits,[solved_all_splits(join,[])],[28])).
% SZS output end CNFRefutation

Leo-III 1.7.0

Sample solution for SET014^4

% SZS output start Refutation for /home/lex/TPTP/Problems/SET/SET014^4.p
thf(union_type, type, union: (($i > $o) > (($i > $o) > ($i > $o)))).
thf(union_def, definition, (union = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))))).
thf(subset_type, type, subset: (($i > $o) > (($i > $o) > $o))).
thf(subset_def, definition, (subset = (^ [A:($i > $o),B:($i > $o)]: ! [C:$i]: ((A @ C) => (B @ C))))).
thf(sk1_type, type, sk1: ($i > $o)).
thf(sk2_type, type, sk2: ($i > $o)).
thf(sk3_type, type, sk3: ($i > $o)).
thf(sk4_type, type, sk4: $i).
thf(1,conjecture,((! [A:($i > $o),B:($i > $o),C:($i > $o)]: (((subset @ A @ C) & (subset @ B @ C)) => (subset @ (union @ A @ B) @ C)))),file('/home/lex/TPTP/Problems/SET/SET014^4.p',thm)).
thf(2,negated_conjecture,((~ (! [A:($i > $o),B:($i > $o),C:($i > $o)]: (((subset @ A @ C) & (subset @ B @ C)) => (subset @ (union @ A @ B) @ C))))),inference(neg_conjecture,[status(cth)],[1])).
thf(3,plain,((~ (! [A:($i > $o),B:($i > $o),C:($i > $o)]: ((! [D:$i]: ((A @ D) => (C @ D)) & ! [D:$i]: ((B @ D) => (C @ D))) => (! [D:$i]: (((A @ D) | (B @ D)) => (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(5,plain,((sk1 @ sk4) | (sk2 @ sk4)),inference(cnf,[status(esa)],[3])).
thf(7,plain,(! [A:$i] : ((~ (sk1 @ A)) | (sk3 @ A))),inference(cnf,[status(esa)],[3])).
thf(4,plain,((~ (sk3 @ sk4))),inference(cnf,[status(esa)],[3])).
thf(9,plain,(! [A:$i] : ((~ (sk1 @ A)) | ((sk3 @ A) != (sk3 @
sk4)))),inference(paramod_ordered,[status(thm)],[7,4])).
thf(10,plain,((~ (sk1 @ sk4))),inference(pattern_uni,[status(thm)],[9:[bind(A,$thf(sk4))]])).
thf(11,plain,(($false) | (sk2 @ sk4)),inference(rewrite,[status(thm)],[5,10])).
thf(12,plain,((sk2 @ sk4)),inference(simp,[status(thm)],[11])).
thf(6,plain,(! [A:$i] : ((~ (sk2 @ A)) | (sk3 @
A))),inference(cnf,[status(esa)],[3])).
thf(8,plain,(! [A:$i] : ((~ (sk2 @ A)) | (sk3 @
A))),inference(simp,[status(thm)],[6])).
thf(13,plain,(! [A:$i] : ((~ (sk2 @ A)) | ((sk3 @ A) != (sk3 @
sk4)))),inference(paramod_ordered,[status(thm)],[8,4])).
thf(14,plain,((~ (sk2 @ sk4))),inference(pattern_uni,[status(thm)],[13:[bind(A,$thf(sk4))]])).
thf(15,plain,(($false)),inference(rewrite,[status(thm)],[12,14])).
thf(16,plain,(($false)),inference(simp,[status(thm)],[15])).
% SZS output end Refutation for /home/lex/TPTP/Problems/SET/SET014^4.p

Prover9 1109a

Sample solution for SEU140+2

8 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
26 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
42 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -((exists C (in(C,A) & in(C,B))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
55 -(all A all B all C (subset(A,B) & disjoint(B,C) -> disjoint(A,C))) # label(t63_xboole_1) # label(negated_conjecture) # label(non_clause).  [assumption].
60 subset(c3,c4) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
61 disjoint(c4,c5) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
75 disjoint(A,B) | in(f7(A,B),A) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
76 disjoint(A,B) | in(f7(A,B),B) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
92 -disjoint(c3,c5) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
101 -in(A,B) | -in(A,C) | -disjoint(B,C) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
109 -disjoint(A,B) | disjoint(B,A) # label(symmetry_r1_xboole_0) # label(axiom).  [clausify(26)].
123 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom).  [clausify(8)].
273 -disjoint(c5,c3).  [ur(109,b,92,a)].
300 -in(A,c3) | in(A,c4).  [resolve(123,a,60,a)].
959 in(f7(c5,c3),c3).  [resolve(273,a,76,a)].
960 in(f7(c5,c3),c5).  [resolve(273,a,75,a)].
1084 -in(f7(c5,c3),c4).  [ur(101,b,960,a,c,61,a)].
1292 $F.  [resolve(300,a,959,a),unit_del(a,1084)].

Satallax 3.4

Sample solution for SET014^4

% SZS output start Proof
thf(ty_eigen__2, type, eigen__2 : ($i>$o)).
thf(ty_eigen__1, type, eigen__1 : ($i>$o)).
thf(ty_eigen__0, type, eigen__0 : ($i>$o)).
thf(ty_eigen__3, type, eigen__3 : $i).
thf(sP1,plain,sP1 <=> (eigen__0 @ eigen__3),introduced(definition,[new_symbols(definition,[sP1])])).
thf(sP2,plain,sP2 <=> (sP1 => (eigen__2 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP2])])).
thf(sP3,plain,sP3 <=> (eigen__1 @ eigen__3),introduced(definition,[new_symbols(definition,[sP3])])).
thf(sP4,plain,sP4 <=> (sP3 => (eigen__2 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP4])])).
thf(sP5,plain,sP5 <=> (![X1:$i]:((eigen__1 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP5])])).
thf(sP6,plain,sP6 <=> (eigen__2 @ eigen__3),introduced(definition,[new_symbols(definition,[sP6])])).
thf(sP7,plain,sP7 <=> (![X1:$i]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
thf(def_in,definition,(in = (^[X1:$i]:(^[X2:$i>$o]:(X2 @ X1))))).
thf(def_is_a,definition,(is_a = (^[X1:$i]:(^[X2:$i>$o]:(X2 @ X1))))).
thf(def_emptyset,definition,(emptyset = (^[X1:$i]:$false))).
thf(def_unord_pair,definition,(unord_pair = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((~((X3 = X1))) => (X3 = X2))))))).
thf(def_singleton,definition,(singleton = (^[X1:$i]:(^[X2:$i]:(X2 = X1))))).
thf(def_union,definition,(union = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
thf(def_excl_union,definition,(excl_union = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(((X1 @ X3) => (X2 @ X3)) => (~(((~((X1 @ X3))) => (~((X2 @ X3)))))))))))).
thf(def_intersection,definition,(intersection = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
thf(def_setminus,definition,(setminus = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (X2 @ X3))))))))).
thf(def_complement,definition,(complement = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
thf(def_disjoint,definition,(disjoint = (^[X1:$i>$o]:(^[X2:$i>$o]:(((intersection @ X1) @ X2) = emptyset))))).
thf(def_subset,definition,(subset = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:((X1 @ X3) => (X2 @ X3))))))).
thf(def_meets,definition,(meets = (^[X1:$i>$o]:(^[X2:$i>$o]:(~((![X3:$i]:((X1 @ X3) => (~((X2 @ X3))))))))))).
thf(def_misses,definition,(misses = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:((X1 @ X3) => (~((X2 @ X3))))))))).
thf(thm,conjecture,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:((~(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4)))))))).
thf(h0,negated_conjecture,(~((![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:((~(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4))))))))),inference(assume_negation,[status(cth)],[thm])).
thf(h1,assumption,(~((![X1:$i>$o]:(![X2:$i>$o]:((~(((![X3:$i]:((eigen__0 @ X3) => (X2 @ X3))) => (~((![X3:$i]:((X1 @ X3) => (X2 @ X3)))))))) => (![X3:$i]:(((~((eigen__0 @ X3))) => (X1 @ X3)) => (X2 @ X3)))))))),introduced(assumption,[])).
thf(h2,assumption,(~((![X1:$i>$o]:((~(((![X2:$i]:((eigen__0 @ X2) => (X1 @ X2))) => (~((![X2:$i]:((eigen__1 @ X2) => (X1 @ X2)))))))) => (![X2:$i]:(((~((eigen__0 @ X2))) => (eigen__1 @ X2)) => (X1 @ X2))))))),introduced(assumption,[])).
thf(h3,assumption,(~(((~((sP7 => (~(sP5))))) => (![X1:$i]:(((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (eigen__2 @ X1)))))),introduced(assumption,[])).
thf(h4,assumption,(~((sP7 => (~(sP5))))),introduced(assumption,[])).
thf(h5,assumption,(~((![X1:$i]:(((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (eigen__2 @ X1))))),introduced(assumption,[])).
thf(h6,assumption,sP7,introduced(assumption,[])).
thf(h7,assumption,sP5,introduced(assumption,[])).
thf(h8,assumption,(~((((~(sP1)) => sP3) => sP6))),introduced(assumption,[])).
thf(h9,assumption,((~(sP1)) => sP3),introduced(assumption,[])).
thf(h10,assumption,(~(sP6)),introduced(assumption,[])).
thf(h11,assumption,sP1,introduced(assumption,[])).
thf(h12,assumption,sP3,introduced(assumption,[])).
thf(1,plain,(~(sP7) | sP2),inference(all_rule,[status(thm)],[])).
thf(2,plain,((~(sP2) | ~(sP1)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(3,plain,$false,inference(prop_unsat,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,h6,h11,h10])).
thf(4,plain,(~(sP5) | sP4),inference(all_rule,[status(thm)],[])).
thf(5,plain,((~(sP4) | ~(sP3)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(6,plain,$false,inference(prop_unsat,[status(thm),assumptions([h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[4,5,h7,h12,h10])).
thf(7,plain,$false,inference(tab_imp,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,3,6,h11,h12])).
thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,7,h9,h10])).
thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,8,h8])).
thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,9,h6,h7])).
thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,10,h4,h5])).
thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,11,h3])).
thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2])).
thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1])).
thf(0,theorem,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:((~(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4))))))),inference(contra,[status(thm),contra(discharge,[h0])],[14,h0])).
% SZS output end Proof

SnakeForV4.7 1.0

Sample solution for DAT013=1

% SZS output start Proof for DAT013=1
tff(type_def_5, type, array: $tType).
tff(func_def_0, type, read: (array * $int) > $int).
tff(func_def_1, type, write: (array * $int * $int) > array).
tff(func_def_7, type, sK0: array).
tff(func_def_8, type, sK1: $int).
tff(func_def_9, type, sK2: $int).
tff(func_def_10, type, sK3: $int).
tff(f361,plain,(
  $false),
  inference(avatar_sat_refutation,[],[f321,f327,f358])).
tff(f358,plain,(
  ~spl4_6),
  inference(avatar_contradiction_clause,[],[f357])).
tff(f357,plain,(
  $false | ~spl4_6),
  inference(subsumption_resolution,[],[f356,f79])).
tff(f79,plain,(
  ~$less(sK1,sK3)),
  inference(resolution,[],[f75,f11])).
tff(f11,plain,(
  ( ! [X0 : $int] : (~$less(X0,X0)) )),
  introduced(theory_axiom_146,[])).
tff(f75,plain,(
  ( ! [X2 : $int] : ($less(X2,sK1) | ~$less(X2,sK3)) )),
  inference(resolution,[],[f12,f32])).
tff(f32,plain,(
  $less(sK3,sK1)),
  inference(subsumption_resolution,[],[f31,f29])).
tff(f29,plain,(
  ~$less(sK2,sK3)),
  inference(cnf_transformation,[],[f24])).
tff(f24,plain,(
  (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f23,f22])).
tff(f22,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1))) => (? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)))),
  introduced(choice_axiom,[])).
tff(f23,plain,(
  ? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) => (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3)))),
  introduced(choice_axiom,[])).
tff(f21,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1)))),
  inference(rectify,[],[f20])).
tff(f20,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & ~$less(X2,X4) & ~$less(X4,$sum(X1,3))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | $less(X2,X3) | $less(X3,X1)))),
  inference(flattening,[],[f19])).
tff(f19,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & (~$less(X2,X4) & ~$less(X4,$sum(X1,3)))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | ($less(X2,X3) | $less(X3,X1))))),
  inference(ennf_transformation,[],[f5])).
tff(f5,plain,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : ((~$less(X2,X3) & ~$less(X3,X1)) => $less(0,read(X0,X3))) => ! [X4 : $int] : ((~$less(X2,X4) & ~$less(X4,$sum(X1,3))) => $less(0,read(X0,X4))))),
  inference(theory_normalization,[],[f4])).
tff(f4,negated_conjecture,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
  inference(negated_conjecture,[],[f3])).
tff(f3,conjecture,(
  ! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
  file('/home/filip/TPTP-v7.5.0/Problems/DAT/DAT013=1.p',unknown)).
tff(f31,plain,(
  $less(sK2,sK3) | $less(sK3,sK1)),
  inference(resolution,[],[f27,f30])).
tff(f30,plain,(
  ~$less(0,read(sK0,sK3))),
  inference(cnf_transformation,[],[f24])).
tff(f27,plain,(
  ( ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)) )),
  inference(cnf_transformation,[],[f24])).
tff(f12,plain,(
  ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
  introduced(theory_axiom_147,[])).
tff(f356,plain,(
  $less(sK1,sK3) | ~spl4_6),
  inference(evaluation,[],[f353])).
tff(f353,plain,(
  $less(sK1,sK3) | ~$less(0,3) | ~spl4_6),
  inference(superposition,[],[f347,f38])).
tff(f38,plain,(
  ( ! [X0 : $int] : ($sum(0,X0) = X0) )),
  inference(superposition,[],[f6,f8])).
tff(f8,plain,(
  ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
  introduced(theory_axiom_141,[])).
tff(f6,plain,(
  ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
  introduced(theory_axiom_139,[])).
tff(f347,plain,(
  ( ! [X2 : $int] : ($less($sum(X2,sK1),sK3) | ~$less(X2,3)) ) | ~spl4_6),
  inference(resolution,[],[f330,f14])).
tff(f14,plain,(
  ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
  introduced(theory_axiom_149,[])).
tff(f330,plain,(
  ( ! [X0 : $int] : (~$less(X0,$sum(3,sK1)) | $less(X0,sK3)) ) | ~spl4_6),
  inference(resolution,[],[f121,f12])).
tff(f121,plain,(
  $less($sum(3,sK1),sK3) | ~spl4_6),
  inference(avatar_component_clause,[],[f119])).
tff(f119,plain,(
  spl4_6 <=> $less($sum(3,sK1),sK3)),
  introduced(avatar_definition,[new_symbols(naming,[spl4_6])])).
tff(f327,plain,(
  spl4_5 | spl4_6),
  inference(avatar_split_clause,[],[f325,f119,f115])).
tff(f115,plain,(
  spl4_5 <=> sK3 = $sum(3,sK1)),
  introduced(avatar_definition,[new_symbols(naming,[spl4_5])])).
tff(f325,plain,(
  $less($sum(3,sK1),sK3) | sK3 = $sum(3,sK1)),
  inference(resolution,[],[f37,f13])).
tff(f13,plain,(
  ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
  introduced(theory_axiom_148,[])).
tff(f37,plain,(
  ~$less(sK3,$sum(3,sK1))),
  inference(backward_demodulation,[],[f28,f6])).
tff(f28,plain,(
  ~$less(sK3,$sum(sK1,3))),
  inference(cnf_transformation,[],[f24])).
tff(f321,plain,(
  ~spl4_5),
  inference(avatar_contradiction_clause,[],[f320])).
tff(f320,plain,(
  $false | ~spl4_5),
  inference(subsumption_resolution,[],[f319,f79])).
tff(f319,plain,(
  $less(sK1,sK3) | ~spl4_5),
  inference(evaluation,[],[f315])).
tff(f315,plain,(
  $less(sK1,sK3) | ~$less(0,3) | ~spl4_5),
  inference(superposition,[],[f207,f38])).
tff(f207,plain,(
  ( ! [X12 : $int] : ($less($sum(X12,sK1),sK3) | ~$less(X12,3)) ) | ~spl4_5),
  inference(superposition,[],[f14,f117])).
tff(f117,plain,(
  sK3 = $sum(3,sK1) | ~spl4_5),
  inference(avatar_component_clause,[],[f115])).
% SZS output end Proof for DAT013=1

Sample solution for SEU140+2

% SZS output start Proof for SEU140+2
fof(f539,plain,(
  $false),
  inference(subsumption_resolution,[],[f523,f416])).
fof(f416,plain,(
  in(sK0(sK2,sK4),sK3)),
  inference(unit_resulting_resolution,[],[f150,f337,f181])).
fof(f181,plain,(
  ( ! [X3,X0,X1] : (~subset(X0,X1) | ~in(X3,X0) | in(X3,X1)) )),
  inference(cnf_transformation,[],[f115])).
fof(f115,plain,(
  ! [X0,X1] : ((subset(X0,X1) | (~in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f113,f114])).
fof(f114,plain,(
  ! [X0,X1] : (? [X2] : (~in(X2,X1) & in(X2,X0)) => (~in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)))),
  introduced(choice_axiom,[])).
fof(f113,plain,(
  ! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
  inference(rectify,[],[f112])).
fof(f112,plain,(
  ! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X2] : (in(X2,X1) | ~in(X2,X0)) | ~subset(X0,X1)))),
  inference(nnf_transformation,[],[f83])).
fof(f83,plain,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X1) | ~in(X2,X0)))),
  inference(ennf_transformation,[],[f8])).
fof(f8,axiom,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
  file('/home/filip/TPTP-v7.5.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f337,plain,(
  in(sK0(sK2,sK4),sK2)),
  inference(unit_resulting_resolution,[],[f152,f140])).
fof(f140,plain,(
  ( ! [X0,X1] : (in(sK0(X0,X1),X0) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f92])).
fof(f92,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK0(X0,X1),X1) & in(sK0(X0,X1),X0)) | disjoint(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f73,f91])).
fof(f91,plain,(
  ! [X0,X1] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK0(X0,X1),X1) & in(sK0(X0,X1),X0)))),
  introduced(choice_axiom,[])).
fof(f73,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
  inference(ennf_transformation,[],[f58])).
fof(f58,plain,(
  ! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
  inference(rectify,[],[f43])).
fof(f43,axiom,(
  ! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
  file('/home/filip/TPTP-v7.5.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f152,plain,(
  ~disjoint(sK2,sK4)),
  inference(cnf_transformation,[],[f96])).
fof(f96,plain,(
  ~disjoint(sK2,sK4) & disjoint(sK3,sK4) & subset(sK2,sK3)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f79,f95])).
fof(f95,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK2,sK4) & disjoint(sK3,sK4) & subset(sK2,sK3))),
  introduced(choice_axiom,[])).
fof(f79,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
  inference(flattening,[],[f78])).
fof(f78,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
  inference(ennf_transformation,[],[f52])).
fof(f52,negated_conjecture,(
  ~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  inference(negated_conjecture,[],[f51])).
fof(f51,conjecture,(
  ! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  file('/home/filip/TPTP-v7.5.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f150,plain,(
  subset(sK2,sK3)),
  inference(cnf_transformation,[],[f96])).
fof(f523,plain,(
  ~in(sK0(sK2,sK4),sK3)),
  inference(unit_resulting_resolution,[],[f151,f341,f142])).
fof(f142,plain,(
  ( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
  inference(cnf_transformation,[],[f92])).
fof(f341,plain,(
  in(sK0(sK2,sK4),sK4)),
  inference(unit_resulting_resolution,[],[f152,f141])).
fof(f141,plain,(
  ( ! [X0,X1] : (in(sK0(X0,X1),X1) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f92])).
fof(f151,plain,(
  disjoint(sK3,sK4)),
  inference(cnf_transformation,[],[f96])).
% SZS output end Proof for SEU140+2

