TSTP Solution File: HAL003+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n012.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 01:53:26 EDT 2023
% Result : Theorem 0.91s 0.97s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 02:29:25 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.91/0.96 %-------------------------------------------
% 0.91/0.96 % File :CSE---1.6
% 0.91/0.96 % Problem :theBenchmark
% 0.91/0.96 % Transform :cnf
% 0.91/0.96 % Format :tptp:raw
% 0.91/0.96 % Command :java -jar mcs_scs.jar %d %s
% 0.91/0.96
% 0.91/0.96 % Result :Theorem 0.310000s
% 0.91/0.96 % Output :CNFRefutation 0.310000s
% 0.91/0.96 %-------------------------------------------
% 0.91/0.96 %--------------------------------------------------------------------------
% 0.91/0.96 % File : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 0.91/0.96 % Domain : Homological Algebra
% 0.91/0.96 % Problem : Short Five Lemma, Part 2
% 0.91/0.96 % Version : [TPTP] axioms : Augmented.
% 0.91/0.96 % English :
% 0.91/0.96
% 0.91/0.96 % Refs : [Wei94] Weibel (1994), An Introduction to Homological Algebra
% 0.91/0.96 % Source : [TPTP]
% 0.91/0.96 % Names :
% 0.91/0.96
% 0.91/0.96 % Status : Theorem
% 0.91/0.96 % Rating : 0.25 v8.1.0, 0.22 v7.4.0, 0.23 v7.3.0, 0.24 v7.2.0, 0.21 v7.1.0, 0.26 v7.0.0, 0.27 v6.4.0, 0.31 v6.3.0, 0.33 v6.2.0, 0.24 v6.1.0, 0.33 v6.0.0, 0.35 v5.5.0, 0.33 v5.4.0, 0.39 v5.3.0, 0.41 v5.2.0, 0.30 v5.1.0, 0.29 v5.0.0, 0.33 v4.1.0, 0.35 v4.0.1, 0.39 v4.0.0, 0.38 v3.7.0, 0.35 v3.5.0, 0.37 v3.3.0, 0.29 v3.2.0, 0.45 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0
% 0.91/0.96 % Syntax : Number of formulae : 34 ( 18 unt; 0 def)
% 0.91/0.96 % Number of atoms : 101 ( 23 equ)
% 0.91/0.96 % Maximal formula atoms : 7 ( 2 avg)
% 0.91/0.96 % Number of connectives : 67 ( 0 ~; 0 |; 41 &)
% 0.91/0.96 % ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% 0.91/0.97 % Maximal formula depth : 16 ( 5 avg)
% 0.91/0.97 % Maximal term depth : 3 ( 1 avg)
% 0.91/0.97 % Number of predicates : 7 ( 6 usr; 0 prp; 1-4 aty)
% 0.91/0.97 % Number of functors : 17 ( 17 usr; 14 con; 0-3 aty)
% 0.91/0.97 % Number of variables : 79 ( 68 !; 11 ?)
% 0.91/0.97 % SPC : FOF_THM_RFO_SEQ
% 0.91/0.97
% 0.91/0.97 % Comments : Augmented with lemmas suggested by YiLT.
% 0.91/0.97 %--------------------------------------------------------------------------
% 0.91/0.97 %----Include Standard homological algebra axioms
% 0.91/0.97 include('Axioms/HAL001+0.ax').
% 0.91/0.97 %--------------------------------------------------------------------------
% 0.91/0.97 fof(alpha_morphism,axiom,
% 0.91/0.97 morphism(alpha,a,b) ).
% 0.91/0.97
% 0.91/0.97 fof(beta_morphism,axiom,
% 0.91/0.97 morphism(beta,b,c) ).
% 0.91/0.97
% 0.91/0.97 fof(gamma_morphism,axiom,
% 0.91/0.97 morphism(gamma,d,e) ).
% 0.91/0.97
% 0.91/0.97 fof(delta_morphism,axiom,
% 0.91/0.97 morphism(delta,e,r) ).
% 0.91/0.97
% 0.91/0.97 fof(f_morphism,axiom,
% 0.91/0.97 morphism(f,a,d) ).
