TSTP Solution File: NUN076+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUN076+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 12:45:24 EDT 2023
% Result : Theorem 1.16s 1.29s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUN076+1 : TPTP v8.1.2. Released v7.3.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 09:41:53 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.63 start to proof:theBenchmark
% 1.16/1.28 %-------------------------------------------
% 1.16/1.28 % File :CSE---1.6
% 1.16/1.28 % Problem :theBenchmark
% 1.16/1.28 % Transform :cnf
% 1.16/1.28 % Format :tptp:raw
% 1.16/1.28 % Command :java -jar mcs_scs.jar %d %s
% 1.16/1.28
% 1.16/1.28 % Result :Theorem 0.600000s
% 1.16/1.28 % Output :CNFRefutation 0.600000s
% 1.16/1.28 %-------------------------------------------
% 1.16/1.29 %------------------------------------------------------------------------------
% 1.16/1.29 % File : NUN076+1 : TPTP v8.1.2. Released v7.3.0.
% 1.16/1.29 % Domain : Number Theory
% 1.16/1.29 % Problem : Robinson arithmetic: There exists even X
% 1.16/1.29 % Version : Especial.
% 1.16/1.29 % English :
% 1.16/1.29
% 1.16/1.29 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 1.16/1.29 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 1.16/1.29 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 1.16/1.29 % Source : [Lam18]
% 1.16/1.29 % Names : thereexistsanevennumberid [Lam18]
% 1.16/1.29
% 1.16/1.29 % Status : Theorem
% 1.16/1.29 % Rating : 0.27 v8.1.0, 0.36 v7.5.0, 0.33 v7.4.0, 0.25 v7.3.0
% 1.16/1.29 % Syntax : Number of formulae : 19 ( 1 unt; 0 def)
% 1.16/1.29 % Number of atoms : 82 ( 0 equ)
% 1.16/1.29 % Maximal formula atoms : 7 ( 4 avg)
% 1.16/1.29 % Number of connectives : 97 ( 34 ~; 26 |; 37 &)
% 1.16/1.29 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 1.16/1.29 % Maximal formula depth : 13 ( 8 avg)
% 1.16/1.29 % Maximal term depth : 1 ( 1 avg)
% 1.16/1.29 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 1.16/1.29 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 1.16/1.29 % Number of variables : 75 ( 47 !; 28 ?)
% 1.16/1.29 % SPC : FOF_THM_RFO_NEQ
% 1.16/1.29
% 1.16/1.29 % Comments : Translated to FOL without equality.
% 1.16/1.29 %------------------------------------------------------------------------------
% 1.16/1.29 include('Axioms/NUM009+0.ax').
% 1.16/1.29 %------------------------------------------------------------------------------
% 1.16/1.29 fof(thereexistsanevennumberid,conjecture,
% 1.16/1.29 ? [Y1,Y2,Y3] :
% 1.16/1.29 ( ? [Y4] :
% 1.16/1.29 ( id(Y4,Y1)
% 1.16/1.29 & ? [Y6] :
% 1.16/1.29 ( r4(Y6,Y2,Y4)
% 1.16/1.29 & ? [Y7] :
% 1.16/1.29 ( r2(Y7,Y6)
% 1.16/1.29 & ? [Y8] :
% 1.16/1.29 ( r1(Y8)
% 1.16/1.29 & r2(Y8,Y7) ) ) ) )
% 1.16/1.29 & ? [Y5] :
% 1.16/1.29 ( id(Y5,Y1)
% 1.16/1.29 & r3(Y2,Y3,Y5) ) ) ).
% 1.16/1.29
% 1.16/1.29 %------------------------------------------------------------------------------
% 1.16/1.29 %-------------------------------------------
% 1.16/1.29 % Proof found
% 1.16/1.29 % SZS status Theorem for theBenchmark
% 1.16/1.29 % SZS output start Proof
% 1.16/1.29 %ClaNum:43(EqnAxiom:0)
% 1.16/1.29 %VarNum:216(SingletonVarNum:106)
% 1.16/1.29 %MaxLitNum:7
% 1.16/1.29 %MaxfuncDepth:1
% 1.16/1.29 %SharedTerms:1
% 1.16/1.29 %goalClause: 43
% 1.16/1.29 [4]P2(x41,x41)
% 1.16/1.29 [1]P1(f1(x11))
% 1.16/1.29 [2]P1(f6(x21))
% 1.16/1.29 [3]P1(f8(x31))
% 1.16/1.29 [5]P2(f2(x51),x51)
% 1.16/1.29 [6]P2(f7(x61),f8(x61))
% 1.16/1.29 [12]P4(x121,f1(x121),f2(x121))
% 1.16/1.29 [13]P5(x131,f6(x131),f7(x131))
% 1.16/1.29 [7]P3(x71,f9(x72,x71))
% 1.16/1.29 [8]P3(x81,f3(x82,x81))
% 1.16/1.29 [9]P2(f10(x91,x92),f11(x91,x92))
% 1.16/1.29 [10]P2(f4(x101,x102),f19(x101,x102))
% 1.16/1.29 [11]P3(f20(x111,x112),f11(x111,x112))
% 1.16/1.29 [14]P4(x141,x142,f20(x141,x142))
% 1.16/1.29 [15]P5(x151,x152,f5(x151,x152))