Sample solution for NLP042+1

% (11912)# SZS output start Saturation.
cnf(u143,negated_conjecture,
    patient(sK0,sK4,sK3)).

cnf(u146,axiom,
    ~patient(X0,X1,X3) | ~agent(X0,X1,X3) | ~nonreflexive(X0,X1)).

cnf(u142,negated_conjecture,
    agent(sK0,sK4,sK1)).

cnf(u190,negated_conjecture,
    ~agent(sK0,sK4,sK3)).

cnf(u144,negated_conjecture,
    nonreflexive(sK0,sK4)).

cnf(u136,negated_conjecture,
    of(sK0,sK2,sK1)).

cnf(u193,negated_conjecture,
    ~of(sK0,X0,sK1) | sK2 = X0 | ~forename(sK0,X0)).

cnf(u134,axiom,
    ~of(X0,X3,X1) | X2 = X3 | ~forename(X0,X3) | ~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1)).

cnf(u177,negated_conjecture,
    act(sK0,sK4)).

cnf(u126,axiom,
    ~act(X0,X1) | event(X0,X1)).

cnf(u175,negated_conjecture,
    nonexistent(sK0,sK4)).

cnf(u129,axiom,
    ~nonexistent(X0,X1) | ~existent(X0,X1)).

cnf(u173,negated_conjecture,
    eventuality(sK0,sK4)).

cnf(u122,axiom,
    ~eventuality(X0,X1) | unisex(X0,X1)).

cnf(u123,axiom,
    ~eventuality(X0,X1) | nonexistent(X0,X1)).

cnf(u124,axiom,
    ~eventuality(X0,X1) | specific(X0,X1)).

cnf(u141,negated_conjecture,
    event(sK0,sK4)).

cnf(u125,axiom,
    ~event(X0,X1) | eventuality(X0,X1)).

cnf(u145,negated_conjecture,
    order(sK0,sK4)).

cnf(u121,axiom,
    ~order(X0,X1) | event(X0,X1)).

cnf(u127,axiom,
    ~order(X0,X1) | act(X0,X1)).

cnf(u140,negated_conjecture,
    shake_beverage(sK0,sK3)).

cnf(u120,axiom,
    ~shake_beverage(X0,X1) | beverage(X0,X1)).

cnf(u163,negated_conjecture,
    beverage(sK0,sK3)).

cnf(u119,axiom,
    ~beverage(X0,X1) | food(X0,X1)).

cnf(u164,negated_conjecture,
    food(sK0,sK3)).

cnf(u118,axiom,
    ~food(X0,X1) | substance_matter(X0,X1)).

cnf(u166,negated_conjecture,
    substance_matter(sK0,sK3)).

cnf(u117,axiom,
    ~substance_matter(X0,X1) | object(X0,X1)).

cnf(u174,negated_conjecture,
    specific(sK0,sK4)).

cnf(u171,negated_conjecture,
    specific(sK0,sK3)).

cnf(u162,negated_conjecture,
    specific(sK0,sK1)).

cnf(u132,axiom,
    ~specific(X0,X1) | ~general(X0,X1)).

cnf(u172,negated_conjecture,
    existent(sK0,sK3)).

cnf(u161,negated_conjecture,
    existent(sK0,sK1)).

cnf(u180,negated_conjecture,
    ~existent(sK0,sK4)).

cnf(u169,negated_conjecture,
    nonliving(sK0,sK3)).

cnf(u128,axiom,
    ~nonliving(X0,X1) | ~animate(X0,X1)).

cnf(u131,axiom,
    ~nonliving(X0,X1) | ~living(X0,X1)).

cnf(u167,negated_conjecture,
    object(sK0,sK3)).

cnf(u112,axiom,
    ~object(X0,X1) | unisex(X0,X1)).

cnf(u113,axiom,
    ~object(X0,X1) | nonliving(X0,X1)).

cnf(u116,axiom,
    ~object(X0,X1) | entity(X0,X1)).

cnf(u155,negated_conjecture,
    relname(sK0,sK2)).

cnf(u110,axiom,
    ~relname(X0,X1) | relation(X0,X1)).

cnf(u156,negated_conjecture,
    relation(sK0,sK2)).

cnf(u109,axiom,
    ~relation(X0,X1) | abstraction(X0,X1)).

cnf(u158,negated_conjecture,
    nonhuman(sK0,sK2)).

cnf(u130,axiom,
    ~nonhuman(X0,X1) | ~human(X0,X1)).

cnf(u159,negated_conjecture,
    general(sK0,sK2)).

cnf(u184,negated_conjecture,
    ~general(sK0,sK3)).

cnf(u183,negated_conjecture,
    ~general(sK0,sK1)).

cnf(u185,negated_conjecture,
    ~general(sK0,sK4)).

cnf(u176,negated_conjecture,
    unisex(sK0,sK4)).

cnf(u170,negated_conjecture,
    unisex(sK0,sK3)).

cnf(u160,negated_conjecture,
    unisex(sK0,sK2)).

cnf(u133,axiom,
    ~unisex(X0,X1) | ~female(X0,X1)).

cnf(u157,negated_conjecture,
    abstraction(sK0,sK2)).

cnf(u106,axiom,
    ~abstraction(X0,X1) | unisex(X0,X1)).

cnf(u107,axiom,
    ~abstraction(X0,X1) | general(X0,X1)).

cnf(u108,axiom,
    ~abstraction(X0,X1) | nonhuman(X0,X1)).

cnf(u139,negated_conjecture,
    forename(sK0,sK2)).

cnf(u111,axiom,
    ~forename(X0,X1) | relname(X0,X1)).

cnf(u138,negated_conjecture,
    mia_forename(sK0,sK2)).

cnf(u105,axiom,
    ~mia_forename(X0,X1) | forename(X0,X1)).

cnf(u168,negated_conjecture,
    entity(sK0,sK3)).

cnf(u153,negated_conjecture,
    entity(sK0,sK1)).

cnf(u114,axiom,
    ~entity(X0,X1) | existent(X0,X1)).

cnf(u115,axiom,
    ~entity(X0,X1) | specific(X0,X1)).

cnf(u154,negated_conjecture,
    living(sK0,sK1)).

cnf(u182,negated_conjecture,
    ~living(sK0,sK3)).

cnf(u149,negated_conjecture,
    organism(sK0,sK1)).

cnf(u101,axiom,
    ~organism(X0,X1) | living(X0,X1)).

cnf(u102,axiom,
    ~organism(X0,X1) | entity(X0,X1)).

cnf(u150,negated_conjecture,
    human(sK0,sK1)).

cnf(u181,negated_conjecture,
    ~human(sK0,sK2)).

cnf(u151,negated_conjecture,
    animate(sK0,sK1)).

cnf(u179,negated_conjecture,
    ~animate(sK0,sK3)).

cnf(u148,negated_conjecture,
    human_person(sK0,sK1)).

cnf(u99,axiom,
    ~human_person(X0,X1) | animate(X0,X1)).

cnf(u100,axiom,
    ~human_person(X0,X1) | human(X0,X1)).

cnf(u103,axiom,
    ~human_person(X0,X1) | organism(X0,X1)).

cnf(u147,negated_conjecture,
    female(sK0,sK1)).

cnf(u187,negated_conjecture,
    ~female(sK0,sK3)).

cnf(u186,negated_conjecture,
    ~female(sK0,sK2)).

cnf(u188,negated_conjecture,
    ~female(sK0,sK4)).

cnf(u137,negated_conjecture,
    woman(sK0,sK1)).

cnf(u98,axiom,
    ~woman(X0,X1) | female(X0,X1)).

cnf(u104,axiom,
    ~woman(X0,X1) | human_person(X0,X1)).

% (11912)# SZS output end Saturation.

Sample solution for SWV017+1

% (11974)# SZS output start Saturation.
cnf(u126,axiom,
    intruder_message(encrypt(X1,X2)) | ~intruder_message(X2) | ~intruder_message(X1)).

cnf(u166,axiom,
    ~intruder_message(at)).

cnf(u183,axiom,
    intruder_message(generate_b_nonce(X2)) | ~fresh_to_b(X2) | ~intruder_message(X2)).

cnf(u231,axiom,
    ~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))).

cnf(u235,axiom,
    ~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))).

cnf(u276,axiom,
    intruder_message(encrypt(X2,generate_key(an_a_nonce))) | ~intruder_message(X2)).

cnf(u327,axiom,
    ~a_nonce(generate_key(an_a_nonce))).

cnf(u334,axiom,
    ~intruder_message(bt)).

cnf(u103,axiom,
    fresh_intruder_nonce(generate_intruder_nonce(X0)) | ~fresh_intruder_nonce(X0)).

cnf(u102,axiom,
    fresh_intruder_nonce(an_intruder_nonce)).

cnf(u104,axiom,
    ~fresh_intruder_nonce(X0) | fresh_to_b(X0)).

cnf(u105,axiom,
    ~fresh_intruder_nonce(X0) | intruder_message(X0)).

cnf(u94,axiom,
    intruder_holds(key(X0,X1)) | ~party_of_protocol(X1) | ~intruder_message(X0)).

cnf(u95,axiom,
    ~intruder_holds(key(X1,X2)) | ~party_of_protocol(X2) | intruder_message(encrypt(X0,X1)) | ~intruder_message(X0)).

cnf(u111,axiom,
    intruder_message(generate_intruder_nonce(X0)) | ~fresh_intruder_nonce(X0)).

cnf(u110,axiom,
    intruder_message(an_intruder_nonce)).

cnf(u148,axiom,
    intruder_message(generate_b_nonce(an_a_nonce))).

cnf(u359,axiom,
    intruder_message(triple(encrypt(quadruple(b,X0,generate_key(X0),generate_expiration_time(X0)),bt),encrypt(triple(b,generate_key(X0),generate_expiration_time(X0)),bt),X1)) | ~intruder_message(X1) | ~intruder_message(X0) | ~fresh_to_b(X0) | ~a_nonce(X0)).

cnf(u351,axiom,
    intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2)) | ~intruder_message(X2) | ~intruder_message(X1) | ~fresh_to_b(X1) | ~a_nonce(X1)).

cnf(u348,axiom,
    intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1)) | ~intruder_message(X1)).

cnf(u241,axiom,
    intruder_message(triple(encrypt(quadruple(b,X0,generate_key(X0),generate_expiration_time(X0)),bt),encrypt(triple(b,generate_key(X0),generate_expiration_time(X0)),bt),generate_b_nonce(X0))) | ~fresh_to_b(X0) | ~intruder_message(X0) | ~a_nonce(X0)).

cnf(u224,axiom,
    intruder_message(triple(encrypt(quadruple(b,X0,generate_key(X0),generate_expiration_time(X0)),at),encrypt(triple(a,generate_key(X0),generate_expiration_time(X0)),bt),generate_b_nonce(X0))) | ~fresh_to_b(X0) | ~intruder_message(X0) | ~a_nonce(X0)).

cnf(u221,axiom,
    intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce)))).

cnf(u171,axiom,
    intruder_message(triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt))) | ~fresh_to_b(X1) | ~intruder_message(X1) | ~intruder_message(X0) | ~party_of_protocol(X0)).

cnf(u145,axiom,
    intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))).

cnf(u90,axiom,
    intruder_message(triple(X0,X1,X2)) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)).

cnf(u226,axiom,
    intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))).

cnf(u266,axiom,
    intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt)) | ~intruder_message(X1) | ~a_nonce(X1) | ~fresh_to_b(X1)).

cnf(u175,axiom,
    intruder_message(encrypt(triple(X1,X0,generate_expiration_time(X0)),bt)) | ~intruder_message(X0) | ~intruder_message(X1) | ~party_of_protocol(X1) | ~fresh_to_b(X0)).

cnf(u260,axiom,
    intruder_message(encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt)) | ~intruder_message(X1) | ~a_nonce(X1) | ~fresh_to_b(X1)).

cnf(u227,axiom,
    intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))).

cnf(u147,axiom,
    intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))).

cnf(u267,axiom,
    intruder_message(encrypt(quadruple(b,X2,generate_key(X2),generate_expiration_time(X2)),bt)) | ~intruder_message(X2) | ~a_nonce(X2) | ~fresh_to_b(X2)).

cnf(u261,axiom,
    intruder_message(encrypt(quadruple(b,X2,generate_key(X2),generate_expiration_time(X2)),at)) | ~intruder_message(X2) | ~a_nonce(X2) | ~fresh_to_b(X2)).

cnf(u253,axiom,
    intruder_message(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at))).

cnf(u91,axiom,
    intruder_message(quadruple(X0,X1,X2,X3)) | ~intruder_message(X3) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)).

cnf(u349,axiom,
    intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X0,generate_key(an_a_nonce)))) | ~intruder_message(X0)).

cnf(u222,axiom,
    intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))).

cnf(u263,axiom,
    intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce)))) | ~intruder_message(X2) | ~intruder_message(X1)).

cnf(u89,axiom,
    intruder_message(pair(X0,X1)) | ~intruder_message(X1) | ~intruder_message(X0)).

cnf(u113,axiom,
    intruder_message(pair(a,an_a_nonce))).

cnf(u114,axiom,
    intruder_message(an_a_nonce)).

cnf(u149,axiom,
    intruder_message(b)).

cnf(u115,axiom,
    intruder_message(a)).

cnf(u156,axiom,
    ~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X2,X3),at),X0,X1)) | message(sent(a,b,pair(X0,encrypt(X1,X2))))).

cnf(u219,axiom,
    ~intruder_message(triple(b,X3,encrypt(triple(b,X1,X2),bt))) | message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3))) | ~a_nonce(X1)).

cnf(u190,axiom,
    ~intruder_message(triple(b,X3,encrypt(triple(a,X1,X2),bt))) | message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3))) | ~a_nonce(X1)).

cnf(u213,axiom,
    ~intruder_message(triple(a,X2,encrypt(triple(b,X0,X1),at))) | message(sent(t,b,triple(encrypt(quadruple(a,X0,generate_key(X0),X1),bt),encrypt(triple(b,generate_key(X0),X1),at),X2))) | ~a_nonce(X0)).

cnf(u174,axiom,
    ~intruder_message(triple(a,X2,encrypt(triple(a,X0,X1),at))) | message(sent(t,a,triple(encrypt(quadruple(a,X0,generate_key(X0),X1),at),encrypt(triple(a,generate_key(X0),X1),at),X2))) | ~a_nonce(X0)).

cnf(u82,axiom,
    ~intruder_message(triple(X0,X1,X2)) | intruder_message(X0)).

cnf(u83,axiom,
    ~intruder_message(triple(X0,X1,X2)) | intruder_message(X1)).

cnf(u84,axiom,
    ~intruder_message(triple(X0,X1,X2)) | intruder_message(X2)).

cnf(u256,axiom,
    ~intruder_message(encrypt(triple(b,X1,X2),bt)) | ~a_nonce(X1) | message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3))) | ~intruder_message(X3)).

cnf(u247,axiom,
    ~intruder_message(encrypt(triple(a,X1,X2),bt)) | ~a_nonce(X1) | message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3))) | ~intruder_message(X3)).

cnf(u249,axiom,
    ~intruder_message(encrypt(triple(b,X0,X1),at)) | ~a_nonce(X0) | message(sent(t,b,triple(encrypt(quadruple(a,X0,generate_key(X0),X1),bt),encrypt(triple(b,generate_key(X0),X1),at),X2))) | ~intruder_message(X2)).

cnf(u243,axiom,
    ~intruder_message(encrypt(triple(a,X0,X1),at)) | ~a_nonce(X0) | message(sent(t,a,triple(encrypt(quadruple(a,X0,generate_key(X0),X1),at),encrypt(triple(a,generate_key(X0),X1),at),X2))) | ~intruder_message(X2)).

cnf(u159,axiom,
    ~intruder_message(encrypt(quadruple(b,an_a_nonce,X2,X3),at)) | ~intruder_message(X1) | ~intruder_message(X0) | message(sent(a,b,pair(X0,encrypt(X1,X2))))).

cnf(u85,axiom,
    ~intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X0)).

cnf(u86,axiom,
    ~intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X1)).

cnf(u87,axiom,
    ~intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X2)).

cnf(u88,axiom,
    ~intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X3)).

cnf(u80,axiom,
    ~intruder_message(pair(X0,X1)) | intruder_message(X0)).

cnf(u81,axiom,
    ~intruder_message(pair(X0,X1)) | intruder_message(X1)).

cnf(u144,axiom,
    ~intruder_message(pair(X1,X0)) | message(sent(b,t,triple(b,generate_b_nonce(X0),encrypt(triple(X1,X0,generate_expiration_time(X0)),bt)))) | ~party_of_protocol(X1) | ~fresh_to_b(X0)).

cnf(u99,axiom,
    a_nonce(generate_b_nonce(X0))).

cnf(u98,axiom,
    a_nonce(generate_expiration_time(X0))).