% 0.91/0.97
% 0.91/0.97 fof(g_morphism,axiom,
% 0.91/0.97 morphism(g,b,e) ).
% 0.91/0.97
% 0.91/0.97 fof(h_morphism,axiom,
% 0.91/0.97 morphism(h,c,r) ).
% 0.91/0.97
% 0.91/0.97 fof(alpha_injection,axiom,
% 0.91/0.97 injection(alpha) ).
% 0.91/0.97
% 0.91/0.97 fof(gamma_injection,axiom,
% 0.91/0.97 injection(gamma) ).
% 0.91/0.97
% 0.91/0.97 fof(beta_surjection,axiom,
% 0.91/0.97 surjection(beta) ).
% 0.91/0.97
% 0.91/0.97 fof(delta_surjection,axiom,
% 0.91/0.97 surjection(delta) ).
% 0.91/0.97
% 0.91/0.97 fof(alpha_beta_exact,axiom,
% 0.91/0.97 exact(alpha,beta) ).
% 0.91/0.97
% 0.91/0.97 fof(gamma_delta_exact,axiom,
% 0.91/0.97 exact(gammma,delta) ).
% 0.91/0.97
% 0.91/0.97 fof(alpha_g_f_gamma_commute,axiom,
% 0.91/0.97 commute(alpha,g,f,gamma) ).
% 0.91/0.97
% 0.91/0.97 fof(beta_h_g_delta_commute,axiom,
% 0.91/0.97 commute(beta,h,g,delta) ).
% 0.91/0.97
% 0.91/0.97 fof(f_surjection,hypothesis,
% 0.91/0.97 surjection(f) ).
% 0.91/0.97
% 0.91/0.97 fof(h_surjection,hypothesis,
% 0.91/0.97 surjection(h) ).
% 0.91/0.97
% 0.91/0.97 fof(lemma3,axiom,
% 0.91/0.97 ! [E] :
% 0.91/0.97 ( element(E,e)
% 0.91/0.97 => ? [R,B1] :
% 0.91/0.97 ( element(R,r)
% 0.91/0.97 & apply(delta,E) = R
% 0.91/0.97 & element(B1,b)
% 0.91/0.97 & apply(h,apply(beta,B1)) = R
% 0.91/0.97 & apply(delta,apply(g,B1)) = R ) ) ).
% 0.91/0.97
% 0.91/0.97 fof(lemma8,axiom,
% 0.91/0.97 ! [E] :
% 0.91/0.97 ( element(E,e)
% 0.91/0.97 => ? [B1,E1,A] :
% 0.91/0.97 ( element(B1,b)
% 0.91/0.97 & element(E1,e)
% 0.91/0.97 & subtract(e,apply(g,B1),E) = E1
% 0.91/0.97 & element(A,a)
% 0.91/0.97 & apply(gamma,apply(f,A)) = E1
% 0.91/0.97 & apply(g,apply(alpha,A)) = E1 ) ) ).
% 0.91/0.97
% 0.91/0.97 fof(lemma12,axiom,
% 0.91/0.97 ! [E] :
% 0.91/0.97 ( element(E,e)
% 0.91/0.97 => ? [B1,B2] :
% 0.91/0.97 ( element(B1,b)
% 0.91/0.97 & element(B2,b)
% 0.91/0.97 & apply(g,subtract(b,B1,B2)) = E ) ) ).
% 0.91/0.97
% 0.91/0.97 fof(g_surjection,conjecture,
% 0.91/0.97 surjection(g) ).