% 1.16/1.29 [16]P4(x161,f9(x161,x162),f10(x161,x162))
% 1.16/1.29 [17]P5(x171,f3(x171,x172),f4(x171,x172))
% 1.16/1.29 [18]P4(f5(x181,x182),x181,f19(x181,x182))
% 1.16/1.29 [19]~P1(x191)+P2(x191,a12)
% 1.16/1.29 [20]P1(x201)+~P2(x201,a12)
% 1.16/1.29 [21]P2(x211,f15(x211))+P1(f13(x211))
% 1.16/1.29 [25]P3(f14(x251),f15(x251))+P1(f13(x251))
% 1.16/1.29 [26]P2(x261,f15(x261))+P2(x261,f13(x261))
% 1.16/1.29 [29]P3(f14(x291),f15(x291))+P2(x291,f13(x291))
% 1.16/1.29 [24]~P2(x242,x241)+P2(x241,x242)
% 1.16/1.29 [27]~P3(x272,x271)+P2(x271,f16(x272))
% 1.16/1.29 [28]P3(x281,x282)+~P2(x282,f16(x281))
% 1.16/1.29 [35]P4(x351,x352,x353)+~P2(x353,f17(x351,x352))
% 1.16/1.29 [36]P5(x361,x362,x363)+~P2(x363,f18(x361,x362))
% 1.16/1.29 [37]~P4(x372,x373,x371)+P2(x371,f17(x372,x373))
% 1.16/1.29 [38]~P5(x382,x383,x381)+P2(x381,f18(x382,x383))
% 1.16/1.29 [22]~P2(x222,x221)+P1(x221)+~P1(x222)
% 1.16/1.29 [23]~P2(x231,x232)+P1(x231)+~P1(x232)
% 1.16/1.29 [30]~P1(x301)+~P2(x301,x302)+~P3(x303,x302)
% 1.16/1.29 [31]~P2(x311,x313)+P2(x311,x312)+~P2(x313,x312)
% 1.16/1.29 [32]~P3(x322,x324)+~P3(x321,x323)+P2(x321,x322)+~P2(x323,x324)
% 1.16/1.29 [33]~P3(x334,x333)+P3(x331,x332)+~P2(x333,x332)+~P2(x334,x331)
% 1.16/1.29 [34]~P3(x344,x343)+P3(x341,x342)+~P2(x342,x343)+~P2(x341,x344)
% 1.16/1.29 [39]~P4(x396,x395,x394)+P4(x391,x392,x393)+~P2(x394,x393)+~P2(x395,x392)+~P2(x396,x391)
% 1.16/1.29 [40]~P4(x406,x405,x404)+P4(x401,x402,x403)+~P2(x403,x404)+~P2(x402,x405)+~P2(x401,x406)
% 1.16/1.29 [41]~P5(x416,x415,x414)+P5(x411,x412,x413)+~P2(x414,x413)+~P2(x415,x412)+~P2(x416,x411)
% 1.16/1.29 [42]~P5(x426,x425,x424)+P5(x421,x422,x423)+~P2(x423,x424)+~P2(x422,x425)+~P2(x421,x426)
% 1.16/1.29 [43]~P5(x436,x437,x434)+~P1(x431)+~P2(x432,x433)+~P2(x434,x433)+~P3(x431,x435)+~P4(x437,x438,x432)+~P3(x435,x436)
% 1.16/1.29 %EqnAxiom
% 1.16/1.29
% 1.16/1.29 %-------------------------------------------
% 1.16/1.30 cnf(44,plain,
% 1.16/1.30 (P1(a12)),
% 1.16/1.30 inference(scs_inference,[],[4,20])).
% 1.16/1.30 cnf(45,plain,
% 1.16/1.30 (P2(x451,x451)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(46,plain,
% 1.16/1.30 (P3(x461,f16(x461))),
% 1.16/1.30 inference(scs_inference,[],[4,45,20,28])).
% 1.16/1.30 cnf(47,plain,
% 1.16/1.30 (P2(x471,x471)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(49,plain,
% 1.16/1.30 (P5(x491,x492,f18(x491,x492))),
% 1.16/1.30 inference(scs_inference,[],[4,45,47,20,28,36])).
% 1.16/1.30 cnf(50,plain,
% 1.16/1.30 (P2(x501,x501)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(52,plain,
% 1.16/1.30 (P4(x521,x522,f17(x521,x522))),
% 1.16/1.30 inference(scs_inference,[],[4,45,47,50,20,28,36,35])).
% 1.16/1.30 cnf(53,plain,
% 1.16/1.30 (P2(x531,x531)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(55,plain,
% 1.16/1.30 (~P3(x551,f1(x552))),
% 1.16/1.30 inference(scs_inference,[],[1,4,45,47,50,53,20,28,36,35,30])).
% 1.16/1.30 cnf(57,plain,
% 1.16/1.30 (~P3(f1(x571),f2(f1(x571)))),
% 1.16/1.30 inference(scs_inference,[],[1,4,45,47,50,53,5,20,28,36,35,30,33])).
% 1.16/1.30 cnf(58,plain,
% 1.16/1.30 (P2(f2(x581),x581)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(59,plain,
% 1.16/1.30 (P2(x591,x591)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(61,plain,
% 1.16/1.30 (P5(x611,x611,f2(f5(x611,x611)))),
% 1.16/1.30 inference(scs_inference,[],[1,4,45,47,50,53,59,15,5,58,20,28,36,35,30,33,42])).
% 1.16/1.30 cnf(62,plain,
% 1.16/1.30 (P2(f2(x621),x621)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(64,plain,
% 1.16/1.30 (P2(x641,x641)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(65,plain,
% 1.16/1.30 (P5(x651,x652,f5(x651,x652))),
% 1.16/1.30 inference(rename_variables,[],[15])).
% 1.16/1.30 cnf(67,plain,
% 1.16/1.30 (P4(x671,x671,f2(f20(x671,x671)))),
% 1.16/1.30 inference(scs_inference,[],[1,4,45,47,50,53,59,64,14,15,5,58,62,20,28,36,35,30,33,42,40])).