cnf(u96,axiom,
    a_nonce(an_a_nonce)).

cnf(u344,axiom,
    ~a_nonce(generate_key(X0)) | ~a_nonce(X0) | ~fresh_to_b(X0) | ~intruder_message(X0) | message(sent(t,a,triple(encrypt(quadruple(b,generate_key(X0),generate_key(generate_key(X0)),generate_expiration_time(X0)),at),encrypt(triple(a,generate_key(generate_key(X0)),generate_expiration_time(X0)),bt),X1))) | ~intruder_message(X1)).

cnf(u345,axiom,
    ~a_nonce(generate_key(X0)) | ~a_nonce(X0) | ~fresh_to_b(X0) | ~intruder_message(X0) | message(sent(t,b,triple(encrypt(quadruple(b,generate_key(X0),generate_key(generate_key(X0)),generate_expiration_time(X0)),bt),encrypt(triple(b,generate_key(generate_key(X0)),generate_expiration_time(X0)),bt),X1))) | ~intruder_message(X1)).

cnf(u100,axiom,
    ~a_nonce(X0) | ~a_key(X0)).

cnf(u76,axiom,
    t_holds(key(bt,b))).

cnf(u75,axiom,
    t_holds(key(at,a))).

cnf(u78,axiom,
    ~t_holds(key(X6,X2)) | ~a_nonce(X3) | message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))) | ~t_holds(key(X5,X0)) | ~message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5))))).

cnf(u150,axiom,
    ~t_holds(key(X3,X1)) | message(sent(t,a,triple(encrypt(quadruple(X1,X0,generate_key(X0),X2),at),encrypt(triple(a,generate_key(X0),X2),X3),X4))) | ~a_nonce(X0) | ~message(sent(X1,t,triple(X1,X4,encrypt(triple(a,X0,X2),X3))))).

cnf(u151,axiom,
    ~t_holds(key(X8,X6)) | message(sent(t,b,triple(encrypt(quadruple(X6,X5,generate_key(X5),X7),bt),encrypt(triple(b,generate_key(X5),X7),X8),X9))) | ~a_nonce(X5) | ~message(sent(X6,t,triple(X6,X9,encrypt(triple(b,X5,X7),X8))))).

cnf(u101,axiom,
    a_key(generate_key(X0))).

cnf(u108,axiom,
    ~a_key(generate_b_nonce(X1))).

cnf(u107,axiom,
    ~a_key(generate_expiration_time(X0))).

cnf(u106,axiom,
    ~a_key(an_a_nonce)).

cnf(u112,axiom,
    fresh_to_b(generate_intruder_nonce(X1)) | ~fresh_intruder_nonce(X1)).

cnf(u109,axiom,
    fresh_to_b(an_intruder_nonce)).

cnf(u73,axiom,
    fresh_to_b(an_a_nonce)).

cnf(u264,axiom,
    ~fresh_to_b(encrypt(X0,generate_key(an_a_nonce))) | ~intruder_message(X0) | message(sent(b,t,triple(b,generate_b_nonce(encrypt(X0,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X0,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X0,generate_key(an_a_nonce)))),bt))))).

cnf(u268,axiom,
    ~fresh_to_b(encrypt(X0,generate_key(an_a_nonce))) | ~intruder_message(X1) | message(sent(b,t,triple(b,generate_b_nonce(encrypt(X0,generate_key(an_a_nonce))),encrypt(triple(X1,encrypt(X0,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X0,generate_key(an_a_nonce)))),bt)))) | ~party_of_protocol(X1) | ~intruder_message(X0)).

cnf(u70,axiom,
    a_stored(pair(b,an_a_nonce))).

cnf(u71,axiom,
    ~a_stored(pair(X4,X5)) | message(sent(a,X4,pair(X3,encrypt(X0,X2)))) | ~message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0)))).

cnf(u153,axiom,
    message(sent(b,t,triple(b,generate_b_nonce(X0),encrypt(triple(X1,X0,generate_expiration_time(X0)),bt)))) | ~party_of_protocol(X1) | ~fresh_to_b(X0) | ~intruder_message(X0) | ~intruder_message(X1)).

cnf(u143,axiom,
    message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))).

cnf(u257,axiom,
    message(sent(a,b,pair(X1,encrypt(X0,generate_key(an_a_nonce))))) | ~intruder_message(X1) | ~intruder_message(X0)).

cnf(u347,axiom,
    message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X0,generate_key(an_a_nonce))))) | ~intruder_message(X0)).

cnf(u220,axiom,
    message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))))).

cnf(u69,axiom,
    message(sent(a,b,pair(a,an_a_nonce)))).

cnf(u343,axiom,
    message(sent(t,b,triple(encrypt(quadruple(b,X0,generate_key(X0),generate_expiration_time(X0)),bt),encrypt(triple(b,generate_key(X0),generate_expiration_time(X0)),bt),X1))) | ~a_nonce(X0) | ~intruder_message(X1) | ~intruder_message(X0) | ~fresh_to_b(X0)).

cnf(u330,axiom,
    message(sent(t,a,triple(encrypt(quadruple(b,X2,generate_key(X2),generate_expiration_time(X2)),at),encrypt(triple(a,generate_key(X2),generate_expiration_time(X2)),bt),X3))) | ~a_nonce(X2) | ~intruder_message(X3) | ~intruder_message(X2) | ~fresh_to_b(X2)).

cnf(u320,axiom,
    message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X0))) | ~intruder_message(X0)).

cnf(u217,axiom,
    message(sent(t,b,triple(encrypt(quadruple(b,X0,generate_key(X0),generate_expiration_time(X0)),bt),encrypt(triple(b,generate_key(X0),generate_expiration_time(X0)),bt),generate_b_nonce(X0)))) | ~a_nonce(X0) | ~fresh_to_b(X0) | ~intruder_message(X0)).

cnf(u210,axiom,
    message(sent(t,a,triple(encrypt(quadruple(b,X0,generate_key(X0),generate_expiration_time(X0)),at),encrypt(triple(a,generate_key(X0),generate_expiration_time(X0)),bt),generate_b_nonce(X0)))) | ~a_nonce(X0) | ~fresh_to_b(X0) | ~intruder_message(X0)).

cnf(u188,axiom,
    message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce))))).

cnf(u93,axiom,
    message(sent(X1,X2,X0)) | ~party_of_protocol(X2) | ~party_of_protocol(X1) | ~intruder_message(X0)).

cnf(u161,axiom,
    ~message(sent(b,t,triple(b,X5,encrypt(triple(b,X3,X4),bt)))) | ~a_nonce(X3) | message(sent(t,b,triple(encrypt(quadruple(b,X3,generate_key(X3),X4),bt),encrypt(triple(b,generate_key(X3),X4),bt),X5)))).

cnf(u158,axiom,
    ~message(sent(b,t,triple(b,X5,encrypt(triple(a,X3,X4),bt)))) | ~a_nonce(X3) | message(sent(t,a,triple(encrypt(quadruple(b,X3,generate_key(X3),X4),at),encrypt(triple(a,generate_key(X3),X4),bt),X5)))).

cnf(u160,axiom,
    ~message(sent(a,t,triple(a,X2,encrypt(triple(b,X0,X1),at)))) | ~a_nonce(X0) | message(sent(t,b,triple(encrypt(quadruple(a,X0,generate_key(X0),X1),bt),encrypt(triple(b,generate_key(X0),X1),at),X2)))).

cnf(u157,axiom,
    ~message(sent(a,t,triple(a,X2,encrypt(triple(a,X0,X1),at)))) | ~a_nonce(X0) | message(sent(t,a,triple(encrypt(quadruple(a,X0,generate_key(X0),X1),at),encrypt(triple(a,generate_key(X0),X1),at),X2)))).

cnf(u146,axiom,
    ~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X2,X3),at),X0,X1))) | message(sent(a,b,pair(X0,encrypt(X1,X2))))).

cnf(u74,axiom,
    ~message(sent(X0,b,pair(X0,X1))) | ~fresh_to_b(X1) | message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt))))).

cnf(u79,axiom,
    ~message(sent(X0,X1,X2)) | intruder_message(X2)).

cnf(u77,axiom,
    party_of_protocol(t)).

cnf(u72,axiom,
    party_of_protocol(b)).

cnf(u68,axiom,
    party_of_protocol(a)).

% (11974)# SZS output end Saturation.

Sample solution for BOO001-1

% SZS output start Proof for BOO001-1
fof(f209,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f204])).
fof(f204,plain,(
  a != a),
  inference(superposition,[],[f6,f146])).
fof(f146,plain,(
  ( ! [X21] : (inverse(inverse(X21)) = X21) )),
  inference(superposition,[],[f130,f5])).
fof(f5,axiom,(
  ( ! [X2,X3] : (multiply(X2,X3,inverse(X3)) = X2) )),
  file('/home/filip/TPTP-v7.5.0/Problems/BOO/BOO001-1.p',unknown)).
fof(f130,plain,(
  ( ! [X31,X32] : (multiply(X32,inverse(X32),X31) = X31) )),
  inference(superposition,[],[f32,f5])).
fof(f32,plain,(
  ( ! [X3,X4,X5] : (multiply(X5,X3,X4) = multiply(X3,X4,multiply(X5,X3,X4))) )),
  inference(superposition,[],[f7,f2])).
fof(f2,axiom,(
  ( ! [X2,X3] : (multiply(X3,X2,X2) = X2) )),
  file('/home/filip/TPTP-v7.5.0/Problems/BOO/BOO001-1.p',unknown)).
fof(f7,plain,(
  ( ! [X2,X3,X0,X1] : (multiply(X0,X1,multiply(X1,X2,X3)) = multiply(X1,X2,multiply(X0,X1,X3))) )),
  inference(superposition,[],[f1,f2])).
fof(f1,axiom,(
  ( ! [X2,X3,X0,X1,X4] : (multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4))) )),
  file('/home/filip/TPTP-v7.5.0/Problems/BOO/BOO001-1.p',unknown)).
fof(f6,axiom,(
  a != inverse(inverse(a))),
  file('/home/filip/TPTP-v7.5.0/Problems/BOO/BOO001-1.p',unknown)).
% SZS output end Proof for BOO001-1

Toma 0.2

Sample solution for BOO003-4

% SZS status Unsatisfiable
% SZS output start Proof
To show the unsatisfiability,
it suffices to show that multiply(a,a) = a (skolemized goal) is valid under the axioms.
This is an equational proof:
0: add(X,Y) = add(Y,X).
Proof: Axiom.

2: add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)).
Proof: Axiom.

3: multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)).
Proof: Axiom.

4: add(X,additive_identity) = X.
Proof: Axiom.

5: multiply(X,multiplicative_identity) = X.
Proof: Axiom.

6: add(X,inverse(X)) = multiplicative_identity.
Proof: Axiom.

7: multiply(X,inverse(X)) = additive_identity.
Proof: Axiom.

8: multiply(X,add(Y,Z)) = multiply(multiply(add(X,X),add(X,Y)),add(multiply(X,Y),Z)).
Proof: Rewrite equation 3,
               lhs with equations []
               rhs with equations [2,0,2].

10: X1 = add(additive_identity,X1).
Proof: A critical pair between equations 4 and 0.

11: multiply(add(X0,X3),add(X0,multiplicative_identity)) = add(X0,X3).
Proof: A critical pair between equations 2 and 5.

12: multiply(add(X0,X3),add(X0,inverse(X3))) = add(X0,additive_identity).
Proof: A critical pair between equations 2 and 7.

14: multiply(X3,add(multiplicative_identity,Z2)) = multiply(multiply(add(X3,X3),add(X3,multiplicative_identity)),add(X3,Z2)).
Proof: A critical pair between equations 8 and 5.

19: multiply(X3,add(inverse(X3),Z2)) = multiply(multiply(add(X3,X3),add(X3,inverse(X3))),add(additive_identity,Z2)).
Proof: A critical pair between equations 8 and 7.

20: multiply(X3,add(inverse(X3),Z2)) = multiply(multiply(add(X3,X3),multiplicative_identity),add(multiply(X3,inverse(X3)),Z2)).
Proof: A critical pair between equations 8 and 6.

21: multiply(add(X0,X3),add(X0,inverse(X3))) = X0.
Proof: Rewrite equation 12,
               lhs with equations []
               rhs with equations [4].

22: multiply(X3,add(multiplicative_identity,Z2)) = multiply(add(X3,X3),add(X3,Z2)).
Proof: Rewrite equation 14,
               lhs with equations []
               rhs with equations [11].

27: multiply(X3,add(inverse(X3),Z2)) = multiply(X3,Z2).
Proof: Rewrite equation 19,
               lhs with equations []
               rhs with equations [21,10].

28: multiply(X3,Z2) = multiply(add(X3,X3),add(multiply(X3,inverse(X3)),Z2)).
Proof: Rewrite equation 20,
               lhs with equations [27]
               rhs with equations [5].

29: inverse(additive_identity) = multiplicative_identity.
Proof: A critical pair between equations 10 and 6.

30: X2 = multiply(add(X2,X2),multiplicative_identity).
Proof: A critical pair between equations 21 and 6.

37: X2 = multiply(X2,add(X2,inverse(additive_identity))).
Proof: A critical pair between equations 21 and 4.

41: multiply(X3,Z2) = multiply(add(X3,X3),Z2).
Proof: Rewrite equation 28,
               lhs with equations []
               rhs with equations [7,10].

44: multiply(X3,add(multiplicative_identity,Z2)) = multiply(X3,add(X3,Z2)).
Proof: Rewrite equation 22,
               lhs with equations []
               rhs with equations [41].

48: X2 = add(X2,X2).
Proof: Rewrite equation 30,
               lhs with equations []
               rhs with equations [5].

51: X2 = multiply(X2,add(X2,multiplicative_identity)).
Proof: Rewrite equation 37,
               lhs with equations []
               rhs with equations [29].

57: X1 = multiply(X1,add(multiplicative_identity,X1)).
Proof: A critical pair between equations 51 and 0.

59: multiply(X22,add(multiplicative_identity,X22)) = multiply(X22,X22).
Proof: A critical pair between equations 44 and 48.

68: X1 = multiply(X1,X1).
Proof: Rewrite equation 57,
               lhs with equations []
               rhs with equations [59].

70: multiply(a,a) = a.
Proof: Rewrite lhs with equations [68]
               rhs with equations [].

% SZS output end Proof

Twee 2.4

Sample solution for BOO001-1

% SZS status Unsatisfiable

% SZS output start Proof
Axiom 1 (ternary_multiply_1): multiply(X, Y, Y) = Y.
Axiom 2 (right_inverse): multiply(X, Y, inverse(Y)) = X.
Axiom 3 (associativity): multiply(multiply(X, Y, Z), W, multiply(X, Y, V)) = multiply(X, Y, multiply(Z, W, V)).

Goal 1 (prove_inverse_is_self_cancelling): inverse(inverse(a)) = a.
Proof:
  inverse(inverse(a))
= { by axiom 2 (right_inverse) R->L }
  multiply(inverse(inverse(a)), a, inverse(a))
= { by axiom 1 (ternary_multiply_1) R->L }
  multiply(inverse(inverse(a)), a, multiply(a, inverse(a), inverse(a)))
= { by axiom 3 (associativity) R->L }
  multiply(multiply(inverse(inverse(a)), a, a), inverse(a), multiply(inverse(inverse(a)), a, inverse(a)))
= { by axiom 1 (ternary_multiply_1) }
  multiply(a, inverse(a), multiply(inverse(inverse(a)), a, inverse(a)))
= { by axiom 2 (right_inverse) }
  multiply(a, inverse(a), inverse(inverse(a)))
= { by axiom 2 (right_inverse) }
  a
% SZS output end Proof

Twee 2.4

Sample solution for BOO001-1

% SZS output start Proof
Axiom 1 (ternary_multiply_1): multiply(X, Y, Y) = Y.
Axiom 2 (right_inverse): multiply(X, Y, inverse(Y)) = X.
Axiom 3 (associativity): multiply(multiply(X, Y, Z), W, multiply(X, Y, V)) = multiply(X, Y, multiply(Z, W, V)).