% 0.91/0.97
% 0.91/0.97 %--------------------------------------------------------------------------
% 0.91/0.97 %-------------------------------------------
% 0.91/0.97 % Proof found
% 0.91/0.97 % SZS status Theorem for theBenchmark
% 0.91/0.97 % SZS output start Proof
% 0.91/0.97 %ClaNum:120(EqnAxiom:61)
% 0.91/0.97 %VarNum:449(SingletonVarNum:143)
% 0.91/0.97 %MaxLitNum:7
% 0.91/0.97 %MaxfuncDepth:3
% 0.91/0.97 %SharedTerms:32
% 0.91/0.97 %goalClause: 79
% 0.91/0.97 %singleGoalClaCount:1
% 0.91/0.97 [62]P1(a1)
% 0.91/0.97 [63]P1(a3)
% 0.91/0.97 [64]P5(a4)
% 0.91/0.97 [65]P5(a7)
% 0.91/0.97 [66]P5(a10)
% 0.91/0.97 [67]P5(a28)
% 0.91/0.97 [68]P2(a1,a4)
% 0.91/0.97 [69]P2(a29,a7)
% 0.91/0.97 [70]P6(a1,a2,a5)
% 0.91/0.97 [71]P6(a4,a5,a8)
% 0.91/0.97 [72]P6(a3,a9,a11)
% 0.91/0.97 [73]P6(a7,a11,a30)
% 0.91/0.97 [74]P6(a10,a2,a9)
% 0.91/0.97 [75]P6(a27,a5,a11)
% 0.91/0.97 [76]P6(a28,a8,a30)
% 0.91/0.97 [77]P3(a1,a27,a10,a3)
% 0.91/0.97 [78]P3(a4,a28,a27,a7)
% 0.91/0.97 [79]~P5(a27)
% 0.91/0.97 [80]~P4(x801,a11)+E(f6(a7,x801),f12(x801))
% 0.91/0.97 [81]~P4(x811,a11)+P4(f12(x811),a30)
% 0.91/0.97 [82]~P4(x821,a11)+P4(f13(x821),a5)
% 0.91/0.97 [83]~P4(x831,a11)+P4(f14(x831),a5)
% 0.91/0.97 [84]~P4(x841,a11)+P4(f15(x841),a11)
% 0.91/0.97 [85]~P4(x851,a11)+P4(f16(x851),a2)
% 0.91/0.97 [86]~P4(x861,a11)+P4(f17(x861),a5)
% 0.91/0.97 [87]~P4(x871,a11)+P4(f18(x871),a5)
% 0.91/0.97 [88]~P4(x881,a11)+E(f6(a3,f6(a10,f16(x881))),f15(x881))
% 0.91/0.97 [89]~P4(x891,a11)+E(f6(a7,f6(a27,f13(x891))),f12(x891))
% 0.91/0.97 [90]~P4(x901,a11)+E(f6(a27,f6(a1,f16(x901))),f15(x901))
% 0.91/0.97 [91]~P4(x911,a11)+E(f6(a28,f6(a4,f13(x911))),f12(x911))
% 0.91/0.97 [94]~P4(x941,a11)+E(f31(a11,f6(a27,f14(x941)),x941),f15(x941))
% 0.91/0.97 [99]~P4(x991,a11)+E(f6(a27,f31(a5,f17(x991),f18(x991))),x991)
% 0.91/0.97 [92]~P4(x922,x921)+E(f31(x921,x922,x922),f32(x921))
% 0.91/0.97 [93]~P6(x931,x932,x933)+E(f6(x931,f32(x932)),f32(x933))
% 0.91/0.97 [95]P1(x951)+~P6(x951,x952,x953)+P4(f19(x951,x952),x952)
% 0.91/0.97 [96]P1(x961)+~P6(x961,x962,x963)+P4(f20(x961,x962),x962)
% 0.91/0.97 [97]P1(x971)+~P6(x971,x972,x973)+~E(f20(x971,x972),f19(x971,x972))
% 0.91/0.97 [100]~P4(x1003,x1001)+~P4(x1002,x1001)+P4(f31(x1001,x1002,x1003),x1001)
% 0.91/0.97 [104]~P6(x1041,x1042,x1043)+P5(x1041)+P4(f21(x1041,x1042,x1043),x1043)
% 0.91/0.97 [101]P1(x1011)+~P6(x1011,x1012,x1013)+E(f6(x1011,f20(x1011,x1012)),f6(x1011,f19(x1011,x1012)))