% 1.16/1.30 cnf(68,plain,
% 1.16/1.30 (P2(f2(x681),x681)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(70,plain,
% 1.16/1.30 (P2(x701,x701)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(71,plain,
% 1.16/1.30 (P4(x711,x712,f20(x711,x712))),
% 1.16/1.30 inference(rename_variables,[],[14])).
% 1.16/1.30 cnf(73,plain,
% 1.16/1.30 (P2(x731,f2(x731))),
% 1.16/1.30 inference(scs_inference,[],[1,4,45,47,50,53,59,64,14,15,5,58,62,68,20,28,36,35,30,33,42,40,24])).
% 1.16/1.30 cnf(75,plain,
% 1.16/1.30 (P2(f1(x751),a12)),
% 1.16/1.30 inference(scs_inference,[],[1,4,45,47,50,53,59,64,14,15,5,58,62,68,20,28,36,35,30,33,42,40,24,19])).
% 1.16/1.30 cnf(77,plain,
% 1.16/1.30 (P2(f9(x771,x772),f16(x772))),
% 1.16/1.30 inference(scs_inference,[],[1,4,45,47,50,53,59,64,14,15,5,58,62,68,7,20,28,36,35,30,33,42,40,24,19,27])).
% 1.16/1.30 cnf(79,plain,
% 1.16/1.30 (P2(f5(x791,x792),f18(x791,x792))),
% 1.16/1.30 inference(scs_inference,[],[1,4,45,47,50,53,59,64,14,15,65,5,58,62,68,7,20,28,36,35,30,33,42,40,24,19,27,38])).
% 1.16/1.30 cnf(81,plain,
% 1.16/1.30 (P2(f20(x811,x812),f17(x811,x812))),
% 1.16/1.30 inference(scs_inference,[],[1,4,45,47,50,53,59,64,14,71,15,65,5,58,62,68,7,20,28,36,35,30,33,42,40,24,19,27,38,37])).
% 1.16/1.30 cnf(83,plain,
% 1.16/1.30 (~P2(f1(x831),f9(x832,f1(x831)))),
% 1.16/1.30 inference(scs_inference,[],[1,4,45,47,50,53,59,64,70,14,71,15,65,5,58,62,68,7,20,28,36,35,30,33,42,40,24,19,27,38,37,34])).
% 1.16/1.30 cnf(104,plain,
% 1.16/1.30 (P2(f4(x1041,x1042),f2(f19(x1041,x1042)))),
% 1.16/1.30 inference(scs_inference,[],[10,73,31])).
% 1.16/1.30 cnf(105,plain,
% 1.16/1.30 (P2(x1051,f2(x1051))),
% 1.16/1.30 inference(rename_variables,[],[73])).
% 1.16/1.30 cnf(110,plain,
% 1.16/1.30 (P2(x1101,x1101)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(112,plain,
% 1.16/1.30 (~P2(f1(x1121),f3(x1122,x1123))),
% 1.16/1.30 inference(scs_inference,[],[1,8,10,4,73,55,31,28,30,22])).
% 1.16/1.30 cnf(116,plain,
% 1.16/1.30 (P2(x1161,x1161)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(124,plain,
% 1.16/1.30 (P2(x1241,x1241)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(127,plain,
% 1.16/1.30 (P2(x1271,x1271)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(129,plain,
% 1.16/1.30 (P2(x1291,f2(x1291))),
% 1.16/1.30 inference(rename_variables,[],[73])).
% 1.16/1.30 cnf(135,plain,
% 1.16/1.30 (P5(x1351,f2(f6(x1351)),f8(x1351))),
% 1.16/1.30 inference(scs_inference,[],[1,8,2,12,13,10,4,110,116,124,127,14,15,5,6,73,105,129,83,55,31,28,30,22,42,33,40,39,24,23,41])).
% 1.16/1.30 cnf(144,plain,
% 1.16/1.30 (P2(f2(f10(x1441,x1442)),f11(x1441,x1442))),
% 1.16/1.30 inference(scs_inference,[],[9,5,31])).
% 1.16/1.30 cnf(145,plain,
% 1.16/1.30 (P2(f2(x1451),x1451)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(147,plain,
% 1.16/1.30 (P1(f2(a12))),
% 1.16/1.30 inference(scs_inference,[],[9,5,145,31,20])).
% 1.16/1.30 cnf(148,plain,
% 1.16/1.30 (P2(f2(x1481),x1481)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(151,plain,
% 1.16/1.30 (P2(f2(x1511),x1511)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(153,plain,
% 1.16/1.30 (~P1(f10(x1531,x1532))),
% 1.16/1.30 inference(scs_inference,[],[11,9,5,145,148,31,20,28,30])).
% 1.16/1.30 cnf(158,plain,
% 1.16/1.30 (P2(x1581,x1581)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(159,plain,
% 1.16/1.30 (P2(f2(x1591),x1591)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(162,plain,
% 1.16/1.30 (P4(x1621,f9(x1621,x1622),f10(x1621,x1622))),
% 1.16/1.30 inference(rename_variables,[],[16])).
% 1.16/1.30 cnf(163,plain,
% 1.16/1.30 (P2(x1631,x1631)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(164,plain,
% 1.16/1.30 (P2(f2(x1641),x1641)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(166,plain,
% 1.16/1.30 (P4(x1661,f16(x1662),f11(x1661,x1662))),
% 1.16/1.30 inference(scs_inference,[],[16,162,17,11,9,4,158,163,5,145,148,151,159,77,75,31,20,28,30,42,40,39])).
% 1.16/1.30 cnf(168,plain,
% 1.16/1.30 (~P1(f2(f10(x1681,x1682)))),
% 1.16/1.30 inference(scs_inference,[],[16,162,17,11,9,4,158,163,5,145,148,151,159,164,77,75,31,20,28,30,42,40,39,22])).