Goal 1 (prove_inverse_is_self_cancelling): inverse(inverse(a)) = a.
Proof:
  inverse(inverse(a))
= { by axiom 2 (right_inverse) R->L }
  multiply(inverse(inverse(a)), a, inverse(a))
= { by axiom 1 (ternary_multiply_1) R->L }
  multiply(inverse(inverse(a)), a, multiply(a, inverse(a), inverse(a)))
= { by axiom 3 (associativity) R->L }
  multiply(multiply(inverse(inverse(a)), a, a), inverse(a), multiply(inverse(inverse(a)), a, inverse(a)))
= { by axiom 1 (ternary_multiply_1) }
  multiply(a, inverse(a), multiply(inverse(inverse(a)), a, inverse(a)))
= { by axiom 2 (right_inverse) }
  multiply(a, inverse(a), inverse(inverse(a)))
= { by axiom 2 (right_inverse) }
  a
% SZS output end Proof

Vampire 4.5

Sample solution for DAT013=1

% SZS output start Proof for DAT013=1
tff(type_def_5, type, array: $tType).
tff(func_def_0, type, read: (array * $int) > $int).
tff(func_def_1, type, write: (array * $int * $int) > array).
tff(func_def_7, type, sK0: array).
tff(func_def_8, type, sK1: $int).
tff(func_def_9, type, sK2: $int).
tff(func_def_10, type, sK3: $int).
tff(f2323,plain,(
  $false),
  inference(subsumption_resolution,[],[f2316,f143])).
tff(f143,plain,(
  $less(sK3,sK1)),
  inference(subsumption_resolution,[],[f140,f29])).
tff(f29,plain,(
  ~$less(sK2,sK3)),
  inference(cnf_transformation,[],[f24])).
tff(f24,plain,(
  (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f23,f22])).
tff(f22,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1))) => (? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)))),
  introduced(choice_axiom,[])).
tff(f23,plain,(
  ? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) => (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3)))),
  introduced(choice_axiom,[])).
tff(f21,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1)))),
  inference(rectify,[],[f20])).
tff(f20,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & ~$less(X2,X4) & ~$less(X4,$sum(X1,3))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | $less(X2,X3) | $less(X3,X1)))),
  inference(flattening,[],[f19])).
tff(f19,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & (~$less(X2,X4) & ~$less(X4,$sum(X1,3)))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | ($less(X2,X3) | $less(X3,X1))))),
  inference(ennf_transformation,[],[f5])).
tff(f5,plain,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : ((~$less(X2,X3) & ~$less(X3,X1)) => $less(0,read(X0,X3))) => ! [X4 : $int] : ((~$less(X2,X4) & ~$less(X4,$sum(X1,3))) => $less(0,read(X0,X4))))),
  inference(theory_normalization,[],[f4])).
tff(f4,negated_conjecture,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
  inference(negated_conjecture,[],[f3])).
tff(f3,conjecture,(
  ! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
  file('Problems/DAT/DAT013=1.p',unknown)).
tff(f140,plain,(
  $less(sK2,sK3) | $less(sK3,sK1)),
  inference(resolution,[],[f27,f30])).
tff(f30,plain,(
  ~$less(0,read(sK0,sK3))),
  inference(cnf_transformation,[],[f24])).
tff(f27,plain,(
  ( ! [X4:$int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)) )),
  inference(cnf_transformation,[],[f24])).
tff(f2316,plain,(
  ~$less(sK3,sK1)),
  inference(backward_demodulation,[],[f31,f2315])).
tff(f2315,plain,(
  sK1 = $sum(3,sK1)),
  inference(subsumption_resolution,[],[f2282,f1467])).
tff(f1467,plain,(
  ( ! [X3:$int] : (~$less($sum(3,X3),X3)) )),
  inference(resolution,[],[f1229,f125])).
tff(f125,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($less($sum(X6,X5),$sum(X5,X4)) | ~$less(X6,X4)) )),
  inference(superposition,[],[f14,f6])).
tff(f6,plain,(
  ( ! [X0:$int,X1:$int] : ($sum(X0,X1) = $sum(X1,X0)) )),
  introduced(theory_axiom,[])).
tff(f14,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
  introduced(theory_axiom,[])).
tff(f1229,plain,(
  ( ! [X8:$int] : (~$less($sum(X8,3),X8)) )),
  inference(evaluation,[],[f1219])).
tff(f1219,plain,(
  ( ! [X8:$int] : (~$less($sum($sum(X8,1),2),X8)) )),
  inference(resolution,[],[f1070,f73])).
tff(f73,plain,(
  ( ! [X4:$int,X3:$int] : ($less(X3,$sum(X4,1)) | ~$less(X3,X4)) )),
  inference(resolution,[],[f12,f43])).
tff(f43,plain,(
  ( ! [X0:$int] : ($less(X0,$sum(X0,1))) )),
  inference(resolution,[],[f15,f11])).
tff(f11,plain,(
  ( ! [X0:$int] : (~$less(X0,X0)) )),
  introduced(theory_axiom,[])).
tff(f15,plain,(
  ( ! [X0:$int,X1:$int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
  introduced(theory_axiom,[])).
tff(f12,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
  introduced(theory_axiom,[])).
tff(f1070,plain,(
  ( ! [X8:$int] : (~$less($sum(X8,2),X8)) )),
  inference(evaluation,[],[f1060])).
tff(f1060,plain,(
  ( ! [X8:$int] : (~$less($sum($sum(X8,1),1),X8)) )),
  inference(resolution,[],[f986,f73])).
tff(f986,plain,(
  ( ! [X6:$int] : (~$less($sum(X6,1),X6)) )),
  inference(resolution,[],[f73,f11])).
tff(f2282,plain,(
  $less($sum(3,sK1),sK1) | sK1 = $sum(3,sK1)),
  inference(resolution,[],[f742,f31])).
tff(f742,plain,(
  ( ! [X56:$int] : ($less(sK3,X56) | $less(X56,sK1) | sK1 = X56) )),
  inference(resolution,[],[f84,f143])).
tff(f84,plain,(
  ( ! [X4:$int,X5:$int,X3:$int] : (~$less(X5,X4) | X3 = X4 | $less(X3,X4) | $less(X5,X3)) )),
  inference(resolution,[],[f13,f12])).
tff(f13,plain,(
  ( ! [X0:$int,X1:$int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
  introduced(theory_axiom,[])).
tff(f31,plain,(
  ~$less(sK3,$sum(3,sK1))),
  inference(forward_demodulation,[],[f28,f6])).
tff(f28,plain,(
  ~$less(sK3,$sum(sK1,3))),
  inference(cnf_transformation,[],[f24])).
% SZS output end Proof for DAT013=1

Vampire 4.6

Sample solution for SEU140+2

% SZS status Theorem for SEU140+2
% SZS output start Proof for SEU140+2
fof(f746,plain,(
  $false),
  inference(subsumption_resolution,[],[f697,f465])).
fof(f465,plain,(
  in(sK10(sK6,sK8),sK7)),
  inference(unit_resulting_resolution,[],[f176,f420,f249])).
fof(f249,plain,(
  ( ! [X0 : $i,X3 : $i,X1 : $i] : (in(X3,X1) | ~in(X3,X0) | ~subset(X0,X1)) )),
  inference(cnf_transformation,[],[f170])).
fof(f170,plain,(
  ! [X0,X1] : ((subset(X0,X1) | (~in(sK15(X0,X1),X1) & in(sK15(X0,X1),X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f168,f169])).
fof(f169,plain,(
  ! [X0,X1] : (? [X2] : (~in(X2,X1) & in(X2,X0)) => (~in(sK15(X0,X1),X1) & in(sK15(X0,X1),X0)))),
  introduced(choice_axiom,[])).
fof(f168,plain,(
  ! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
  inference(rectify,[],[f167])).
fof(f167,plain,(
  ! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X2] : (in(X2,X1) | ~in(X2,X0)) | ~subset(X0,X1)))),
  inference(nnf_transformation,[],[f115])).
fof(f115,plain,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X1) | ~in(X2,X0)))),
  inference(ennf_transformation,[],[f91])).
fof(f91,plain,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
  inference(flattening,[],[f8])).
fof(f8,axiom,(
  ! [X0] : ! [X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
  file('/tmp/SystemOnTPTP17979/SEU140+2.tptp',d3_tarski)).
fof(f420,plain,(
  in(sK10(sK6,sK8),sK6)),
  inference(unit_resulting_resolution,[],[f178,f189])).
fof(f189,plain,(
  ( ! [X0 : $i,X1 : $i] : (disjoint(X0,X1) | in(sK10(X0,X1),X0)) )),
  inference(cnf_transformation,[],[f133])).
fof(f133,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK10(X0,X1),X1) & in(sK10(X0,X1),X0)) | disjoint(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f101,f132])).
fof(f132,plain,(
  ! [X0,X1] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK10(X0,X1),X1) & in(sK10(X0,X1),X0)))),
  introduced(choice_axiom,[])).
fof(f101,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
  inference(ennf_transformation,[],[f68])).
fof(f68,plain,(
  ! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
  inference(flattening,[],[f67])).
fof(f67,plain,(
  ! [X0] : ! [X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
  inference(rectify,[],[f43])).
fof(f43,axiom,(
  ! [X0] : ! [X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
  file('/tmp/SystemOnTPTP17979/SEU140+2.tptp',t3_xboole_0)).
fof(f178,plain,(
  ~disjoint(sK6,sK8)),
  inference(cnf_transformation,[],[f129])).
fof(f129,plain,(
  ~disjoint(sK6,sK8) & disjoint(sK7,sK8) & subset(sK6,sK7)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f98,f128])).
fof(f128,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK6,sK8) & disjoint(sK7,sK8) & subset(sK6,sK7))),
  introduced(choice_axiom,[])).
fof(f98,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
  inference(flattening,[],[f97])).
fof(f97,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
  inference(ennf_transformation,[],[f58])).
fof(f58,plain,(
  ~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  inference(flattening,[],[f52])).
fof(f52,negated_conjecture,(
  ~! [X0] : ! [X1] : ! [X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  inference(negated_conjecture,[],[f51])).
fof(f51,conjecture,(
  ! [X0] : ! [X1] : ! [X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  file('/tmp/SystemOnTPTP17979/SEU140+2.tptp',t63_xboole_1)).
fof(f176,plain,(
  subset(sK6,sK7)),
  inference(cnf_transformation,[],[f129])).
fof(f697,plain,(
  ~in(sK10(sK6,sK8),sK7)),
  inference(unit_resulting_resolution,[],[f429,f287,f191])).
fof(f191,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
  inference(cnf_transformation,[],[f133])).
fof(f287,plain,(
  disjoint(sK8,sK7)),
  inference(unit_resulting_resolution,[],[f177,f207])).
fof(f207,plain,(
  ( ! [X0 : $i,X1 : $i] : (disjoint(X1,X0) | ~disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f114])).
fof(f114,plain,(
  ! [X0,X1] : (disjoint(X1,X0) | ~disjoint(X0,X1))),
  inference(ennf_transformation,[],[f81])).
fof(f81,plain,(
  ! [X0,X1] : (disjoint(X0,X1) => disjoint(X1,X0))),
  inference(flattening,[],[f27])).
fof(f27,axiom,(
  ! [X0] : ! [X1] : (disjoint(X0,X1) => disjoint(X1,X0))),
  file('/tmp/SystemOnTPTP17979/SEU140+2.tptp',symmetry_r1_xboole_0)).
fof(f177,plain,(
  disjoint(sK7,sK8)),
  inference(cnf_transformation,[],[f129])).
fof(f429,plain,(
  in(sK10(sK6,sK8),sK8)),
  inference(unit_resulting_resolution,[],[f178,f190])).
fof(f190,plain,(
  ( ! [X0 : $i,X1 : $i] : (disjoint(X0,X1) | in(sK10(X0,X1),X1)) )),
  inference(cnf_transformation,[],[f133])).
% SZS output end Proof for SEU140+2

Sample solution for NLP042+1

% SZS status CounterSatisfiable for NLP042+1
% # SZS output start Saturation.
tff(u703,negated_conjecture,
    ((~~woman(sK0,sK3)) | ~woman(sK0,sK3))).

tff(u702,negated_conjecture,
    ((~~woman(sK0,sK4)) | ~woman(sK0,sK4))).

tff(u701,negated_conjecture,
    ((~~woman(sK0,sK2)) | ~woman(sK0,sK2))).

tff(u700,axiom,
    ((~(![X1, X0] : ((~woman(X0,X1) | ~unisex(X0,X1))))) | (![X1, X0] : ((~woman(X0,X1) | ~unisex(X0,X1)))))).

tff(u699,negated_conjecture,
    ((~woman(sK0,sK1)) | woman(sK0,sK1))).

tff(u698,axiom,
    ((~(![X1, X0] : ((~female(X0,X1) | ~unisex(X0,X1))))) | (![X1, X0] : ((~female(X0,X1) | ~unisex(X0,X1)))))).

tff(u697,axiom,
    ((~(![X1, X0] : ((female(X0,X1) | ~woman(X0,X1))))) | (![X1, X0] : ((female(X0,X1) | ~woman(X0,X1)))))).

tff(u696,negated_conjecture,
    ((~~human_person(sK0,sK2)) | ~human_person(sK0,sK2))).

tff(u695,negated_conjecture,
    ((~~human_person(sK0,sK3)) | ~human_person(sK0,sK3))).

tff(u694,negated_conjecture,
    ((~~human_person(sK0,sK4)) | ~human_person(sK0,sK4))).

tff(u693,axiom,
    ((~(![X1, X0] : ((human_person(X0,X1) | ~woman(X0,X1))))) | (![X1, X0] : ((human_person(X0,X1) | ~woman(X0,X1)))))).

tff(u692,negated_conjecture,
    ((~~animate(sK0,sK3)) | ~animate(sK0,sK3))).

tff(u691,axiom,
    ((~(![X1, X0] : ((animate(X0,X1) | ~human_person(X0,X1))))) | (![X1, X0] : ((animate(X0,X1) | ~human_person(X0,X1)))))).

tff(u690,negated_conjecture,
    ((~~human(sK0,sK2)) | ~human(sK0,sK2))).

tff(u689,axiom,
    ((~(![X1, X0] : ((human(X0,X1) | ~human_person(X0,X1))))) | (![X1, X0] : ((human(X0,X1) | ~human_person(X0,X1)))))).

tff(u688,negated_conjecture,
    ((~~organism(sK0,sK3)) | ~organism(sK0,sK3))).

tff(u687,negated_conjecture,
    ((~~organism(sK0,sK4)) | ~organism(sK0,sK4))).

tff(u686,negated_conjecture,
    ((~~organism(sK0,sK2)) | ~organism(sK0,sK2))).

tff(u685,axiom,
    ((~(![X1, X0] : ((organism(X0,X1) | ~human_person(X0,X1))))) | (![X1, X0] : ((organism(X0,X1) | ~human_person(X0,X1)))))).

tff(u684,negated_conjecture,
    ((~~living(sK0,sK3)) | ~living(sK0,sK3))).

tff(u683,axiom,
    ((~(![X1, X0] : ((living(X0,X1) | ~organism(X0,X1))))) | (![X1, X0] : ((living(X0,X1) | ~organism(X0,X1)))))).

tff(u682,negated_conjecture,
    ((~~entity(sK0,sK4)) | ~entity(sK0,sK4))).

tff(u681,negated_conjecture,
    ((~~entity(sK0,sK2)) | ~entity(sK0,sK2))).

tff(u680,axiom,
    ((~(![X1, X0] : ((entity(X0,X1) | ~organism(X0,X1))))) | (![X1, X0] : ((entity(X0,X1) | ~organism(X0,X1)))))).

tff(u679,negated_conjecture,
    ((~entity(sK0,sK3)) | entity(sK0,sK3))).

tff(u678,axiom,
    ((~(![X1, X0] : ((~mia_forename(X0,X1) | abstraction(X0,X1))))) | (![X1, X0] : ((~mia_forename(X0,X1) | abstraction(X0,X1)))))).

tff(u677,negated_conjecture,
    ((~mia_forename(sK0,sK2)) | mia_forename(sK0,sK2))).

tff(u676,axiom,
    ((~(![X1, X0] : ((~forename(X0,X1) | abstraction(X0,X1))))) | (![X1, X0] : ((~forename(X0,X1) | abstraction(X0,X1)))))).

tff(u675,negated_conjecture,
    ((~forename(sK0,sK2)) | forename(sK0,sK2))).

tff(u674,axiom,
    ((~(![X1, X0] : ((forename(X0,X1) | ~mia_forename(X0,X1))))) | (![X1, X0] : ((forename(X0,X1) | ~mia_forename(X0,X1)))))).

tff(u673,axiom,
    ((~(![X1, X0] : ((~abstraction(X0,X1) | ~entity(X0,X1))))) | (![X1, X0] : ((~abstraction(X0,X1) | ~entity(X0,X1)))))).

tff(u672,axiom,
    ((~(![X1, X0] : ((~abstraction(X0,X1) | nonhuman(X0,X1))))) | (![X1, X0] : ((~abstraction(X0,X1) | nonhuman(X0,X1)))))).

tff(u671,negated_conjecture,
    ((~~abstraction(sK0,sK4)) | ~abstraction(sK0,sK4))).

tff(u670,negated_conjecture,
    ((~~abstraction(sK0,sK1)) | ~abstraction(sK0,sK1))).

tff(u669,negated_conjecture,
    ((~abstraction(sK0,sK2)) | abstraction(sK0,sK2))).

tff(u668,negated_conjecture,
    ((~~unisex(sK0,sK1)) | ~unisex(sK0,sK1))).

tff(u667,axiom,
    ((~(![X1, X0] : ((unisex(X0,X1) | ~abstraction(X0,X1))))) | (![X1, X0] : ((unisex(X0,X1) | ~abstraction(X0,X1)))))).

tff(u666,negated_conjecture,
    ((~unisex(sK0,sK3)) | unisex(sK0,sK3))).

tff(u665,negated_conjecture,
    ((~unisex(sK0,sK4)) | unisex(sK0,sK4))).

tff(u664,negated_conjecture,
    ((~~general(sK0,sK4)) | ~general(sK0,sK4))).

tff(u663,axiom,
    ((~(![X1, X0] : ((~general(X0,X1) | ~entity(X0,X1))))) | (![X1, X0] : ((~general(X0,X1) | ~entity(X0,X1)))))).

tff(u662,axiom,
    ((~(![X1, X0] : ((general(X0,X1) | ~abstraction(X0,X1))))) | (![X1, X0] : ((general(X0,X1) | ~abstraction(X0,X1)))))).

tff(u661,axiom,
    ((~(![X1, X0] : ((~nonhuman(X0,X1) | ~human(X0,X1))))) | (![X1, X0] : ((~nonhuman(X0,X1) | ~human(X0,X1)))))).

tff(u660,negated_conjecture,
    ((~nonhuman(sK0,sK2)) | nonhuman(sK0,sK2))).

tff(u659,axiom,
    ((~(![X1, X0] : ((~relation(X0,X1) | abstraction(X0,X1))))) | (![X1, X0] : ((~relation(X0,X1) | abstraction(X0,X1)))))).

tff(u658,axiom,
    ((~(![X1, X0] : ((relation(X0,X1) | ~forename(X0,X1))))) | (![X1, X0] : ((relation(X0,X1) | ~forename(X0,X1)))))).

tff(u657,axiom,
    ((~(![X1, X0] : ((~relname(X0,X1) | relation(X0,X1))))) | (![X1, X0] : ((~relname(X0,X1) | relation(X0,X1)))))).

tff(u656,axiom,
    ((~(![X1, X0] : ((relname(X0,X1) | ~forename(X0,X1))))) | (![X1, X0] : ((relname(X0,X1) | ~forename(X0,X1)))))).

tff(u655,axiom,
    ((~(![X1, X0] : ((~object(X0,X1) | unisex(X0,X1))))) | (![X1, X0] : ((~object(X0,X1) | unisex(X0,X1)))))).

tff(u654,axiom,
    ((~(![X1, X0] : ((~object(X0,X1) | entity(X0,X1))))) | (![X1, X0] : ((~object(X0,X1) | entity(X0,X1)))))).

tff(u653,axiom,
    ((~(![X1, X0] : ((~object(X0,X1) | nonliving(X0,X1))))) | (![X1, X0] : ((~object(X0,X1) | nonliving(X0,X1)))))).

tff(u652,negated_conjecture,
    ((~object(sK0,sK3)) | object(sK0,sK3))).

tff(u651,axiom,
    ((~(![X1, X0] : ((~nonliving(X0,X1) | ~living(X0,X1))))) | (![X1, X0] : ((~nonliving(X0,X1) | ~living(X0,X1)))))).