% 0.91/0.97 [103]~P4(x1033,x1031)+~P4(x1032,x1031)+E(f31(x1031,x1032,f31(x1031,x1032,x1033)),x1033)
% 0.91/0.97 [98]~P6(x981,x984,x983)+~P4(x982,x984)+P4(f6(x981,x982),x983)
% 0.91/0.97 [105]~P4(x1052,x1053)+~P6(x1051,x1053,x1054)+P5(x1051)+~E(f6(x1051,x1052),f21(x1051,x1053,x1054))
% 0.91/0.97 [109]~P5(x1091)+~P4(x1094,x1093)+~P6(x1091,x1092,x1093)+P4(f22(x1091,x1092,x1093,x1094),x1092)
% 0.91/0.97 [110]~P5(x1101)+~P4(x1104,x1103)+~P6(x1101,x1102,x1103)+E(f6(x1101,f22(x1101,x1102,x1103,x1104)),x1104)
% 0.91/0.97 [108]~P4(x1084,x1082)+~P4(x1083,x1082)+~P6(x1081,x1082,x1085)+E(f6(x1081,f31(x1082,x1083,x1084)),f31(x1085,f6(x1081,x1083),f6(x1081,x1084)))
% 0.91/0.97 [113]~P6(x1132,x1134,x1135)+~P6(x1131,x1133,x1134)+P2(x1131,x1132)+P4(f26(x1131,x1132,x1133,x1134,x1135),x1133)+P4(f24(x1131,x1132,x1133,x1134,x1135),x1134)
% 0.91/0.97 [114]P2(x1142,x1141)+~P6(x1141,x1144,x1145)+~P6(x1142,x1143,x1144)+P4(f26(x1142,x1141,x1143,x1144,x1145),x1143)+E(f6(x1141,f24(x1142,x1141,x1143,x1144,x1145)),f32(x1145))
% 0.91/0.97 [115]P2(x1151,x1152)+~P6(x1152,x1154,x1155)+~P6(x1151,x1153,x1154)+P4(f24(x1151,x1152,x1153,x1154,x1155),x1154)+E(f6(x1151,f26(x1151,x1152,x1153,x1154,x1155)),f24(x1151,x1152,x1153,x1154,x1155))
% 0.91/0.97 [116]P2(x1162,x1161)+~P6(x1161,x1164,x1165)+~P6(x1162,x1163,x1164)+E(f6(x1162,f26(x1162,x1161,x1163,x1164,x1165)),f24(x1162,x1161,x1163,x1164,x1165))+E(f6(x1161,f24(x1162,x1161,x1163,x1164,x1165)),f32(x1165))
% 0.91/0.97 [102]~P1(x1023)+~P4(x1021,x1024)+E(x1021,x1022)+~P6(x1023,x1024,x1025)+~P4(x1022,x1024)+~E(f6(x1023,x1021),f6(x1023,x1022))
% 0.91/0.97 [118]~P4(x1186,x1184)+~P2(x1181,x1182)+~P6(x1182,x1184,x1185)+~P6(x1181,x1183,x1184)+~E(f6(x1182,x1186),f32(x1185))+P4(f25(x1181,x1182,x1183,x1184,x1185,x1186),x1183)
% 0.91/0.97 [119]~P4(x1196,x1194)+~P2(x1191,x1192)+~P6(x1192,x1194,x1195)+~P6(x1191,x1193,x1194)+~E(f6(x1192,x1196),f32(x1195))+E(f6(x1191,f25(x1191,x1192,x1193,x1194,x1195,x1196)),x1196)
% 0.91/0.97 [106]~P6(x1063,x1065,x1062)+P4(x1061,x1062)+~P6(x1066,x1062,x1067)+~P4(x1064,x1065)+~P2(x1063,x1066)+~E(f6(x1063,x1064),x1061)
% 0.91/0.97 [107]~P2(x1074,x1071)+~P6(x1071,x1077,x1073)+~P6(x1074,x1076,x1077)+~P4(x1075,x1076)+E(f6(x1071,x1072),f32(x1073))+~E(f6(x1074,x1075),x1072)
% 0.91/0.97 [112]~P6(x1123,x1125,x1126)+~P6(x1121,x1125,x1128)+P3(x1121,x1122,x1123,x1124)+~P6(x1124,x1126,x1127)+~P6(x1122,x1128,x1127)+P4(f23(x1121,x1122,x1123,x1124,x1125),x1125)