% 1.16/1.30 cnf(169,plain,
% 1.16/1.30 (P2(f2(x1691),x1691)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(171,plain,
% 1.16/1.30 (P5(x1711,x1711,f5(f2(x1711),f2(x1711)))),
% 1.16/1.30 inference(scs_inference,[],[16,162,17,11,9,4,158,163,15,5,145,148,151,159,164,169,77,75,31,20,28,30,42,40,39,22,41])).
% 1.16/1.30 cnf(173,plain,
% 1.16/1.30 (P2(f8(x1731),f7(x1731))),
% 1.16/1.30 inference(scs_inference,[],[16,162,17,11,9,4,158,163,15,5,145,148,151,159,164,169,6,77,75,31,20,28,30,42,40,39,22,41,24])).
% 1.16/1.30 cnf(189,plain,
% 1.16/1.30 (P5(x1891,x1891,f2(f18(x1891,x1891)))),
% 1.16/1.30 inference(scs_inference,[],[4,5,49,42])).
% 1.16/1.30 cnf(191,plain,
% 1.16/1.30 (P2(f2(x1911),x1911)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(193,plain,
% 1.16/1.30 (~P2(f10(x1931,x1932),a12)),
% 1.16/1.30 inference(scs_inference,[],[4,5,49,153,42,20])).
% 1.16/1.30 cnf(197,plain,
% 1.16/1.30 (~P3(x1971,f7(x1972))),
% 1.16/1.30 inference(scs_inference,[],[3,18,4,5,191,10,49,173,153,42,20,40,30])).
% 1.16/1.30 cnf(198,plain,
% 1.16/1.30 (P2(f8(x1981),f7(x1981))),
% 1.16/1.30 inference(rename_variables,[],[173])).
% 1.16/1.30 cnf(200,plain,
% 1.16/1.30 (P1(f7(x2001))),
% 1.16/1.30 inference(scs_inference,[],[3,18,4,5,191,10,49,173,198,153,42,20,40,30,22])).
% 1.16/1.30 cnf(203,plain,
% 1.16/1.30 (P3(f17(x2031,x2032),f2(f11(x2031,x2032)))),
% 1.16/1.30 inference(scs_inference,[],[3,18,11,4,5,191,10,49,81,173,198,153,73,42,20,40,30,22,33])).
% 1.16/1.30 cnf(205,plain,
% 1.16/1.30 (P2(x2051,f2(x2051))),
% 1.16/1.30 inference(rename_variables,[],[73])).
% 1.16/1.30 cnf(207,plain,
% 1.16/1.30 (~P1(f11(x2071,x2072))),
% 1.16/1.30 inference(scs_inference,[],[3,18,11,4,5,191,9,10,49,81,173,198,153,73,42,20,40,30,22,33,23])).
% 1.16/1.30 cnf(212,plain,
% 1.16/1.30 (~P2(f3(x2121,x2122),f1(x2123))),
% 1.16/1.30 inference(scs_inference,[],[3,18,11,4,5,191,9,10,49,81,173,198,112,153,73,205,55,42,20,40,30,22,33,23,34,24])).
% 1.16/1.30 cnf(222,plain,
% 1.16/1.30 (P2(f2(x2221),x2221)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(225,plain,
% 1.16/1.30 (P2(f2(f7(x2251)),f8(x2251))),
% 1.16/1.30 inference(scs_inference,[],[6,5,222,67,39,31])).
% 1.16/1.30 cnf(226,plain,
% 1.16/1.30 (P2(f2(x2261),x2261)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(228,plain,
% 1.16/1.30 (P2(f17(x2281,x2282),f20(x2281,x2282))),
% 1.16/1.30 inference(scs_inference,[],[11,6,5,222,226,67,203,39,31,32])).
% 1.16/1.30 cnf(229,plain,
% 1.16/1.30 (P3(f20(x2291,x2292),f11(x2291,x2292))),
% 1.16/1.30 inference(rename_variables,[],[11])).
% 1.16/1.30 cnf(230,plain,
% 1.16/1.30 (P2(f2(x2301),x2301)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(236,plain,
% 1.16/1.30 (~P3(x2361,f7(x2362))),
% 1.16/1.30 inference(rename_variables,[],[197])).
% 1.16/1.30 cnf(239,plain,
% 1.16/1.30 (P2(f2(x2391),x2391)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(244,plain,
% 1.16/1.30 (~P2(f2(f10(x2441,x2442)),f8(x2443))),
% 1.16/1.30 inference(scs_inference,[],[3,46,11,6,5,222,226,230,67,189,203,168,197,173,39,31,32,22,33,41,30,23])).
% 1.16/1.30 cnf(246,plain,
% 1.16/1.30 (~P3(x2461,f8(x2462))),
% 1.16/1.30 inference(scs_inference,[],[3,46,11,6,5,222,226,230,239,67,189,203,168,197,236,173,39,31,32,22,33,41,30,23,34])).
% 1.16/1.30 cnf(250,plain,
% 1.16/1.30 (P2(f11(x2501,x2502),f10(x2501,x2502))),
% 1.16/1.30 inference(scs_inference,[],[3,46,11,6,5,222,226,230,239,9,67,189,203,168,197,236,173,39,31,32,22,33,41,30,23,34,24])).
% 1.16/1.30 cnf(252,plain,
% 1.16/1.30 (P2(f7(x2521),f18(x2521,f6(x2521)))),
% 1.16/1.30 inference(scs_inference,[],[3,46,13,11,6,5,222,226,230,239,9,67,189,203,168,197,236,173,39,31,32,22,33,41,30,23,34,24,38])).