tff(u650,axiom,
    ((~(![X1, X0] : ((~nonliving(X0,X1) | ~animate(X0,X1))))) | (![X1, X0] : ((~nonliving(X0,X1) | ~animate(X0,X1)))))).

tff(u649,negated_conjecture,
    ((~nonliving(sK0,sK3)) | nonliving(sK0,sK3))).

tff(u648,negated_conjecture,
    ((~~existent(sK0,sK4)) | ~existent(sK0,sK4))).

tff(u647,axiom,
    ((~(![X1, X0] : ((existent(X0,X1) | ~entity(X0,X1))))) | (![X1, X0] : ((existent(X0,X1) | ~entity(X0,X1)))))).

tff(u646,axiom,
    ((~(![X1, X0] : ((~specific(X0,X1) | ~general(X0,X1))))) | (![X1, X0] : ((~specific(X0,X1) | ~general(X0,X1)))))).

tff(u645,axiom,
    ((~(![X1, X0] : ((specific(X0,X1) | ~entity(X0,X1))))) | (![X1, X0] : ((specific(X0,X1) | ~entity(X0,X1)))))).

tff(u644,negated_conjecture,
    ((~specific(sK0,sK4)) | specific(sK0,sK4))).

tff(u643,axiom,
    ((~(![X1, X0] : ((~substance_matter(X0,X1) | object(X0,X1))))) | (![X1, X0] : ((~substance_matter(X0,X1) | object(X0,X1)))))).

tff(u642,negated_conjecture,
    ((~substance_matter(sK0,sK3)) | substance_matter(sK0,sK3))).

tff(u641,axiom,
    ((~(![X1, X0] : ((~food(X0,X1) | substance_matter(X0,X1))))) | (![X1, X0] : ((~food(X0,X1) | substance_matter(X0,X1)))))).

tff(u640,negated_conjecture,
    ((~food(sK0,sK3)) | food(sK0,sK3))).

tff(u639,axiom,
    ((~(![X1, X0] : ((~beverage(X0,X1) | food(X0,X1))))) | (![X1, X0] : ((~beverage(X0,X1) | food(X0,X1)))))).

tff(u638,negated_conjecture,
    ((~beverage(sK0,sK3)) | beverage(sK0,sK3))).

tff(u637,axiom,
    ((~(![X1, X0] : ((~shake_beverage(X0,X1) | beverage(X0,X1))))) | (![X1, X0] : ((~shake_beverage(X0,X1) | beverage(X0,X1)))))).

tff(u636,negated_conjecture,
    ((~shake_beverage(sK0,sK3)) | shake_beverage(sK0,sK3))).

tff(u635,axiom,
    ((~(![X1, X0] : ((~order(X0,X1) | eventuality(X0,X1))))) | (![X1, X0] : ((~order(X0,X1) | eventuality(X0,X1)))))).

tff(u634,negated_conjecture,
    ((~order(sK0,sK4)) | order(sK0,sK4))).

tff(u633,axiom,
    ((~(![X1, X0] : ((~event(X0,X1) | eventuality(X0,X1))))) | (![X1, X0] : ((~event(X0,X1) | eventuality(X0,X1)))))).

tff(u632,negated_conjecture,
    ((~event(sK0,sK4)) | event(sK0,sK4))).

tff(u631,axiom,
    ((~(![X1, X0] : ((event(X0,X1) | ~order(X0,X1))))) | (![X1, X0] : ((event(X0,X1) | ~order(X0,X1)))))).

tff(u630,axiom,
    ((~(![X1, X0] : ((~eventuality(X0,X1) | unisex(X0,X1))))) | (![X1, X0] : ((~eventuality(X0,X1) | unisex(X0,X1)))))).

tff(u629,axiom,
    ((~(![X1, X0] : ((~eventuality(X0,X1) | specific(X0,X1))))) | (![X1, X0] : ((~eventuality(X0,X1) | specific(X0,X1)))))).

tff(u628,axiom,
    ((~(![X1, X0] : ((~eventuality(X0,X1) | nonexistent(X0,X1))))) | (![X1, X0] : ((~eventuality(X0,X1) | nonexistent(X0,X1)))))).

tff(u627,negated_conjecture,
    ((~eventuality(sK0,sK4)) | eventuality(sK0,sK4))).

tff(u626,axiom,
    ((~(![X1, X0] : ((~nonexistent(X0,X1) | ~existent(X0,X1))))) | (![X1, X0] : ((~nonexistent(X0,X1) | ~existent(X0,X1)))))).

tff(u625,negated_conjecture,
    ((~nonexistent(sK0,sK4)) | nonexistent(sK0,sK4))).

tff(u624,axiom,
    ((~(![X1, X0] : ((~act(X0,X1) | event(X0,X1))))) | (![X1, X0] : ((~act(X0,X1) | event(X0,X1)))))).

tff(u623,axiom,
    ((~(![X1, X0] : ((act(X0,X1) | ~order(X0,X1))))) | (![X1, X0] : ((act(X0,X1) | ~order(X0,X1)))))).

tff(u622,axiom,
    ((~(![X1, X3, X0, X2] : ((~of(X0,X3,X1) | ~forename(X0,X2) | ~of(X0,X2,X1) | ~forename(X0,X3) | (X2 = X3) | ~entity(X0,X1))))) | (![X1, X3, X0, X2] : ((~of(X0,X3,X1) | ~forename(X0,X2) | ~of(X0,X2,X1) | ~forename(X0,X3) | (X2 = X3) | ~entity(X0,X1)))))).

tff(u621,negated_conjecture,
    ((~(![X0] : ((~of(sK0,X0,sK1) | (sK2 = X0) | ~forename(sK0,X0))))) | (![X0] : ((~of(sK0,X0,sK1) | (sK2 = X0) | ~forename(sK0,X0)))))).

tff(u620,negated_conjecture,
    ((~of(sK0,sK2,sK1)) | of(sK0,sK2,sK1))).

tff(u619,axiom,
    ((~(![X1, X3, X0] : ((~nonreflexive(X0,X1) | ~agent(X0,X1,X3) | ~patient(X0,X1,X3))))) | (![X1, X3, X0] : ((~nonreflexive(X0,X1) | ~agent(X0,X1,X3) | ~patient(X0,X1,X3)))))).

tff(u618,negated_conjecture,
    ((~nonreflexive(sK0,sK4)) | nonreflexive(sK0,sK4))).

tff(u617,negated_conjecture,
    ((~~agent(sK0,sK4,sK3)) | ~agent(sK0,sK4,sK3))).

tff(u616,negated_conjecture,
    ((~agent(sK0,sK4,sK1)) | agent(sK0,sK4,sK1))).

tff(u615,negated_conjecture,
    ((~(![X0] : ((~patient(sK0,sK4,X0) | ~agent(sK0,sK4,X0))))) | (![X0] : ((~patient(sK0,sK4,X0) | ~agent(sK0,sK4,X0)))))).

tff(u614,negated_conjecture,
    ((~patient(sK0,sK4,sK3)) | patient(sK0,sK4,sK3))).

% # SZS output end Saturation.

Sample solution for SWV017+1

% SZS status Satisfiable for SWV017+1
% SZS output start FiniteModel for SWV017+1
tff(declare_$i,type,$i:$tType).
tff(declare_$i1,type,at:$i).
tff(declare_$i2,type,t:$i).
tff(finite_domain,axiom,
      ! [X:$i] : (
         X = at | X = t
      ) ).

tff(distinct_domain,axiom,
         at != t
).

tff(declare_bool,type,$o:$tType).
tff(declare_bool1,type,fmb_bool_1:$o).
tff(finite_domain,axiom,
      ! [X:$o] : (
         X = fmb_bool_1
      ) ).

tff(declare_a,type,a:$i).
tff(a_definition,axiom,a = at).
tff(declare_b,type,b:$i).
tff(b_definition,axiom,b = at).
tff(declare_an_a_nonce,type,an_a_nonce:$i).
tff(an_a_nonce_definition,axiom,an_a_nonce = at).
tff(declare_bt,type,bt:$i).
tff(bt_definition,axiom,bt = t).
tff(declare_an_intruder_nonce,type,an_intruder_nonce:$i).
tff(an_intruder_nonce_definition,axiom,an_intruder_nonce = at).
tff(declare_key,type,key: $i * $i > $i).
tff(function_key,axiom,
           key(at,at) = at
         & key(at,t) = at
         & key(t,at) = t
         & key(t,t) = t

).

tff(declare_pair,type,pair: $i * $i > $i).
tff(function_pair,axiom,
           pair(at,at) = at
         & pair(at,t) = t
         & pair(t,at) = t
         & pair(t,t) = t

).

tff(declare_sent,type,sent: $i * $i * $i > $i).
tff(function_sent,axiom,
           sent(at,at,at) = at
         & sent(at,at,t) = t
         & sent(at,t,at) = at
         & sent(at,t,t) = t
         & sent(t,at,at) = at
         & sent(t,at,t) = t
         & sent(t,t,at) = at
         & sent(t,t,t) = t

).

tff(declare_quadruple,type,quadruple: $i * $i * $i * $i > $i).
tff(function_quadruple,axiom,
           quadruple(at,at,at,at) = at
         & quadruple(at,at,at,t) = t
         & quadruple(at,at,t,at) = t
         & quadruple(at,at,t,t) = t
         & quadruple(at,t,at,at) = t
         & quadruple(at,t,at,t) = t
         & quadruple(at,t,t,at) = t
         & quadruple(at,t,t,t) = t
         & quadruple(t,at,at,at) = t
         & quadruple(t,at,at,t) = t
         & quadruple(t,at,t,at) = t
         & quadruple(t,at,t,t) = t
         & quadruple(t,t,at,at) = t
         & quadruple(t,t,at,t) = t
         & quadruple(t,t,t,at) = t
         & quadruple(t,t,t,t) = t

).

tff(declare_encrypt,type,encrypt: $i * $i > $i).
tff(function_encrypt,axiom,
           encrypt(at,at) = at
         & encrypt(at,t) = at
         & encrypt(t,at) = at
         & encrypt(t,t) = at

).

tff(declare_triple,type,triple: $i * $i * $i > $i).
tff(function_triple,axiom,
           triple(at,at,at) = at
         & triple(at,at,t) = t
         & triple(at,t,at) = t
         & triple(at,t,t) = t
         & triple(t,at,at) = t
         & triple(t,at,t) = t
         & triple(t,t,at) = t
         & triple(t,t,t) = t

).

tff(declare_generate_b_nonce,type,generate_b_nonce: $i > $i).
tff(function_generate_b_nonce,axiom,
           generate_b_nonce(at) = at
         & generate_b_nonce(t) = at

).

tff(declare_generate_expiration_time,type,generate_expiration_time: $i > $i).
tff(function_generate_expiration_time,axiom,
           generate_expiration_time(at) = at
         & generate_expiration_time(t) = at

).

tff(declare_generate_key,type,generate_key: $i > $i).
tff(function_generate_key,axiom,
           generate_key(at) = t
         & generate_key(t) = t

).

tff(declare_generate_intruder_nonce,type,generate_intruder_nonce: $i > $i).
tff(function_generate_intruder_nonce,axiom,
           generate_intruder_nonce(at) = at
         & generate_intruder_nonce(t) = t

).

tff(declare_a_holds,type,a_holds: $i > $o ).
tff(predicate_a_holds,axiom,
%         a_holds(at) undefined in model
%         a_holds(t) undefined in model

).

tff(declare_party_of_protocol,type,party_of_protocol: $i > $o ).
tff(predicate_party_of_protocol,axiom,
           party_of_protocol(at)
         & party_of_protocol(t)

).

tff(declare_message,type,message: $i > $o ).
tff(predicate_message,axiom,
           message(at)
         & ~message(t)

).

tff(declare_a_stored,type,a_stored: $i > $o ).
tff(predicate_a_stored,axiom,
           a_stored(at)
         & ~a_stored(t)

).

tff(declare_b_holds,type,b_holds: $i > $o ).
tff(predicate_b_holds,axiom,
%         b_holds(at) undefined in model
%         b_holds(t) undefined in model

).

tff(declare_fresh_to_b,type,fresh_to_b: $i > $o ).
tff(predicate_fresh_to_b,axiom,
           fresh_to_b(at)
         & fresh_to_b(t)

).

tff(declare_b_stored,type,b_stored: $i > $o ).
tff(predicate_b_stored,axiom,
%         b_stored(at) undefined in model
%         b_stored(t) undefined in model

).

tff(declare_a_key,type,a_key: $i > $o ).
tff(predicate_a_key,axiom,
           ~a_key(at)
         & a_key(t)

).

tff(declare_t_holds,type,t_holds: $i > $o ).
tff(predicate_t_holds,axiom,
           t_holds(at)
         & t_holds(t)

).

tff(declare_a_nonce,type,a_nonce: $i > $o ).
tff(predicate_a_nonce,axiom,
           a_nonce(at)
         & ~a_nonce(t)

).

tff(declare_intruder_message,type,intruder_message: $i > $o ).
tff(predicate_intruder_message,axiom,
           intruder_message(at)
         & ~intruder_message(t)

).

tff(declare_intruder_holds,type,intruder_holds: $i > $o ).
tff(predicate_intruder_holds,axiom,
           intruder_holds(at)
         & ~intruder_holds(t)

).

tff(declare_fresh_intruder_nonce,type,fresh_intruder_nonce: $i > $o ).
tff(predicate_fresh_intruder_nonce,axiom,
           fresh_intruder_nonce(at)
         & ~fresh_intruder_nonce(t)

).