% 0.91/0.97 [120]~P6(x1203,x1205,x1206)+~P6(x1202,x1208,x1207)+P3(x1201,x1202,x1203,x1204)+~P6(x1204,x1206,x1207)+~P6(x1201,x1205,x1208)+~E(f6(x1202,f6(x1201,f23(x1201,x1202,x1203,x1204,x1205))),f6(x1204,f6(x1203,f23(x1201,x1202,x1203,x1204,x1205))))
% 0.91/0.97 [117]~P4(x1173,x1174)+~P6(x1172,x1175,x1176)+~P6(x1171,x1174,x1175)+P2(x1171,x1172)+~E(f6(x1171,x1173),f24(x1171,x1172,x1174,x1175,x1176))+~P4(f24(x1171,x1172,x1174,x1175,x1176),x1175)+~E(f6(x1172,f24(x1171,x1172,x1174,x1175,x1176)),f32(x1176))
% 0.91/0.97 [111]~P6(x1115,x1116,x1117)+~P6(x1112,x1116,x1119)+~P3(x1112,x1111,x1115,x1114)+~P6(x1114,x1117,x1118)+~P6(x1111,x1119,x1118)+~P4(x1113,x1116)+E(f6(x1111,f6(x1112,x1113)),f6(x1114,f6(x1115,x1113)))
% 0.91/0.97 %EqnAxiom
% 0.91/0.97 [1]E(x11,x11)
% 0.91/0.97 [2]E(x22,x21)+~E(x21,x22)
% 0.91/0.97 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.91/0.97 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.91/0.97 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.91/0.97 [6]~E(x61,x62)+E(f12(x61),f12(x62))
% 0.91/0.97 [7]~E(x71,x72)+E(f22(x71,x73,x74,x75),f22(x72,x73,x74,x75))
% 0.91/0.97 [8]~E(x81,x82)+E(f22(x83,x81,x84,x85),f22(x83,x82,x84,x85))
% 0.91/0.97 [9]~E(x91,x92)+E(f22(x93,x94,x91,x95),f22(x93,x94,x92,x95))
% 0.91/0.97 [10]~E(x101,x102)+E(f22(x103,x104,x105,x101),f22(x103,x104,x105,x102))
% 0.91/0.97 [11]~E(x111,x112)+E(f13(x111),f13(x112))
% 0.91/0.97 [12]~E(x121,x122)+E(f14(x121),f14(x122))
% 0.91/0.97 [13]~E(x131,x132)+E(f15(x131),f15(x132))
% 0.91/0.97 [14]~E(x141,x142)+E(f16(x141),f16(x142))
% 0.91/0.97 [15]~E(x151,x152)+E(f17(x151),f17(x152))
% 0.91/0.97 [16]~E(x161,x162)+E(f18(x161),f18(x162))
% 0.91/0.97 [17]~E(x171,x172)+E(f26(x171,x173,x174,x175,x176),f26(x172,x173,x174,x175,x176))
% 0.91/0.97 [18]~E(x181,x182)+E(f26(x183,x181,x184,x185,x186),f26(x183,x182,x184,x185,x186))
% 0.91/0.97 [19]~E(x191,x192)+E(f26(x193,x194,x191,x195,x196),f26(x193,x194,x192,x195,x196))
% 0.91/0.97 [20]~E(x201,x202)+E(f26(x203,x204,x205,x201,x206),f26(x203,x204,x205,x202,x206))
% 0.91/0.97 [21]~E(x211,x212)+E(f26(x213,x214,x215,x216,x211),f26(x213,x214,x215,x216,x212))
% 0.91/0.97 [22]~E(x221,x222)+E(f23(x221,x223,x224,x225,x226),f23(x222,x223,x224,x225,x226))
% 0.91/0.97 [23]~E(x231,x232)+E(f23(x233,x231,x234,x235,x236),f23(x233,x232,x234,x235,x236))