% 1.16/1.30 cnf(255,plain,
% 1.16/1.30 (P2(f2(x2551),x2551)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(259,plain,
% 1.16/1.30 (P2(f2(x2591),f17(x2591,f1(x2591)))),
% 1.16/1.30 inference(scs_inference,[],[3,46,12,13,11,229,6,5,222,226,230,239,9,67,189,203,168,197,236,173,39,31,32,22,33,41,30,23,34,24,38,36,27,37])).
% 1.16/1.30 cnf(264,plain,
% 1.16/1.30 (P2(f8(x2641),a12)),
% 1.16/1.30 inference(scs_inference,[],[3,46,12,13,11,229,6,5,222,226,230,239,255,9,67,189,203,168,197,236,173,39,31,32,22,33,41,30,23,34,24,38,36,27,37,35,19])).
% 1.16/1.30 cnf(268,plain,
% 1.16/1.30 (~P2(f10(x2681,x2682),f8(x2683))),
% 1.16/1.30 inference(scs_inference,[],[5,244,31])).
% 1.16/1.30 cnf(269,plain,
% 1.16/1.30 (P2(f2(x2691),x2691)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(271,plain,
% 1.16/1.30 (P3(f20(x2711,x2712),f10(x2711,x2712))),
% 1.16/1.30 inference(scs_inference,[],[11,5,4,250,244,31,33])).
% 1.16/1.30 cnf(277,plain,
% 1.16/1.30 (P1(f2(f8(x2771)))),
% 1.16/1.30 inference(scs_inference,[],[3,11,5,269,4,250,244,31,33,30,23])).
% 1.16/1.30 cnf(289,plain,
% 1.16/1.30 (P3(x2891,f16(x2891))),
% 1.16/1.30 inference(rename_variables,[],[46])).
% 1.16/1.30 cnf(296,plain,
% 1.16/1.30 (~P3(x2961,a12)),
% 1.16/1.30 inference(scs_inference,[],[4,44,46,289,7,246,193,32,33,30])).
% 1.16/1.30 cnf(299,plain,
% 1.16/1.30 (P1(f2(f7(x2991)))),
% 1.16/1.30 inference(scs_inference,[],[4,44,46,289,7,225,246,193,3,32,33,30,23])).
% 1.16/1.30 cnf(302,plain,
% 1.16/1.30 (P2(f19(x3021,x3022),f4(x3021,x3022))),
% 1.16/1.30 inference(scs_inference,[],[4,44,46,289,7,10,225,246,193,3,32,33,30,23,24])).
% 1.16/1.30 cnf(313,plain,
% 1.16/1.30 (P3(x3131,f16(f2(x3131)))),
% 1.16/1.30 inference(scs_inference,[],[4,46,5,33])).
% 1.16/1.30 cnf(314,plain,
% 1.16/1.30 (P3(x3141,f16(x3141))),
% 1.16/1.30 inference(rename_variables,[],[46])).
% 1.16/1.30 cnf(315,plain,
% 1.16/1.30 (P2(x3151,x3151)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(317,plain,
% 1.16/1.30 (~P1(f16(x3171))),
% 1.16/1.30 inference(scs_inference,[],[4,315,46,314,5,33,30])).
% 1.16/1.30 cnf(318,plain,
% 1.16/1.30 (P2(x3181,x3181)),
% 1.16/1.30 inference(rename_variables,[],[4])).
% 1.16/1.30 cnf(320,plain,
% 1.16/1.30 (P3(x3201,f2(f3(x3202,x3201)))),
% 1.16/1.30 inference(scs_inference,[],[4,315,318,46,314,8,5,33,30,34])).
% 1.16/1.30 cnf(345,plain,
% 1.16/1.30 (P4(x3451,x3452,f17(x3451,x3452))),
% 1.16/1.30 inference(rename_variables,[],[52])).
% 1.16/1.30 cnf(349,plain,
% 1.16/1.30 (P2(f2(x3491),x3491)),
% 1.16/1.30 inference(rename_variables,[],[5])).
% 1.16/1.30 cnf(351,plain,
% 1.16/1.30 (P2(f7(x3511),a12)),
% 1.16/1.30 inference(scs_inference,[],[5,52,228,200,212,39,31,19])).
% 1.16/1.30 cnf(353,plain,
% 1.16/1.30 (P5(f2(x3531),f6(x3531),f7(x3531))),
% 1.16/1.30 inference(scs_inference,[],[5,349,52,6,135,228,200,212,73,39,31,19,42])).
% 1.16/1.30 cnf(356,plain,
% 1.16/1.30 (P2(x3561,f2(x3561))),
% 1.16/1.30 inference(rename_variables,[],[73])).
% 1.16/1.30 cnf(358,plain,
% 1.16/1.30 (P1(f2(f6(x3581)))),
% 1.16/1.30 inference(scs_inference,[],[5,349,52,6,135,228,200,212,2,73,356,39,31,19,42,22])).
% 1.16/1.31 cnf(362,plain,
% 1.16/1.31 (P2(f2(x3621),x3621)),
% 1.16/1.31 inference(rename_variables,[],[5])).
% 1.16/1.31 cnf(363,plain,
% 1.16/1.31 (P2(f2(x3631),x3631)),
% 1.16/1.31 inference(rename_variables,[],[5])).
% 1.16/1.31 cnf(366,plain,
% 1.16/1.31 (~P1(f2(f16(x3661)))),
% 1.16/1.31 inference(scs_inference,[],[5,349,363,52,46,6,135,228,200,212,296,2,73,356,39,31,19,42,22,33,30])).
% 1.16/1.31 cnf(367,plain,
% 1.16/1.31 (P2(f2(x3671),x3671)),
% 1.16/1.31 inference(rename_variables,[],[5])).