% SZS output end FiniteModel for SWV017+1

Vampire 4.7

Sample solution for SET014^4

% SZS output start Proof for SET014^4
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, in: $i > ($i > $o) > $o).
thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
thf(func_def_3, type, emptyset: $i > $o).
thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
thf(func_def_5, type, singleton: $i > $i > $o).
thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_10, type, complement: ($i > $o) > $i > $o).
thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
thf(func_def_15, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
thf(func_def_18, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
thf(func_def_19, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
thf(func_def_20, type, vNOT: $o > $o).
thf(func_def_21, type, vAND: $o > $o > $o).
thf(func_def_22, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
thf(func_def_23, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
thf(func_def_24, type, iCOMB: !>[X0: $tType]:(X0 > X0)).
thf(func_def_25, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
thf(func_def_26, type, vOR: $o > $o > $o).
thf(func_def_27, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
thf(func_def_28, type, vIMP: $o > $o > $o).
thf(func_def_29, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
thf(func_def_30, type, sK0: $i > $o).
thf(func_def_31, type, sK1: $i > $o).
thf(func_def_32, type, sK2: $i > $o).
thf(f95,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f94])).
thf(f94,plain,(
  ($true = $false)),
  inference(backward_demodulation,[],[f89,f93])).
thf(f93,plain,(
  ($false = vAPP($i,$o,sK1,sK3))),
  inference(trivial_inequality_removal,[],[f90])).
thf(f90,plain,(
  ($true = $false) | ($false = vAPP($i,$o,sK1,sK3))),
  inference(superposition,[],[f77,f81])).
thf(f81,plain,(
  ($false = vAPP($i,$o,sK2,sK3))),
  inference(binary_proxy_clausification,[],[f80])).
thf(f80,plain,(
  ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,sK0,sK3)),vAPP($i,$o,sK1,sK3))),vAPP($i,$o,sK2,sK3)))),
  inference(combinator_demodulation,[],[f79])).
thf(f79,plain,(
  ($false = vAPP($i,$o,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o)),sCOMB,vAPP(sTfun($i,$o),sTfun($i,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP),vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o)),sCOMB,vAPP(sTfun($i,$o),sTfun($i,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vOR),sK0)),sK1))),sK2),sK3))),
  inference(sigma_clausification,[],[f78])).
thf(f78,plain,(
  ($true != vAPP(sTfun($i,$o),$o,vPI($i),vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o)),sCOMB,vAPP(sTfun($i,$o),sTfun($i,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP),vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o)),sCOMB,vAPP(sTfun($i,$o),sTfun($i,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vOR),sK0)),sK1))),sK2)))),
  inference(combinator_demodulation,[],[f67])).
thf(f67,plain,(
  ($true != vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),vAPP(sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),$o)),vAPP(sTfun(sTfun(sTfun($i,$o),sTfun($i,$o)),sTfun(sTfun($i,$o),$o)),sTfun(sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),$o))),bCOMB,vAPP(sTfun(sTfun($i,$o),$o),sTfun(sTfun(sTfun($i,$o),sTfun($i,$o)),sTfun(sTfun($i,$o),$o)),bCOMB,vPI($i))),vAPP(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),vAPP(sTfun(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP))),vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),vAPP(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),vAPP(sTfun(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vOR)),sK0),sK1)),sK2))),
  inference(definition_unfolding,[],[f51,f65,f64])).
thf(f64,plain,(
  (union = vAPP(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),vAPP(sTfun(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vOR)))),
  inference(cnf_transformation,[],[f42])).
thf(f42,plain,(
  (union = vAPP(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),vAPP(sTfun(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vOR)))),
  inference(fool_elimination,[],[f41])).
thf(f41,plain,(
  (union = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : (vAPP($i,$o,X1,X2) | vAPP($i,$o,X0,X2))))),
  inference(rectify,[],[f6])).
thf(f6,axiom,(
  (union = (^[X0 : $i > $o, X2 : $i > $o, X3 : $i] : (vAPP($i,$o,X2,X3) | vAPP($i,$o,X0,X3))))),
  file('samples/SET014^4.p',unknown)).
thf(f65,plain,(
  (subset = vAPP(sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),$o)),vAPP(sTfun(sTfun(sTfun($i,$o),sTfun($i,$o)),sTfun(sTfun($i,$o),$o)),sTfun(sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),$o))),bCOMB,vAPP(sTfun(sTfun($i,$o),$o),sTfun(sTfun(sTfun($i,$o),sTfun($i,$o)),sTfun(sTfun($i,$o),$o)),bCOMB,vPI($i))),vAPP(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),vAPP(sTfun(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP))))),
  inference(cnf_transformation,[],[f44])).
thf(f44,plain,(
  (subset = vAPP(sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),$o)),vAPP(sTfun(sTfun(sTfun($i,$o),sTfun($i,$o)),sTfun(sTfun($i,$o),$o)),sTfun(sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),$o))),bCOMB,vAPP(sTfun(sTfun($i,$o),$o),sTfun(sTfun(sTfun($i,$o),sTfun($i,$o)),sTfun(sTfun($i,$o),$o)),bCOMB,vPI($i))),vAPP(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),vAPP(sTfun(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP))))),
  inference(fool_elimination,[],[f43])).
thf(f43,plain,(
  (subset = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : (vAPP($i,$o,X0,X2) => vAPP($i,$o,X1,X2)))))),
  inference(rectify,[],[f12])).
thf(f12,axiom,(
  (subset = (^[X0 : $i > $o, X2 : $i > $o] : (! [X3] : (vAPP($i,$o,X0,X3) => vAPP($i,$o,X2,X3)))))),
  file('samples/SET014^4.p',unknown)).
thf(f51,plain,(
  ($true != vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),union,sK0),sK1)),sK2))),
  inference(cnf_transformation,[],[f48])).
thf(f48,plain,(
  ($true != vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),union,sK0),sK1)),sK2)) & ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,sK1),sK2)) & ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,sK0),sK2))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f46,f47])).
thf(f47,plain,(
  ? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (($true != vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),union,X0),X1)),X2)) & ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X1),X2)) & ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X0),X2))) => (($true != vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),union,sK0),sK1)),sK2)) & ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,sK1),sK2)) & ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,sK0),sK2)))),
  introduced(choice_axiom,[])).
thf(f46,plain,(
  ? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (($true != vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),union,X0),X1)),X2)) & ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X1),X2)) & ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X0),X2)))),
  inference(flattening,[],[f45])).
thf(f45,plain,(
  ? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (($true != vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),union,X0),X1)),X2)) & (($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X1),X2)) & ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X0),X2))))),
  inference(ennf_transformation,[],[f19])).
thf(f19,plain,(
  ~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : ((($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X1),X2)) & ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X0),X2))) => ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),union,X0),X1)),X2)))),
  inference(fool_elimination,[],[f18])).
thf(f18,plain,(
  ~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : ((vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X1),X2) & vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X0),X2)) => vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),union,X0),X1)),X2))),
  inference(rectify,[],[f16])).
thf(f16,negated_conjecture,(
  ~! [X0 : $i > $o,X2 : $i > $o,X4 : $i > $o] : ((vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X2),X4) & vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X0),X4)) => vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),union,X0),X2)),X4))),
  inference(negated_conjecture,[],[f15])).
thf(f15,conjecture,(
  ! [X0 : $i > $o,X2 : $i > $o,X4 : $i > $o] : ((vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X2),X4) & vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,X0),X4)) => vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)),union,X0),X2)),X4))),
  file('samples/SET014^4.p',unknown)).
thf(f77,plain,(
  ( ! [X1 : $i] : (($true = vAPP($i,$o,sK2,X1)) | ($false = vAPP($i,$o,sK1,X1))) )),
  inference(binary_proxy_clausification,[],[f76])).
thf(f76,plain,(
  ( ! [X1 : $i] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,vAPP($i,$o,sK1,X1)),vAPP($i,$o,sK2,X1)))) )),
  inference(combinator_demodulation,[],[f75])).
thf(f75,plain,(
  ( ! [X1 : $i] : (($true = vAPP($i,$o,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o)),sCOMB,vAPP(sTfun($i,$o),sTfun($i,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP),sK1)),sK2),X1))) )),
  inference(pi_clausification,[],[f74])).
thf(f74,plain,(
  ($true = vAPP(sTfun($i,$o),$o,vPI($i),vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o)),sCOMB,vAPP(sTfun($i,$o),sTfun($i,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP),sK1)),sK2)))),
  inference(combinator_demodulation,[],[f68])).
thf(f68,plain,(
  ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),vAPP(sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),$o)),vAPP(sTfun(sTfun(sTfun($i,$o),sTfun($i,$o)),sTfun(sTfun($i,$o),$o)),sTfun(sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),$o))),bCOMB,vAPP(sTfun(sTfun($i,$o),$o),sTfun(sTfun(sTfun($i,$o),sTfun($i,$o)),sTfun(sTfun($i,$o),$o)),bCOMB,vPI($i))),vAPP(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),vAPP(sTfun(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP))),sK1),sK2))),
  inference(definition_unfolding,[],[f50,f65])).
thf(f50,plain,(
  ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,sK1),sK2))),
  inference(cnf_transformation,[],[f48])).
thf(f89,plain,(
  ($true = vAPP($i,$o,sK1,sK3))),
  inference(trivial_inequality_removal,[],[f88])).
thf(f88,plain,(
  ($true = $false) | ($true = vAPP($i,$o,sK1,sK3))),
  inference(backward_demodulation,[],[f83,f87])).
thf(f87,plain,(
  ($false = vAPP($i,$o,sK0,sK3))),
  inference(trivial_inequality_removal,[],[f84])).
thf(f84,plain,(
  ($true = $false) | ($false = vAPP($i,$o,sK0,sK3))),
  inference(superposition,[],[f73,f81])).
thf(f73,plain,(
  ( ! [X1 : $i] : (($true = vAPP($i,$o,sK2,X1)) | ($false = vAPP($i,$o,sK0,X1))) )),
  inference(binary_proxy_clausification,[],[f72])).
thf(f72,plain,(
  ( ! [X1 : $i] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,vAPP($i,$o,sK0,X1)),vAPP($i,$o,sK2,X1)))) )),
  inference(combinator_demodulation,[],[f71])).
thf(f71,plain,(
  ( ! [X1 : $i] : (($true = vAPP($i,$o,vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o)),sCOMB,vAPP(sTfun($i,$o),sTfun($i,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP),sK0)),sK2),X1))) )),
  inference(pi_clausification,[],[f70])).
thf(f70,plain,(
  ($true = vAPP(sTfun($i,$o),$o,vPI($i),vAPP(sTfun($i,$o),sTfun($i,$o),vAPP(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o)),sCOMB,vAPP(sTfun($i,$o),sTfun($i,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP),sK0)),sK2)))),
  inference(combinator_demodulation,[],[f69])).
thf(f69,plain,(
  ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),vAPP(sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),$o)),vAPP(sTfun(sTfun(sTfun($i,$o),sTfun($i,$o)),sTfun(sTfun($i,$o),$o)),sTfun(sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),$o))),bCOMB,vAPP(sTfun(sTfun($i,$o),$o),sTfun(sTfun(sTfun($i,$o),sTfun($i,$o)),sTfun(sTfun($i,$o),$o)),bCOMB,vPI($i))),vAPP(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o))),vAPP(sTfun(sTfun($i,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,$o))),sTfun(sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),sTfun(sTfun($i,$o),sTfun(sTfun($i,$o),sTfun($i,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun($i,$o),sTfun($i,sTfun($o,$o))),bCOMB,vIMP))),sK0),sK2))),
  inference(definition_unfolding,[],[f49,f65])).
thf(f49,plain,(
  ($true = vAPP(sTfun($i,$o),$o,vAPP(sTfun($i,$o),sTfun(sTfun($i,$o),$o),subset,sK0),sK2))),
  inference(cnf_transformation,[],[f48])).
thf(f83,plain,(
  ($true = vAPP($i,$o,sK1,sK3)) | ($true = vAPP($i,$o,sK0,sK3))),
  inference(binary_proxy_clausification,[],[f82])).
thf(f82,plain,(
  ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,sK0,sK3)),vAPP($i,$o,sK1,sK3)))),
  inference(binary_proxy_clausification,[],[f80])).
% SZS output end Proof for SET014^4

Sample solution for DAT013=1

% SZS output start Proof for DAT013=1
tff(type_def_5, type, array: $tType).
tff(func_def_0, type, read: (array * $int) > $int).
tff(func_def_1, type, write: (array * $int * $int) > array).
tff(func_def_7, type, sK0: array).
tff(func_def_8, type, sK1: $int).
tff(func_def_9, type, sK2: $int).
tff(func_def_10, type, sK3: $int).
tff(f1876,plain,(
  $false),
  inference(avatar_sat_refutation,[],[f123,f1541,f1875])).
tff(f1875,plain,(
  ~spl4_6),
  inference(avatar_contradiction_clause,[],[f1874])).
tff(f1874,plain,(
  $false | ~spl4_6),
  inference(subsumption_resolution,[],[f1870,f11])).
tff(f11,plain,(
  ( ! [X0 : $int] : (~$less(X0,X0)) )),
  introduced(theory_axiom_146,[])).
tff(f1870,plain,(
  $less(sK1,sK1) | ~spl4_6),
  inference(resolution,[],[f1866,f693])).
tff(f693,plain,(
  ( ! [X1 : $int] : (~$less(X1,sK3) | $less(X1,sK1)) )),
  inference(resolution,[],[f689,f12])).
tff(f12,plain,(
  ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
  introduced(theory_axiom_147,[])).
tff(f689,plain,(
  $less(sK3,sK1)),
  inference(subsumption_resolution,[],[f685,f29])).
tff(f29,plain,(
  ~$less(sK2,sK3)),
  inference(cnf_transformation,[],[f24])).
tff(f24,plain,(
  (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f23,f22])).
tff(f22,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1))) => (? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)))),
  introduced(choice_axiom,[])).
tff(f23,plain,(
  ? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) => (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3)))),
  introduced(choice_axiom,[])).
tff(f21,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1)))),
  inference(rectify,[],[f20])).
tff(f20,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & ~$less(X2,X4) & ~$less(X4,$sum(X1,3))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | $less(X2,X3) | $less(X3,X1)))),
  inference(flattening,[],[f19])).
tff(f19,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & (~$less(X2,X4) & ~$less(X4,$sum(X1,3)))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | ($less(X2,X3) | $less(X3,X1))))),
  inference(ennf_transformation,[],[f5])).
tff(f5,plain,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : ((~$less(X2,X3) & ~$less(X3,X1)) => $less(0,read(X0,X3))) => ! [X4 : $int] : ((~$less(X2,X4) & ~$less(X4,$sum(X1,3))) => $less(0,read(X0,X4))))),
  inference(theory_normalization,[],[f4])).
tff(f4,negated_conjecture,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
  inference(negated_conjecture,[],[f3])).
tff(f3,conjecture,(
  ! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
  file('samples/DAT013=1.p',unknown)).
tff(f685,plain,(
  $less(sK2,sK3) | $less(sK3,sK1)),
  inference(resolution,[],[f27,f30])).
tff(f30,plain,(
  ~$less(0,read(sK0,sK3))),
  inference(cnf_transformation,[],[f24])).
tff(f27,plain,(
  ( ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)) )),
  inference(cnf_transformation,[],[f24])).
tff(f1866,plain,(
  $less(sK1,sK3) | ~spl4_6),
  inference(evaluation,[],[f1846])).
tff(f1846,plain,(
  ~$less(0,3) | $less(sK1,sK3) | ~spl4_6),
  inference(resolution,[],[f157,f1563])).
tff(f1563,plain,(
  ( ! [X2 : $int] : (~$less(X2,$sum(3,sK1)) | $less(X2,sK3)) ) | ~spl4_6),
  inference(resolution,[],[f119,f12])).
tff(f119,plain,(
  $less($sum(3,sK1),sK3) | ~spl4_6),
  inference(avatar_component_clause,[],[f117])).
tff(f117,plain,(
  spl4_6 <=> $less($sum(3,sK1),sK3)),
  introduced(avatar_definition,[new_symbols(naming,[spl4_6])])).
tff(f157,plain,(
  ( ! [X10 : $int,X11 : $int] : ($less(X10,$sum(X11,X10)) | ~$less(0,X11)) )),
  inference(superposition,[],[f14,f33])).
tff(f33,plain,(
  ( ! [X0 : $int] : ($sum(0,X0) = X0) )),
  inference(superposition,[],[f6,f8])).
tff(f8,plain,(
  ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
  introduced(theory_axiom_141,[])).
tff(f6,plain,(
  ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
  introduced(theory_axiom_139,[])).
tff(f14,plain,(
  ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
  introduced(theory_axiom_149,[])).
tff(f1541,plain,(
  ~spl4_5),
  inference(avatar_contradiction_clause,[],[f1540])).
tff(f1540,plain,(
  $false | ~spl4_5),
  inference(subsumption_resolution,[],[f1535,f11])).
tff(f1535,plain,(
  $less(sK1,sK1) | ~spl4_5),
  inference(resolution,[],[f1525,f693])).
tff(f1525,plain,(
  $less(sK1,sK3) | ~spl4_5),
  inference(evaluation,[],[f1520])).
tff(f1520,plain,(
  $less(sK1,sK3) | ~$less(0,3) | ~spl4_5),
  inference(superposition,[],[f702,f33])).
tff(f702,plain,(
  ( ! [X1 : $int] : ($less($sum(X1,sK1),sK3) | ~$less(X1,3)) ) | ~spl4_5),
  inference(superposition,[],[f14,f115])).
tff(f115,plain,(
  sK3 = $sum(3,sK1) | ~spl4_5),
  inference(avatar_component_clause,[],[f113])).
tff(f113,plain,(
  spl4_5 <=> sK3 = $sum(3,sK1)),
  introduced(avatar_definition,[new_symbols(naming,[spl4_5])])).
tff(f123,plain,(
  spl4_5 | spl4_6),
  inference(avatar_split_clause,[],[f92,f117,f113])).
tff(f92,plain,(
  $less($sum(3,sK1),sK3) | sK3 = $sum(3,sK1)),
  inference(resolution,[],[f13,f31])).
tff(f31,plain,(
  ~$less(sK3,$sum(3,sK1))),
  inference(forward_demodulation,[],[f28,f6])).
tff(f28,plain,(
  ~$less(sK3,$sum(sK1,3))),
  inference(cnf_transformation,[],[f24])).
tff(f13,plain,(
  ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
  introduced(theory_axiom_148,[])).
% SZS output end Proof for DAT013=1