% 0.91/0.97 [24]~E(x241,x242)+E(f23(x243,x244,x241,x245,x246),f23(x243,x244,x242,x245,x246))
% 0.91/0.97 [25]~E(x251,x252)+E(f23(x253,x254,x255,x251,x256),f23(x253,x254,x255,x252,x256))
% 0.91/0.97 [26]~E(x261,x262)+E(f23(x263,x264,x265,x266,x261),f23(x263,x264,x265,x266,x262))
% 0.91/0.97 [27]~E(x271,x272)+E(f24(x271,x273,x274,x275,x276),f24(x272,x273,x274,x275,x276))
% 0.91/0.97 [28]~E(x281,x282)+E(f24(x283,x281,x284,x285,x286),f24(x283,x282,x284,x285,x286))
% 0.91/0.97 [29]~E(x291,x292)+E(f24(x293,x294,x291,x295,x296),f24(x293,x294,x292,x295,x296))
% 0.91/0.97 [30]~E(x301,x302)+E(f24(x303,x304,x305,x301,x306),f24(x303,x304,x305,x302,x306))
% 0.91/0.97 [31]~E(x311,x312)+E(f24(x313,x314,x315,x316,x311),f24(x313,x314,x315,x316,x312))
% 0.91/0.97 [32]~E(x321,x322)+E(f19(x321,x323),f19(x322,x323))
% 0.91/0.97 [33]~E(x331,x332)+E(f19(x333,x331),f19(x333,x332))
% 0.91/0.97 [34]~E(x341,x342)+E(f32(x341),f32(x342))
% 0.91/0.97 [35]~E(x351,x352)+E(f20(x351,x353),f20(x352,x353))
% 0.91/0.97 [36]~E(x361,x362)+E(f20(x363,x361),f20(x363,x362))
% 0.91/0.97 [37]~E(x371,x372)+E(f25(x371,x373,x374,x375,x376,x377),f25(x372,x373,x374,x375,x376,x377))
% 0.91/0.97 [38]~E(x381,x382)+E(f25(x383,x381,x384,x385,x386,x387),f25(x383,x382,x384,x385,x386,x387))
% 0.91/0.97 [39]~E(x391,x392)+E(f25(x393,x394,x391,x395,x396,x397),f25(x393,x394,x392,x395,x396,x397))
% 0.91/0.97 [40]~E(x401,x402)+E(f25(x403,x404,x405,x401,x406,x407),f25(x403,x404,x405,x402,x406,x407))
% 0.91/0.97 [41]~E(x411,x412)+E(f25(x413,x414,x415,x416,x411,x417),f25(x413,x414,x415,x416,x412,x417))
% 0.91/0.97 [42]~E(x421,x422)+E(f25(x423,x424,x425,x426,x427,x421),f25(x423,x424,x425,x426,x427,x422))
% 0.91/0.97 [43]~E(x431,x432)+E(f31(x431,x433,x434),f31(x432,x433,x434))
% 0.91/0.97 [44]~E(x441,x442)+E(f31(x443,x441,x444),f31(x443,x442,x444))
% 0.91/0.97 [45]~E(x451,x452)+E(f31(x453,x454,x451),f31(x453,x454,x452))
% 0.91/0.97 [46]~E(x461,x462)+E(f21(x461,x463,x464),f21(x462,x463,x464))
% 0.91/0.97 [47]~E(x471,x472)+E(f21(x473,x471,x474),f21(x473,x472,x474))
% 0.91/0.97 [48]~E(x481,x482)+E(f21(x483,x484,x481),f21(x483,x484,x482))
% 0.91/0.97 [49]~P1(x491)+P1(x492)+~E(x491,x492)
% 0.91/0.97 [50]P6(x502,x503,x504)+~E(x501,x502)+~P6(x501,x503,x504)
% 0.91/0.97 [51]P6(x513,x512,x514)+~E(x511,x512)+~P6(x513,x511,x514)
% 0.91/0.97 [52]P6(x523,x524,x522)+~E(x521,x522)+~P6(x523,x524,x521)
% 0.91/0.97 [53]~P5(x531)+P5(x532)+~E(x531,x532)