% 1.16/1.31 cnf(369,plain,
% 1.16/1.31 (P2(f18(x3691,f6(x3691)),f7(x3691))),
% 1.16/1.31 inference(scs_inference,[],[5,349,363,52,46,6,135,252,228,200,212,296,2,73,356,39,31,19,42,22,33,30,24])).
% 1.16/1.31 cnf(371,plain,
% 1.16/1.31 (P2(f4(x3711,x3712),f18(x3711,f3(x3711,x3712)))),
% 1.16/1.31 inference(scs_inference,[],[5,349,363,52,17,46,6,135,252,228,200,212,296,2,73,356,39,31,19,42,22,33,30,24,38])).
% 1.16/1.31 cnf(373,plain,
% 1.16/1.31 (P2(f3(x3731,x3732),f16(x3732))),
% 1.16/1.31 inference(scs_inference,[],[5,349,363,52,17,46,8,6,135,252,228,200,212,296,2,73,356,39,31,19,42,22,33,30,24,38,27])).
% 1.16/1.31 cnf(375,plain,
% 1.16/1.31 (P2(f10(x3751,x3752),f17(x3751,f9(x3751,x3752)))),
% 1.16/1.31 inference(scs_inference,[],[5,349,363,52,17,16,46,8,6,135,252,228,200,212,296,2,73,356,39,31,19,42,22,33,30,24,38,27,37])).
% 1.16/1.31 cnf(378,plain,
% 1.16/1.31 (P2(f2(x3781),x3781)),
% 1.16/1.31 inference(rename_variables,[],[5])).
% 1.16/1.31 cnf(383,plain,
% 1.16/1.31 (P5(x3831,x3831,f18(f2(x3831),f2(x3831)))),
% 1.16/1.31 inference(scs_inference,[],[5,349,363,367,378,362,52,345,17,16,46,15,8,6,135,252,79,228,200,207,212,296,2,73,356,39,31,19,42,22,33,30,24,38,27,37,40,20,41])).
% 1.16/1.31 cnf(393,plain,
% 1.16/1.31 (~P5(f3(x3931,f9(x3932,a12)),x3933,f2(x3933))),
% 1.16/1.31 inference(scs_inference,[],[5,12,44,7,8,43])).
% 1.16/1.31 cnf(395,plain,
% 1.16/1.31 (P3(x3951,f9(x3952,x3951))),
% 1.16/1.31 inference(rename_variables,[],[7])).
% 1.16/1.31 cnf(400,plain,
% 1.16/1.31 (P2(f2(x4001),x4001)),
% 1.16/1.31 inference(rename_variables,[],[5])).
% 1.16/1.31 cnf(401,plain,
% 1.16/1.31 (P2(f17(x4011,x4012),f20(x4011,x4012))),
% 1.16/1.31 inference(rename_variables,[],[228])).
% 1.16/1.31 cnf(402,plain,
% 1.16/1.31 (P2(f2(x4021),x4021)),
% 1.16/1.31 inference(rename_variables,[],[5])).
% 1.16/1.31 cnf(413,plain,
% 1.16/1.31 (P1(f18(x4131,f6(x4131)))),
% 1.16/1.31 inference(scs_inference,[],[5,402,400,52,12,14,44,7,8,252,228,401,200,43,40,39,31,20,22])).
% 1.16/1.31 cnf(414,plain,
% 1.16/1.31 (P2(f7(x4141),f18(x4141,f6(x4141)))),
% 1.16/1.31 inference(rename_variables,[],[252])).
% 1.16/1.31 cnf(417,plain,
% 1.16/1.31 (P2(f2(x4171),x4171)),
% 1.16/1.31 inference(rename_variables,[],[5])).
% 1.16/1.31 cnf(421,plain,
% 1.16/1.31 (~P3(x4211,f18(x4212,f6(x4212)))),
% 1.16/1.31 inference(scs_inference,[],[5,402,400,52,12,14,44,7,395,8,252,414,228,401,200,246,43,40,39,31,20,22,33,30])).
% 1.16/1.31 cnf(424,plain,
% 1.16/1.31 (P3(f2(x4241),f3(x4242,x4241))),
% 1.16/1.31 inference(scs_inference,[],[5,402,417,400,52,12,14,44,7,395,8,46,373,252,414,228,401,200,246,43,40,39,31,20,22,33,30,34])).
% 1.16/1.31 cnf(439,plain,
% 1.16/1.31 (P2(f10(x4391,x4392),f11(x4391,x4392))),
% 1.16/1.31 inference(rename_variables,[],[9])).
% 1.16/1.31 cnf(440,plain,
% 1.16/1.31 (P3(x4401,f9(x4402,x4401))),
% 1.16/1.31 inference(rename_variables,[],[7])).
% 1.16/1.31 cnf(443,plain,
% 1.16/1.31 (P2(f18(x4431,f6(x4431)),a12)),
% 1.16/1.31 inference(scs_inference,[],[16,44,7,8,9,413,43,19])).
% 1.16/1.31 cnf(447,plain,
% 1.16/1.31 (P2(f10(x4471,x4472),f11(x4471,x4472))),
% 1.16/1.31 inference(rename_variables,[],[9])).
% 1.16/1.31 cnf(450,plain,
% 1.16/1.31 (~P2(f11(x4501,x4502),f8(x4503))),
% 1.16/1.31 inference(scs_inference,[],[6,16,44,7,8,9,439,447,413,268,77,43,19,39,31])).
% 1.16/1.31 cnf(458,plain,
% 1.16/1.31 (~P3(x4581,f1(x4582))),
% 1.16/1.31 inference(rename_variables,[],[55])).