Sample solution for SEU140+2

% SZS output start Proof for SEU140+2
fof(f4471,plain,(
  $false),
  inference(subsumption_resolution,[],[f4465,f210])).
fof(f210,plain,(
  ~disjoint(sK10,sK12)),
  inference(cnf_transformation,[],[f134])).
fof(f134,plain,(
  ~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f88,f133])).
fof(f133,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11))),
  introduced(choice_axiom,[])).
fof(f88,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
  inference(flattening,[],[f87])).
fof(f87,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
  inference(ennf_transformation,[],[f52])).
fof(f52,negated_conjecture,(
  ~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  inference(negated_conjecture,[],[f51])).
fof(f51,conjecture,(
  ! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  file('samples/SEU140+2.p',unknown)).
fof(f4465,plain,(
  disjoint(sK10,sK12)),
  inference(superposition,[],[f4351,f2135])).
fof(f2135,plain,(
  sK12 = set_difference(set_union2(sK11,sK12),sK11)),
  inference(superposition,[],[f741,f931])).
fof(f931,plain,(
  sK11 = set_difference(sK11,sK12)),
  inference(forward_demodulation,[],[f930,f338])).
fof(f338,plain,(
  ( ! [X6,X7] : (set_union2(set_difference(X6,X7),X6) = X6) )),
  inference(resolution,[],[f180,f192])).
fof(f192,plain,(
  ( ! [X0,X1] : (subset(set_difference(X0,X1),X0)) )),
  inference(cnf_transformation,[],[f39])).
fof(f39,axiom,(
  ! [X0,X1] : subset(set_difference(X0,X1),X0)),
  file('samples/SEU140+2.p',unknown)).
fof(f180,plain,(
  ( ! [X0,X1] : (~subset(X0,X1) | set_union2(X0,X1) = X1) )),
  inference(cnf_transformation,[],[f73])).
fof(f73,plain,(
  ! [X0,X1] : (set_union2(X0,X1) = X1 | ~subset(X0,X1))),
  inference(ennf_transformation,[],[f28])).
fof(f28,axiom,(
  ! [X0,X1] : (subset(X0,X1) => set_union2(X0,X1) = X1)),
  file('samples/SEU140+2.p',unknown)).
fof(f930,plain,(
  set_difference(sK11,sK12) = set_union2(set_difference(sK11,sK12),sK11)),
  inference(forward_demodulation,[],[f929,f281])).
fof(f281,plain,(
  ( ! [X1] : (set_union2(empty_set,X1) = X1) )),
  inference(superposition,[],[f137,f183])).
fof(f183,plain,(
  ( ! [X0] : (set_union2(X0,empty_set) = X0) )),
  inference(cnf_transformation,[],[f31])).
fof(f31,axiom,(
  ! [X0] : set_union2(X0,empty_set) = X0),
  file('samples/SEU140+2.p',unknown)).
fof(f137,plain,(
  ( ! [X0,X1] : (set_union2(X0,X1) = set_union2(X1,X0)) )),
  inference(cnf_transformation,[],[f3])).
fof(f3,axiom,(
  ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)),
  file('samples/SEU140+2.p',unknown)).
fof(f929,plain,(
  set_union2(set_difference(sK11,sK12),sK11) = set_union2(empty_set,set_difference(sK11,sK12))),
  inference(forward_demodulation,[],[f914,f137])).
fof(f914,plain,(
  set_union2(set_difference(sK11,sK12),sK11) = set_union2(set_difference(sK11,sK12),empty_set)),
  inference(superposition,[],[f195,f587])).
fof(f587,plain,(
  empty_set = set_difference(sK11,set_difference(sK11,sK12))),
  inference(resolution,[],[f224,f209])).
fof(f209,plain,(
  disjoint(sK11,sK12)),
  inference(cnf_transformation,[],[f134])).
fof(f224,plain,(
  ( ! [X0,X1] : (~disjoint(X0,X1) | empty_set = set_difference(X0,set_difference(X0,X1))) )),
  inference(definition_unfolding,[],[f165,f203])).
fof(f203,plain,(
  ( ! [X0,X1] : (set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))) )),
  inference(cnf_transformation,[],[f47])).
fof(f47,axiom,(
  ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))),
  file('samples/SEU140+2.p',unknown)).
fof(f165,plain,(
  ( ! [X0,X1] : (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f119])).
fof(f119,plain,(
  ! [X0,X1] : ((disjoint(X0,X1) | set_intersection2(X0,X1) != empty_set) & (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)))),
  inference(nnf_transformation,[],[f11])).
fof(f11,axiom,(
  ! [X0,X1] : (disjoint(X0,X1) <=> set_intersection2(X0,X1) = empty_set)),
  file('samples/SEU140+2.p',unknown)).
fof(f195,plain,(
  ( ! [X0,X1] : (set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))) )),
  inference(cnf_transformation,[],[f41])).
fof(f41,axiom,(
  ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))),
  file('samples/SEU140+2.p',unknown)).
fof(f741,plain,(
  ( ! [X6,X7] : (set_difference(set_union2(X6,X7),set_difference(X6,X7)) = X7) )),
  inference(forward_demodulation,[],[f740,f196])).
fof(f196,plain,(
  ( ! [X0] : (set_difference(X0,empty_set) = X0) )),
  inference(cnf_transformation,[],[f42])).
fof(f42,axiom,(
  ! [X0] : set_difference(X0,empty_set) = X0),
  file('samples/SEU140+2.p',unknown)).
fof(f740,plain,(
  ( ! [X6,X7] : (set_difference(set_union2(X6,X7),set_difference(X6,X7)) = set_difference(X7,empty_set)) )),
  inference(forward_demodulation,[],[f690,f324])).
fof(f324,plain,(
  ( ! [X3,X4] : (empty_set = set_difference(X3,set_union2(X4,X3))) )),
  inference(resolution,[],[f175,f286])).
fof(f286,plain,(
  ( ! [X6,X7] : (subset(X6,set_union2(X7,X6))) )),
  inference(superposition,[],[f213,f137])).
fof(f213,plain,(
  ( ! [X0,X1] : (subset(X0,set_union2(X0,X1))) )),
  inference(cnf_transformation,[],[f55])).
fof(f55,axiom,(
  ! [X0,X1] : subset(X0,set_union2(X0,X1))),
  file('samples/SEU140+2.p',unknown)).
fof(f175,plain,(
  ( ! [X0,X1] : (~subset(X0,X1) | empty_set = set_difference(X0,X1)) )),
  inference(cnf_transformation,[],[f120])).
fof(f120,plain,(
  ! [X0,X1] : ((empty_set = set_difference(X0,X1) | ~subset(X0,X1)) & (subset(X0,X1) | empty_set != set_difference(X0,X1)))),
  inference(nnf_transformation,[],[f23])).
fof(f23,axiom,(
  ! [X0,X1] : (empty_set = set_difference(X0,X1) <=> subset(X0,X1))),
  file('samples/SEU140+2.p',unknown)).
fof(f690,plain,(
  ( ! [X6,X7] : (set_difference(set_union2(X6,X7),set_difference(X6,X7)) = set_difference(X7,set_difference(X7,set_union2(X6,X7)))) )),
  inference(superposition,[],[f216,f201])).
fof(f201,plain,(
  ( ! [X0,X1] : (set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)) )),
  inference(cnf_transformation,[],[f45])).
fof(f45,axiom,(
  ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)),
  file('samples/SEU140+2.p',unknown)).
fof(f216,plain,(
  ( ! [X0,X1] : (set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0))) )),
  inference(definition_unfolding,[],[f138,f203,f203])).
fof(f138,plain,(
  ( ! [X0,X1] : (set_intersection2(X0,X1) = set_intersection2(X1,X0)) )),
  inference(cnf_transformation,[],[f4])).
fof(f4,axiom,(
  ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)),
  file('samples/SEU140+2.p',unknown)).
fof(f4351,plain,(
  ( ! [X41] : (disjoint(sK10,set_difference(X41,sK11))) )),
  inference(superposition,[],[f4323,f2122])).
fof(f2122,plain,(
  sK10 = set_difference(sK11,set_difference(sK11,sK10))),
  inference(superposition,[],[f741,f434])).
fof(f434,plain,(
  sK11 = set_union2(sK11,sK10)),
  inference(forward_demodulation,[],[f433,f281])).
fof(f433,plain,(
  set_union2(sK11,sK10) = set_union2(empty_set,sK11)),
  inference(forward_demodulation,[],[f421,f137])).
fof(f421,plain,(
  set_union2(sK11,sK10) = set_union2(sK11,empty_set)),
  inference(superposition,[],[f195,f328])).
fof(f328,plain,(
  empty_set = set_difference(sK10,sK11)),
  inference(resolution,[],[f175,f208])).
fof(f208,plain,(
  subset(sK10,sK11)),
  inference(cnf_transformation,[],[f134])).
fof(f4323,plain,(
  ( ! [X2,X3,X4] : (disjoint(set_difference(X2,X3),set_difference(X4,X2))) )),
  inference(duplicate_literal_removal,[],[f4288])).
fof(f4288,plain,(
  ( ! [X2,X3,X4] : (disjoint(set_difference(X2,X3),set_difference(X4,X2)) | disjoint(set_difference(X2,X3),set_difference(X4,X2))) )),
  inference(resolution,[],[f401,f395])).
fof(f395,plain,(
  ( ! [X10,X8,X9] : (~in(sK8(X8,set_difference(X9,X10)),X10) | disjoint(X8,set_difference(X9,X10))) )),
  inference(resolution,[],[f243,f198])).
fof(f198,plain,(
  ( ! [X0,X1] : (in(sK8(X0,X1),X1) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f130])).
fof(f130,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)) | disjoint(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f82,f129])).
fof(f129,plain,(
  ! [X0,X1] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)))),
  introduced(choice_axiom,[])).
fof(f82,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
  inference(ennf_transformation,[],[f62])).
fof(f62,plain,(
  ! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
  inference(rectify,[],[f43])).
fof(f43,axiom,(
  ! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
  file('samples/SEU140+2.p',unknown)).
fof(f243,plain,(
  ( ! [X0,X1,X4] : (~in(X4,set_difference(X0,X1)) | ~in(X4,X1)) )),
  inference(equality_resolution,[],[f160])).
fof(f160,plain,(
  ( ! [X2,X0,X1,X4] : (~in(X4,X1) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
  inference(cnf_transformation,[],[f118])).
fof(f118,plain,(
  ! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ((in(sK4(X0,X1,X2),X1) | ~in(sK4(X0,X1,X2),X0) | ~in(sK4(X0,X1,X2),X2)) & ((~in(sK4(X0,X1,X2),X1) & in(sK4(X0,X1,X2),X0)) | in(sK4(X0,X1,X2),X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f116,f117])).
fof(f117,plain,(
  ! [X0,X1,X2] : (? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2))) => ((in(sK4(X0,X1,X2),X1) | ~in(sK4(X0,X1,X2),X0) | ~in(sK4(X0,X1,X2),X2)) & ((~in(sK4(X0,X1,X2),X1) & in(sK4(X0,X1,X2),X0)) | in(sK4(X0,X1,X2),X2))))),
  introduced(choice_axiom,[])).
fof(f116,plain,(
  ! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
  inference(rectify,[],[f115])).
fof(f115,plain,(
  ! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | in(X3,X1) | ~in(X3,X0)) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
  inference(flattening,[],[f114])).
fof(f114,plain,(
  ! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : (((in(X3,X1) | ~in(X3,X0)) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | (in(X3,X1) | ~in(X3,X0))) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
  inference(nnf_transformation,[],[f10])).
fof(f10,axiom,(
  ! [X0,X1,X2] : (set_difference(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (~in(X3,X1) & in(X3,X0))))),
  file('samples/SEU140+2.p',unknown)).
fof(f401,plain,(
  ( ! [X2,X3,X4] : (in(sK8(set_difference(X2,X3),X4),X2) | disjoint(set_difference(X2,X3),X4)) )),
  inference(resolution,[],[f244,f197])).
fof(f197,plain,(
  ( ! [X0,X1] : (in(sK8(X0,X1),X0) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f130])).
fof(f244,plain,(
  ( ! [X0,X1,X4] : (~in(X4,set_difference(X0,X1)) | in(X4,X0)) )),
  inference(equality_resolution,[],[f159])).
fof(f159,plain,(
  ( ! [X2,X0,X1,X4] : (in(X4,X0) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
  inference(cnf_transformation,[],[f118])).
% SZS output end Proof for SEU140+2

Sample solution for NLP042+1

% # SZS output start Saturation.
cnf(u143,negated_conjecture,
    patient(sK0,sK4,sK3)).

cnf(u146,axiom,
    ~patient(X0,X1,X3) | ~agent(X0,X1,X3) | ~nonreflexive(X0,X1)).

cnf(u142,negated_conjecture,
    agent(sK0,sK4,sK1)).

cnf(u188,negated_conjecture,
    ~agent(sK0,sK4,sK3)).

cnf(u144,negated_conjecture,
    nonreflexive(sK0,sK4)).

cnf(u136,negated_conjecture,
    of(sK0,sK2,sK1)).

cnf(u192,negated_conjecture,
    ~of(sK0,X0,sK1) | sK2 = X0 | ~forename(sK0,X0)).

cnf(u134,axiom,
    ~of(X0,X3,X1) | X2 = X3 | ~forename(X0,X3) | ~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1)).

cnf(u177,negated_conjecture,
    act(sK0,sK4)).

cnf(u126,axiom,
    ~act(X0,X1) | event(X0,X1)).

cnf(u175,negated_conjecture,
    nonexistent(sK0,sK4)).

cnf(u129,axiom,
    ~nonexistent(X0,X1) | ~existent(X0,X1)).

cnf(u173,negated_conjecture,
    eventuality(sK0,sK4)).

cnf(u122,axiom,
    ~eventuality(X0,X1) | unisex(X0,X1)).

cnf(u123,axiom,
    ~eventuality(X0,X1) | nonexistent(X0,X1)).

cnf(u124,axiom,
    ~eventuality(X0,X1) | specific(X0,X1)).

cnf(u141,negated_conjecture,
    event(sK0,sK4)).

cnf(u125,axiom,
    ~event(X0,X1) | eventuality(X0,X1)).

cnf(u145,negated_conjecture,
    order(sK0,sK4)).

cnf(u121,axiom,
    ~order(X0,X1) | event(X0,X1)).

cnf(u127,axiom,
    ~order(X0,X1) | act(X0,X1)).

cnf(u140,negated_conjecture,
    shake_beverage(sK0,sK3)).

cnf(u120,axiom,
    ~shake_beverage(X0,X1) | beverage(X0,X1)).

cnf(u163,negated_conjecture,
    beverage(sK0,sK3)).

cnf(u119,axiom,
    ~beverage(X0,X1) | food(X0,X1)).

cnf(u164,negated_conjecture,
    food(sK0,sK3)).

cnf(u118,axiom,
    ~food(X0,X1) | substance_matter(X0,X1)).

cnf(u166,negated_conjecture,
    substance_matter(sK0,sK3)).

cnf(u117,axiom,
    ~substance_matter(X0,X1) | object(X0,X1)).

cnf(u171,negated_conjecture,
    specific(sK0,sK3)).

cnf(u174,negated_conjecture,
    specific(sK0,sK4)).

cnf(u162,negated_conjecture,
    specific(sK0,sK1)).

cnf(u132,axiom,
    ~specific(X0,X1) | ~general(X0,X1)).

cnf(u172,negated_conjecture,
    existent(sK0,sK3)).

cnf(u158,negated_conjecture,
    existent(sK0,sK1)).

cnf(u179,negated_conjecture,
    ~existent(sK0,sK4)).

cnf(u169,negated_conjecture,
    nonliving(sK0,sK3)).

cnf(u128,axiom,
    ~nonliving(X0,X1) | ~animate(X0,X1)).

cnf(u131,axiom,
    ~nonliving(X0,X1) | ~living(X0,X1)).

cnf(u167,negated_conjecture,
    object(sK0,sK3)).

cnf(u112,axiom,
    ~object(X0,X1) | unisex(X0,X1)).

cnf(u113,axiom,
    ~object(X0,X1) | nonliving(X0,X1)).

cnf(u116,axiom,
    ~object(X0,X1) | entity(X0,X1)).

cnf(u155,negated_conjecture,
    relname(sK0,sK2)).

cnf(u110,axiom,
    ~relname(X0,X1) | relation(X0,X1)).

cnf(u156,negated_conjecture,
    relation(sK0,sK2)).

cnf(u109,axiom,
    ~relation(X0,X1) | abstraction(X0,X1)).

cnf(u159,negated_conjecture,
    nonhuman(sK0,sK2)).

cnf(u130,axiom,
    ~nonhuman(X0,X1) | ~human(X0,X1)).

cnf(u160,negated_conjecture,
    general(sK0,sK2)).

cnf(u194,negated_conjecture,
    ~general(sK0,sK3)).

cnf(u183,negated_conjecture,
    ~general(sK0,sK1)).

cnf(u184,negated_conjecture,
    ~general(sK0,sK4)).

cnf(u170,negated_conjecture,
    unisex(sK0,sK3)).

cnf(u176,negated_conjecture,
    unisex(sK0,sK4)).

cnf(u161,negated_conjecture,
    unisex(sK0,sK2)).

cnf(u133,axiom,
    ~unisex(X0,X1) | ~female(X0,X1)).

cnf(u157,negated_conjecture,
    abstraction(sK0,sK2)).

cnf(u106,axiom,
    ~abstraction(X0,X1) | unisex(X0,X1)).

cnf(u107,axiom,
    ~abstraction(X0,X1) | general(X0,X1)).

cnf(u108,axiom,
    ~abstraction(X0,X1) | nonhuman(X0,X1)).

cnf(u139,negated_conjecture,
    forename(sK0,sK2)).

cnf(u111,axiom,
    ~forename(X0,X1) | relname(X0,X1)).

cnf(u138,negated_conjecture,
    mia_forename(sK0,sK2)).

cnf(u105,axiom,
    ~mia_forename(X0,X1) | forename(X0,X1)).

cnf(u168,negated_conjecture,
    entity(sK0,sK3)).

cnf(u153,negated_conjecture,
    entity(sK0,sK1)).

cnf(u114,axiom,
    ~entity(X0,X1) | existent(X0,X1)).

cnf(u115,axiom,
    ~entity(X0,X1) | specific(X0,X1)).

cnf(u154,negated_conjecture,
    living(sK0,sK1)).

cnf(u181,negated_conjecture,
    ~living(sK0,sK3)).

cnf(u149,negated_conjecture,
    organism(sK0,sK1)).

cnf(u101,axiom,
    ~organism(X0,X1) | living(X0,X1)).

cnf(u102,axiom,
    ~organism(X0,X1) | entity(X0,X1)).

cnf(u150,negated_conjecture,
    human(sK0,sK1)).

cnf(u180,negated_conjecture,
    ~human(sK0,sK2)).

cnf(u151,negated_conjecture,
    animate(sK0,sK1)).

cnf(u182,negated_conjecture,
    ~animate(sK0,sK3)).

cnf(u148,negated_conjecture,
    human_person(sK0,sK1)).

cnf(u99,axiom,
    ~human_person(X0,X1) | animate(X0,X1)).

cnf(u100,axiom,
    ~human_person(X0,X1) | human(X0,X1)).

cnf(u103,axiom,
    ~human_person(X0,X1) | organism(X0,X1)).

cnf(u147,negated_conjecture,
    female(sK0,sK1)).

cnf(u189,negated_conjecture,
    ~female(sK0,sK3)).

cnf(u185,negated_conjecture,
    ~female(sK0,sK2)).

cnf(u186,negated_conjecture,
    ~female(sK0,sK4)).

cnf(u137,negated_conjecture,
    woman(sK0,sK1)).

cnf(u98,axiom,
    ~woman(X0,X1) | female(X0,X1)).

cnf(u104,axiom,
    ~woman(X0,X1) | human_person(X0,X1)).

% # SZS output end Saturation.

Sample solution for SWV017+1

% SZS output start FiniteModel for SWV017+1
tff(declare_$i,type,$i:$tType).
tff(declare_$i1,type,at:$i).
tff(declare_$i2,type,t:$i).
tff(finite_domain,axiom,
      ! [X:$i] : (
         X = at | X = t
      ) ).

tff(distinct_domain,axiom,
         at != t
).

tff(declare_bool,type,$o:$tType).
tff(declare_bool1,type,fmb_bool_1:$o).
tff(finite_domain,axiom,
      ! [X:$o] : (
         X = fmb_bool_1
      ) ).

tff(declare_a,type,a:$i).
tff(a_definition,axiom,a = t).
tff(declare_b,type,b:$i).
tff(b_definition,axiom,b = t).
tff(declare_an_a_nonce,type,an_a_nonce:$i).
tff(an_a_nonce_definition,axiom,an_a_nonce = t).
tff(declare_bt,type,bt:$i).
tff(bt_definition,axiom,bt = at).
tff(declare_an_intruder_nonce,type,an_intruder_nonce:$i).
tff(an_intruder_nonce_definition,axiom,an_intruder_nonce = t).
tff(declare_key,type,key: $i * $i > $i).
tff(function_key,axiom,
           key(at,at) = at
         & key(at,t) = at
         & key(t,at) = t
         & key(t,t) = t

).

tff(declare_pair,type,pair: $i * $i > $i).
tff(function_pair,axiom,
           pair(at,at) = at
         & pair(at,t) = at
         & pair(t,at) = at
         & pair(t,t) = t

).

tff(declare_sent,type,sent: $i * $i * $i > $i).
tff(function_sent,axiom,
           sent(at,at,at) = t
         & sent(at,at,t) = at
         & sent(at,t,at) = t
         & sent(at,t,t) = at
         & sent(t,at,at) = t
         & sent(t,at,t) = at
         & sent(t,t,at) = t
         & sent(t,t,t) = at

).

tff(declare_quadruple,type,quadruple: $i * $i * $i * $i > $i).
tff(function_quadruple,axiom,
           quadruple(at,at,at,at) = at
         & quadruple(at,at,at,t) = at
         & quadruple(at,at,t,at) = at
         & quadruple(at,at,t,t) = at
         & quadruple(at,t,at,at) = at
         & quadruple(at,t,at,t) = at
         & quadruple(at,t,t,at) = at
         & quadruple(at,t,t,t) = at
         & quadruple(t,at,at,at) = at
         & quadruple(t,at,at,t) = at
         & quadruple(t,at,t,at) = at
         & quadruple(t,at,t,t) = at
         & quadruple(t,t,at,at) = at
         & quadruple(t,t,at,t) = at
         & quadruple(t,t,t,at) = at
         & quadruple(t,t,t,t) = t

).

tff(declare_encrypt,type,encrypt: $i * $i > $i).
tff(function_encrypt,axiom,
           encrypt(at,at) = t
         & encrypt(at,t) = t
         & encrypt(t,at) = t
         & encrypt(t,t) = t

).

tff(declare_triple,type,triple: $i * $i * $i > $i).
tff(function_triple,axiom,
           triple(at,at,at) = at
         & triple(at,at,t) = at
         & triple(at,t,at) = at
         & triple(at,t,t) = at
         & triple(t,at,at) = at
         & triple(t,at,t) = at
         & triple(t,t,at) = at
         & triple(t,t,t) = t