% 1.16/1.31 cnf(459,plain,
% 1.16/1.31 (P3(x4591,f9(x4592,x4591))),
% 1.16/1.31 inference(rename_variables,[],[7])).
% 1.16/1.31 cnf(461,plain,
% 1.16/1.31 (~P2(a12,f9(x4611,x4612))),
% 1.16/1.31 inference(scs_inference,[],[6,16,55,44,7,440,459,8,9,439,447,413,366,268,77,43,19,39,31,20,22,33,30])).
% 1.16/1.31 cnf(463,plain,
% 1.16/1.31 (~P2(f1(x4631),f9(x4632,f8(x4633)))),
% 1.16/1.31 inference(scs_inference,[],[6,16,55,458,44,7,440,459,8,9,439,447,413,366,268,77,43,19,39,31,20,22,33,30,34])).
% 1.16/1.31 cnf(467,plain,
% 1.16/1.31 (P2(f17(x4671,f1(x4671)),f2(x4671))),
% 1.16/1.31 inference(scs_inference,[],[6,16,55,458,44,7,440,459,8,9,439,447,259,413,366,268,77,43,19,39,31,20,22,33,30,34,24])).
% 1.16/1.31 cnf(469,plain,
% 1.16/1.31 (~P2(f18(x4691,f6(x4691)),f16(x4692))),
% 1.16/1.31 inference(scs_inference,[],[6,16,55,458,44,7,440,459,8,9,439,447,259,413,421,366,268,77,43,19,39,31,20,22,33,30,34,24,28])).
% 1.16/1.31 cnf(476,plain,
% 1.16/1.31 (~P2(x4761,x4762)+P4(x4763,x4764,x4762)+~P2(x4765,x4764)+~P2(x4766,x4763)+~P4(x4766,x4765,x4761)),
% 1.16/1.31 inference(rename_variables,[],[39])).
% 1.16/1.31 cnf(477,plain,
% 1.16/1.31 (~P2(f11(x4771,x4772),f7(x4773))),
% 1.16/1.31 inference(scs_inference,[],[6,52,450,4,39,31])).
% 1.16/1.31 cnf(480,plain,
% 1.16/1.31 (P1(f17(a12,f1(a12)))),
% 1.16/1.31 inference(scs_inference,[],[6,52,450,147,259,4,39,31,22])).
% 1.16/1.31 cnf(491,plain,
% 1.16/1.31 (~P5(x4911,f6(x4911),f16(x4912))),
% 1.16/1.31 inference(scs_inference,[],[6,52,7,11,44,469,450,147,259,77,4,39,31,22,33,30,24,38])).
% 1.16/1.31 cnf(495,plain,
% 1.16/1.31 (~P1(f17(x4951,f9(x4951,x4952)))),
% 1.16/1.31 inference(scs_inference,[],[6,52,7,11,44,375,469,450,147,259,77,153,4,39,31,22,33,30,24,38,476,23])).
% 1.16/1.31 cnf(500,plain,
% 1.16/1.31 (P2(f5(f2(x5001),f2(x5001)),f18(x5001,x5001))),
% 1.16/1.31 inference(scs_inference,[],[171,38])).
% 1.16/1.31 cnf(510,plain,
% 1.16/1.31 (~P1(f20(x5101,f9(x5101,x5102)))),
% 1.16/1.31 inference(scs_inference,[],[171,353,302,491,495,371,81,73,4,38,42,31,22])).
% 1.16/1.31 cnf(526,plain,
% 1.16/1.31 (P2(f19(x5261,x5262),f17(f5(x5261,x5262),x5261))),
% 1.16/1.31 inference(scs_inference,[],[7,18,46,44,171,353,104,302,491,495,461,371,81,73,4,38,42,31,22,32,30,23,24,36,37])).
% 1.16/1.31 cnf(540,plain,
% 1.16/1.31 (~P5(f3(x5401,f9(x5402,a12)),f10(x5403,x5404),f10(x5403,x5404))),
% 1.16/1.31 inference(scs_inference,[],[7,12,8,9,44,144,43])).
% 1.16/1.31 cnf(541,plain,
% 1.16/1.31 (P3(x5411,f9(x5412,x5411))),
% 1.16/1.31 inference(rename_variables,[],[7])).
% 1.16/1.31 cnf(542,plain,
% 1.16/1.31 (P2(f10(x5421,x5422),f11(x5421,x5422))),
% 1.16/1.31 inference(rename_variables,[],[9])).
% 1.16/1.31 cnf(544,plain,
% 1.16/1.31 (P4(x5441,f1(x5441),f2(x5441))),
% 1.16/1.31 inference(rename_variables,[],[12])).
% 1.16/1.31 cnf(548,plain,
% 1.16/1.31 (P2(f2(f10(x5481,x5482)),f11(x5481,x5482))),
% 1.16/1.31 inference(rename_variables,[],[144])).
% 1.16/1.31 cnf(552,plain,
% 1.16/1.31 (P2(f10(x5521,x5522),f11(x5521,x5522))),
% 1.16/1.31 inference(rename_variables,[],[9])).
% 1.16/1.31 cnf(556,plain,
% 1.16/1.31 (P2(f19(x5561,x5562),f20(f5(x5561,x5562),x5561))),
% 1.16/1.31 inference(scs_inference,[],[7,12,544,8,9,542,44,526,144,548,393,373,228,75,43,42,39,31])).
% 1.16/1.31 cnf(558,plain,
% 1.16/1.31 (P2(f17(x5581,x5582),f20(x5581,x5582))),
% 1.16/1.31 inference(rename_variables,[],[228])).
% 1.16/1.31 cnf(560,plain,
% 1.16/1.31 (~P2(a12,f20(x5601,f9(x5601,x5602)))),
% 1.16/1.31 inference(scs_inference,[],[7,12,544,8,9,542,44,526,144,548,510,393,373,228,75,43,42,39,31,22])).
% 1.16/1.31 cnf(562,plain,
% 1.16/1.31 (~P3(x5621,f20(a12,f1(a12)))),
% 1.16/1.31 inference(scs_inference,[],[7,12,544,8,9,542,44,526,144,548,510,393,480,373,228,558,75,43,42,39,31,22,30])).
% 1.16/1.31 cnf(569,plain,
% 1.16/1.31 (P1(f5(x5691,f6(x5691)))),
% 1.16/1.31 inference(scs_inference,[],[7,541,12,544,8,9,542,552,44,526,144,548,510,393,480,413,79,373,228,558,75,4,43,42,39,31,22,30,33,23])).
% 1.16/1.31 cnf(581,plain,
% 1.16/1.31 (P4(x5811,x5812,f17(x5811,x5812))),
% 1.16/1.31 inference(rename_variables,[],[52])).
% 1.16/1.31 cnf(583,plain,
% 1.16/1.31 (P5(f10(x5831,x5832),f10(x5831,x5832),f5(f11(x5831,x5832),f11(x5831,x5832)))),
% 1.16/1.31 inference(scs_inference,[],[61,52,9,73,4,38,40,42])).
% 1.16/1.31 cnf(584,plain,
% 1.16/1.31 (P2(x5841,f2(x5841))),
% 1.16/1.31 inference(rename_variables,[],[73])).
% 1.16/1.31 cnf(592,plain,
% 1.16/1.31 (~P2(f11(x5921,x5922),f18(x5923,f6(x5923)))),
% 1.16/1.31 inference(scs_inference,[],[61,52,581,9,467,477,369,75,73,4,38,40,42,39,31])).
% 1.16/1.31 cnf(599,plain,
% 1.16/1.31 (P1(f20(a12,f1(a12)))),
% 1.16/1.31 inference(scs_inference,[],[61,52,581,9,467,320,477,369,480,81,75,73,584,4,38,40,42,39,31,34,23])).
% 1.16/1.31 cnf(614,plain,
% 1.16/1.31 (~P1(f9(x6141,x6142))),
% 1.16/1.31 inference(scs_inference,[],[8,61,18,52,581,46,9,44,500,467,569,320,477,562,317,369,480,81,77,75,73,584,4,38,40,42,39,31,34,23,24,28,19,43,20,22])).
% 1.16/1.31 cnf(623,plain,
% 1.16/1.31 (P2(f4(x6231,x6232),f20(f5(x6231,x6232),x6231))),
% 1.16/1.31 inference(scs_inference,[],[10,556,592,38,31])).
% 1.16/1.31 cnf(634,plain,
% 1.16/1.31 (~P2(f18(x6341,f6(x6341)),f11(x6342,x6343))),
% 1.16/1.31 inference(scs_inference,[],[8,57,10,44,556,592,277,614,75,38,31,22,34,23,24])).
% 1.16/1.31 cnf(641,plain,
% 1.16/1.31 (P2(f18(f2(x6411),f2(x6411)),f18(x6411,x6411))),
% 1.16/1.31 inference(scs_inference,[],[383,38])).
% 1.16/1.31 cnf(647,plain,
% 1.16/1.31 (~P2(f2(f1(x6471)),f16(a12))),
% 1.16/1.31 inference(scs_inference,[],[57,46,383,623,81,75,38,31,34])).
% 1.16/1.31 cnf(655,plain,
% 1.16/1.31 (P2(f3(x6551,x6552),f16(f2(x6552)))),
% 1.16/1.31 inference(scs_inference,[],[57,46,383,623,463,424,81,75,38,31,34,24,35,27])).
% 1.16/1.31 cnf(677,plain,
% 1.16/1.31 (P2(f18(f2(x6771),f2(x6771)),f18(x6771,x6771))),
% 1.16/1.31 inference(rename_variables,[],[641])).
% 1.16/1.31 cnf(682,plain,
% 1.16/1.31 (P2(f10(x6821,x6822),f11(x6821,x6822))),
% 1.16/1.31 inference(rename_variables,[],[9])).
% 1.16/1.31 cnf(684,plain,
% 1.16/1.31 (~P2(f18(x6841,f6(x6841)),f10(x6842,x6843))),
% 1.16/1.31 inference(scs_inference,[],[9,682,49,11,641,634,647,351,560,27,42,32,31])).
% 1.16/1.31 cnf(689,plain,
% 1.16/1.31 (P2(x6891,f2(x6891))),
% 1.16/1.31 inference(rename_variables,[],[73])).
% 1.16/1.31 cnf(701,plain,
% 1.16/1.31 (~P3(x7011,f17(a12,f1(a12)))),
% 1.16/1.31 inference(scs_inference,[],[9,682,49,55,11,583,641,677,166,655,634,540,599,647,351,560,81,73,689,4,27,42,32,31,34,24,40,41,30])).
% 1.16/1.31 cnf(725,plain,
% 1.16/1.31 (P2(f2(f6(x7251)),a12)),
% 1.16/1.31 inference(scs_inference,[],[10,73,46,684,299,358,701,271,264,225,207,246,27,30,31,33,23,24,28,38,19])).
% 1.16/1.31 cnf(874,plain,
% 1.16/1.31 ($false),
% 1.16/1.31 inference(scs_inference,[],[12,49,46,44,443,313,725,43]),
% 1.16/1.31 ['proof']).
% 1.16/1.31 % SZS output end Proof
% 1.16/1.31 % Total time :0.600000s
%------------------------------------------------------------------------------