).

tff(declare_generate_b_nonce,type,generate_b_nonce: $i > $i).
tff(function_generate_b_nonce,axiom,
           generate_b_nonce(at) = t
         & generate_b_nonce(t) = t

).

tff(declare_generate_expiration_time,type,generate_expiration_time: $i > $i).
tff(function_generate_expiration_time,axiom,
           generate_expiration_time(at) = t
         & generate_expiration_time(t) = t

).

tff(declare_generate_key,type,generate_key: $i > $i).
tff(function_generate_key,axiom,
           generate_key(at) = at
         & generate_key(t) = at

).

tff(declare_generate_intruder_nonce,type,generate_intruder_nonce: $i > $i).
tff(function_generate_intruder_nonce,axiom,
           generate_intruder_nonce(at) = at
         & generate_intruder_nonce(t) = t

).

tff(declare_a_holds,type,a_holds: $i > $o ).
tff(predicate_a_holds,axiom,
%         a_holds(at) undefined in model
%         a_holds(t) undefined in model

).

tff(declare_party_of_protocol,type,party_of_protocol: $i > $o ).
tff(predicate_party_of_protocol,axiom,
           party_of_protocol(at)
         & party_of_protocol(t)

).

tff(declare_message,type,message: $i > $o ).
tff(predicate_message,axiom,
           message(at)
         & ~message(t)

).

tff(declare_a_stored,type,a_stored: $i > $o ).
tff(predicate_a_stored,axiom,
           ~a_stored(at)
         & a_stored(t)

).

tff(declare_b_holds,type,b_holds: $i > $o ).
tff(predicate_b_holds,axiom,
%         b_holds(at) undefined in model
%         b_holds(t) undefined in model

).

tff(declare_fresh_to_b,type,fresh_to_b: $i > $o ).
tff(predicate_fresh_to_b,axiom,
           fresh_to_b(at)
         & fresh_to_b(t)

).

tff(declare_b_stored,type,b_stored: $i > $o ).
tff(predicate_b_stored,axiom,
%         b_stored(at) undefined in model
%         b_stored(t) undefined in model

).

tff(declare_a_key,type,a_key: $i > $o ).
tff(predicate_a_key,axiom,
           a_key(at)
         & ~a_key(t)

).

tff(declare_t_holds,type,t_holds: $i > $o ).
tff(predicate_t_holds,axiom,
           t_holds(at)
         & ~t_holds(t)

).

tff(declare_a_nonce,type,a_nonce: $i > $o ).
tff(predicate_a_nonce,axiom,
           ~a_nonce(at)
         & a_nonce(t)

).

tff(declare_intruder_message,type,intruder_message: $i > $o ).
tff(predicate_intruder_message,axiom,
           ~intruder_message(at)
         & intruder_message(t)

).

tff(declare_intruder_holds,type,intruder_holds: $i > $o ).
tff(predicate_intruder_holds,axiom,
           ~intruder_holds(at)
         & intruder_holds(t)

).

tff(declare_fresh_intruder_nonce,type,fresh_intruder_nonce: $i > $o ).
tff(predicate_fresh_intruder_nonce,axiom,
           ~fresh_intruder_nonce(at)
         & fresh_intruder_nonce(t)

).

% SZS output end FiniteModel for SWV017+1

Sample solution for BOO001-1

% SZS output start Proof for BOO001-1
fof(f263,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f258])).
fof(f258,plain,(
  a != a),
  inference(superposition,[],[f6,f186])).
fof(f186,plain,(
  ( ! [X24] : (inverse(inverse(X24)) = X24) )),
  inference(superposition,[],[f132,f5])).
fof(f5,axiom,(
  ( ! [X2,X3] : (multiply(X2,X3,inverse(X3)) = X2) )),
  file('samples/BOO001-1.p',unknown)).
fof(f132,plain,(
  ( ! [X31,X32] : (multiply(X32,inverse(X32),X31) = X31) )),
  inference(superposition,[],[f32,f5])).
fof(f32,plain,(
  ( ! [X3,X4,X5] : (multiply(X5,X3,X4) = multiply(X3,X4,multiply(X5,X3,X4))) )),
  inference(superposition,[],[f7,f2])).
fof(f2,axiom,(
  ( ! [X2,X3] : (multiply(X3,X2,X2) = X2) )),
  file('samples/BOO001-1.p',unknown)).
fof(f7,plain,(
  ( ! [X2,X3,X0,X1] : (multiply(X0,X1,multiply(X1,X2,X3)) = multiply(X1,X2,multiply(X0,X1,X3))) )),
  inference(superposition,[],[f1,f2])).
fof(f1,axiom,(
  ( ! [X2,X3,X0,X1,X4] : (multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4))) )),
  file('samples/BOO001-1.p',unknown)).
fof(f6,axiom,(
  a != inverse(inverse(a))),
  file('samples/BOO001-1.p',unknown)).
% SZS output end Proof for BOO001-1

Zipperposition 2.1

Sample solution for SET014^4

% SZS status Theorem for '/home/petar/Documents/tptp/Problems/SET/SET014^4.p'
% SZS output start Refutation
thf(sk__5_type, type, sk__5: $i > $o).
thf(sk__3_type, type, sk__3: $i > $o).
thf(union_type, type, union: ($i > $o) > ($i > $o) > $i > $o).
thf(sk__6_type, type, sk__6: $i).
thf(sk__4_type, type, sk__4: $i > $o).
thf(subset_type, type, subset: ($i > $o) > ($i > $o) > $o).
thf(subset, axiom,(( subset  ) =
  (^[X:( $i > $o ),Y:( $i > $o )]: ( ![U:$i]: ( ( X @ U ) => ( Y @ U ) ) )))).
thf('0', plain,
    (( subset ) =
     ( ^[X:( $i > $o ),Y:( $i > $o )]:
       ( ![U:$i]: ( ( X @ U ) => ( Y @ U ) ) ) )),
    inference('simplify_rw_rule', [status(thm)], [subset])).
thf('1', plain,
    (( subset ) =
     ( ^[V_1:( $i > $o ),V_2:( $i > $o )]:
       ( ![X4:$i]: ( ( V_1 @ X4 ) => ( V_2 @ X4 ) ) ) )),
    define([status(thm)])).
thf(union, axiom,(( union  ) =
  (^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) )))).
thf('2', plain,
    (( union ) =
     ( ^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) ) )),
    inference('simplify_rw_rule', [status(thm)], [union])).
thf('3', plain,
    (( union ) =
     ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]:
       ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )),
    define([status(thm)])).
thf(thm, conjecture,
  (![X:( $i > $o ),Y:( $i > $o ),A:( $i > $o )]:
   ( ( ( subset @ X @ A ) & ( subset @ Y @ A ) ) =>
     ( subset @ ( union @ X @ Y ) @ A ) ))).
thf(zf_stmt_0, conjecture,
  (![X4:( $i > $o ),X6:( $i > $o ),X8:( $i > $o )]:
   ( ( ( ![X10:$i]: ( ( X4 @ X10 ) => ( X8 @ X10 ) ) ) & 
       ( ![X12:$i]: ( ( X6 @ X12 ) => ( X8 @ X12 ) ) ) ) =>
     ( ![X14:$i]: ( ( ( X4 @ X14 ) | ( X6 @ X14 ) ) => ( X8 @ X14 ) ) ) ))).
thf(zf_stmt_1, negated_conjecture,
  (~( ![X4:( $i > $o ),X6:( $i > $o ),X8:( $i > $o )]:
      ( ( ( ![X10:$i]: ( ( X4 @ X10 ) => ( X8 @ X10 ) ) ) & 
          ( ![X12:$i]: ( ( X6 @ X12 ) => ( X8 @ X12 ) ) ) ) =>
        ( ![X14:$i]: ( ( ( X4 @ X14 ) | ( X6 @ X14 ) ) => ( X8 @ X14 ) ) ) ) )),
  inference('cnf.neg', [status(esa)], [zf_stmt_0])).
thf(zip_derived_cl2, plain, (~ (sk__5 @ sk__6)),
    inference('cnf', [status(esa)], [zf_stmt_1])).
thf(zip_derived_cl3, plain, (( (sk__3 @ sk__6) |  (sk__4 @ sk__6))),
    inference('cnf', [status(esa)], [zf_stmt_1])).
thf(zip_derived_cl1, plain, (![X1 : $i]: ( (sk__5 @ X1) | ~ (sk__4 @ X1))),
    inference('cnf', [status(esa)], [zf_stmt_1])).
thf(zip_derived_cl5, plain, (( (sk__3 @ sk__6) |  (sk__5 @ sk__6))),
    inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
thf(zip_derived_cl2, plain, (~ (sk__5 @ sk__6)),
    inference('cnf', [status(esa)], [zf_stmt_1])).
thf(zip_derived_cl8, plain, ( (sk__3 @ sk__6)),
    inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl2])).
thf(zip_derived_cl0, plain, (![X0 : $i]: ( (sk__5 @ X0) | ~ (sk__3 @ X0))),
    inference('cnf', [status(esa)], [zf_stmt_1])).
thf(zip_derived_cl12, plain, ( (sk__5 @ sk__6)),
    inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl0])).
thf(zip_derived_cl16, plain, ($false),
    inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl12])).

% SZS output end Refutation

Zipperposition 2.1.999

Sample solution for SET014^4

% SZS status Theorem for '/Users/blanchette/gits/zipperposition/examples/ho/SET014^4.p'
% SZS output start Refutation
thf(sk__6_type, type, sk__6: $i).
thf(sk__4_type, type, sk__4: $i > $o).
thf(union_type, type, union: ($i > $o) > ($i > $o) > $i > $o).
thf(sk__3_type, type, sk__3: $i > $o).
thf(sk__5_type, type, sk__5: $i > $o).
thf(subset_type, type, subset: ($i > $o) > ($i > $o) > $o).
thf(subset, axiom,(( subset  ) =
  (^[X:( $i > $o ),Y:( $i > $o )]: ( ![U:$i]: ( ( X @ U ) => ( Y @ U ) ) )))).
thf('0', plain,
    (( subset ) =
     ( ^[X:( $i > $o ),Y:( $i > $o )]:
       ( ![U:$i]: ( ( X @ U ) => ( Y @ U ) ) ) )),
    inference('simplify_rw_rule', [status(thm)], [subset])).
thf('1', plain,
    (( subset ) =
     ( ^[V_1:( $i > $o ),V_2:( $i > $o )]:
       ( ![X4:$i]: ( ( V_1 @ X4 ) => ( V_2 @ X4 ) ) ) )),
    define([status(thm)])).
thf(union, axiom,(( union  ) =
  (^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) )))).
thf('2', plain,
    (( union ) =
     ( ^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) ) )),
    inference('simplify_rw_rule', [status(thm)], [union])).
thf('3', plain,
    (( union ) =
     ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]:
       ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )),
    define([status(thm)])).
thf(thm, conjecture,
  (![X:( $i > $o ),Y:( $i > $o ),A:( $i > $o )]:
   ( ( ( subset @ X @ A ) & ( subset @ Y @ A ) ) =>
     ( subset @ ( union @ X @ Y ) @ A ) ))).
thf(zf_stmt_0, conjecture,
  (![X4:( $i > $o ),X6:( $i > $o ),X8:( $i > $o )]:
   ( ( ( ![X10:$i]: ( ( X4 @ X10 ) => ( X8 @ X10 ) ) ) &
       ( ![X12:$i]: ( ( X6 @ X12 ) => ( X8 @ X12 ) ) ) ) =>
     ( ![X14:$i]: ( ( ( X4 @ X14 ) | ( X6 @ X14 ) ) => ( X8 @ X14 ) ) ) ))).
thf(zf_stmt_1, negated_conjecture,
  (~( ![X4:( $i > $o ),X6:( $i > $o ),X8:( $i > $o )]:
      ( ( ( ![X10:$i]: ( ( X4 @ X10 ) => ( X8 @ X10 ) ) ) &
          ( ![X12:$i]: ( ( X6 @ X12 ) => ( X8 @ X12 ) ) ) ) =>
        ( ![X14:$i]: ( ( ( X4 @ X14 ) | ( X6 @ X14 ) ) => ( X8 @ X14 ) ) ) ) )),
  inference('cnf.neg', [status(esa)], [zf_stmt_0])).
thf(zip_derived_cl2, plain, (~ (sk__5 @ sk__6)),
    inference('cnf', [status(esa)], [zf_stmt_1])).
thf(zip_derived_cl3, plain, (( (sk__3 @ sk__6) |  (sk__4 @ sk__6))),
    inference('cnf', [status(esa)], [zf_stmt_1])).
thf(zip_derived_cl0, plain, (![X0 : $i]: ( (sk__5 @ X0) | ~ (sk__3 @ X0))),
    inference('cnf', [status(esa)], [zf_stmt_1])).
thf(zip_derived_cl4, plain, (( (sk__4 @ sk__6) |  (sk__5 @ sk__6))),
    inference('dp-resolution', [status(thm)],
              [zip_derived_cl3, zip_derived_cl0])).
thf(zip_derived_cl1, plain, (![X1 : $i]: ( (sk__5 @ X1) | ~ (sk__4 @ X1))),
    inference('cnf', [status(esa)], [zf_stmt_1])).
thf(zip_derived_cl5, plain, (( (sk__5 @ sk__6) |  (sk__5 @ sk__6))),
    inference('dp-resolution', [status(thm)],
              [zip_derived_cl4, zip_derived_cl1])).
thf(zip_derived_cl6, plain, ( (sk__5 @ sk__6)),
    inference('simplify', [status(thm)], [zip_derived_cl5])).
thf(zip_derived_cl7, plain, ($false),
    inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl6])).

% SZS output end Refutation

Sample solution for SEU140+2

% SZS status Theorem for '/Users/blanchette/gits/zipperposition/examples/SEU140+2.p'
% SZS output start Refutation
thf(sk__11_type, type, sk__11: $i).
thf(sk__10_type, type, sk__10: $i).
thf(disjoint_type, type, disjoint: $i > $i > $o).
thf(empty_set_type, type, empty_set: $i).
thf(sk__12_type, type, sk__12: $i).
thf(subset_type, type, subset: $i > $i > $o).
thf(set_intersection2_type, type, set_intersection2: $i > $i > $i).
thf(d7_xboole_0, axiom,
  (![A:$i,B:$i]:
   ( ( disjoint @ A @ B ) <=>
     ( ( set_intersection2 @ A @ B ) = ( empty_set ) ) ))).
thf(zip_derived_cl30, plain,
    (![X0 : $i, X1 : $i]:
       (((set_intersection2 @ X0 @ X1) = (empty_set))
        | ~ (disjoint @ X0 @ X1))),
    inference('cnf', [status(esa)], [d7_xboole_0])).
thf(t63_xboole_1, conjecture,
  (![A:$i,B:$i,C:$i]:
   ( ( ( subset @ A @ B ) & ( disjoint @ B @ C ) ) => ( disjoint @ A @ C ) ))).
thf(zf_stmt_0, negated_conjecture,
  (~( ![A:$i,B:$i,C:$i]:
      ( ( ( subset @ A @ B ) & ( disjoint @ B @ C ) ) => ( disjoint @ A @ C ) ) )),
  inference('cnf.neg', [status(esa)], [t63_xboole_1])).
thf(zip_derived_cl80, plain, ( (disjoint @ sk__11 @ sk__12)),
    inference('cnf', [status(esa)], [zf_stmt_0])).
thf(zip_derived_cl526, plain,
    (((set_intersection2 @ sk__11 @ sk__12) = (empty_set))),
    inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl80])).
thf(t26_xboole_1, axiom,
  (![A:$i,B:$i,C:$i]:
   ( ( subset @ A @ B ) =>
     ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ))).
thf(zip_derived_cl56, plain,
    (![X0 : $i, X1 : $i, X2 : $i]:
       (~ (subset @ X0 @ X1)
        |  (subset @ (set_intersection2 @ X0 @ X2) @
            (set_intersection2 @ X1 @ X2)))),
    inference('cnf', [status(esa)], [t26_xboole_1])).
thf(zip_derived_cl600, plain,
    (![X0 : $i]:
       ( (subset @ (set_intersection2 @ X0 @ sk__12) @ empty_set)
        | ~ (subset @ X0 @ sk__11))),
    inference('sup+', [status(thm)], [zip_derived_cl526, zip_derived_cl56])).
thf(t3_xboole_1, axiom,
  (![A:$i]: ( ( subset @ A @ empty_set ) => ( ( A ) = ( empty_set ) ) ))).
thf(zip_derived_cl71, plain,
    (![X0 : $i]: (((X0) = (empty_set)) | ~ (subset @ X0 @ empty_set))),
    inference('cnf', [status(esa)], [t3_xboole_1])).
thf(zip_derived_cl649, plain,
    (![X0 : $i]:
       (~ (subset @ X0 @ sk__11)
        | ((set_intersection2 @ X0 @ sk__12) = (empty_set)))),
    inference('sup-', [status(thm)], [zip_derived_cl600, zip_derived_cl71])).
thf(zip_derived_cl31, plain,
    (![X0 : $i, X1 : $i]:
       ( (disjoint @ X0 @ X1)
        | ((set_intersection2 @ X0 @ X1) != (empty_set)))),
    inference('cnf', [status(esa)], [d7_xboole_0])).
thf(zip_derived_cl79, plain, (~ (disjoint @ sk__10 @ sk__12)),
    inference('cnf', [status(esa)], [zf_stmt_0])).
thf(zip_derived_cl367, plain,
    (((set_intersection2 @ sk__10 @ sk__12) != (empty_set))),
    inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl79])).
thf(zip_derived_cl681, plain,
    ((((empty_set) != (empty_set)) | ~ (subset @ sk__10 @ sk__11))),
    inference('sup-', [status(thm)], [zip_derived_cl649, zip_derived_cl367])).
thf(zip_derived_cl81, plain, ( (subset @ sk__10 @ sk__11)),
    inference('cnf', [status(esa)], [zf_stmt_0])).
thf(zip_derived_cl701, plain, (((empty_set) != (empty_set))),
    inference('demod', [status(thm)], [zip_derived_cl681, zip_derived_cl81])).
thf(zip_derived_cl702, plain, ($false),
    inference('simplify', [status(thm)], [zip_derived_cl701])).

% SZS output end Refutation