% 0.91/0.97 [54]P4(x542,x543)+~E(x541,x542)+~P4(x541,x543)
% 0.91/0.97 [55]P4(x553,x552)+~E(x551,x552)+~P4(x553,x551)
% 0.91/0.97 [56]P2(x562,x563)+~E(x561,x562)+~P2(x561,x563)
% 0.91/0.97 [57]P2(x573,x572)+~E(x571,x572)+~P2(x573,x571)
% 0.91/0.97 [58]P3(x582,x583,x584,x585)+~E(x581,x582)+~P3(x581,x583,x584,x585)
% 0.91/0.97 [59]P3(x593,x592,x594,x595)+~E(x591,x592)+~P3(x593,x591,x594,x595)
% 0.91/0.97 [60]P3(x603,x604,x602,x605)+~E(x601,x602)+~P3(x603,x604,x601,x605)
% 0.91/0.98 [61]P3(x613,x614,x615,x612)+~E(x611,x612)+~P3(x613,x614,x615,x611)
% 0.91/0.98
% 0.91/0.98 %-------------------------------------------
% 0.91/0.98 cnf(121,plain,
% 0.91/0.98 (E(f6(a1,f32(a2)),f32(a5))),
% 0.91/0.98 inference(scs_inference,[],[70,93])).
% 0.91/0.98 cnf(124,plain,
% 0.91/0.98 (P4(f21(a27,a5,a11),a11)),
% 0.91/0.98 inference(scs_inference,[],[79,62,64,70,75,93,53,49,104])).
% 0.91/0.98 cnf(126,plain,
% 0.91/0.98 (P4(f31(a11,f21(a27,a5,a11),f21(a27,a5,a11)),a11)),
% 0.91/0.98 inference(scs_inference,[],[79,62,64,70,75,93,53,49,104,100])).
% 0.91/0.98 cnf(128,plain,
% 0.91/0.98 (E(f31(a11,f21(a27,a5,a11),f31(a11,f21(a27,a5,a11),f21(a27,a5,a11))),f21(a27,a5,a11))),
% 0.91/0.98 inference(scs_inference,[],[79,62,64,70,75,93,53,49,104,100,103])).
% 0.91/0.98 cnf(159,plain,
% 0.91/0.98 (P4(f17(f31(a11,f21(a27,a5,a11),f21(a27,a5,a11))),a5)),
% 0.91/0.98 inference(scs_inference,[],[126,87,86])).
% 0.91/0.98 cnf(165,plain,
% 0.91/0.98 (P4(f14(f31(a11,f21(a27,a5,a11),f21(a27,a5,a11))),a5)),
% 0.91/0.98 inference(scs_inference,[],[126,87,86,85,84,83])).
% 0.91/0.98 cnf(167,plain,
% 0.91/0.98 (P4(f13(f31(a11,f21(a27,a5,a11),f21(a27,a5,a11))),a5)),
% 0.91/0.98 inference(scs_inference,[],[126,87,86,85,84,83,82])).
% 0.91/0.98 cnf(179,plain,
% 0.91/0.98 (E(f25(x1791,x1792,x1793,f31(a11,f21(a27,a5,a11),f31(a11,f21(a27,a5,a11),f21(a27,a5,a11))),x1794,x1795),f25(x1791,x1792,x1793,f21(a27,a5,a11),x1794,x1795))),
% 0.91/0.98 inference(scs_inference,[],[128,126,87,86,85,84,83,82,81,48,47,46,45,44,43,42,41,40])).
% 0.91/0.98 cnf(216,plain,
% 0.91/0.98 (E(f6(a27,f31(a5,f17(f21(a27,a5,a11)),f18(f21(a27,a5,a11)))),f21(a27,a5,a11))),
% 0.91/0.98 inference(scs_inference,[],[128,126,124,87,86,85,84,83,82,81,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,99])).
% 0.91/0.98 cnf(230,plain,
% 0.91/0.98 (E(f31(a11,f31(a11,f21(a27,a5,a11),f21(a27,a5,a11)),f31(a11,f21(a27,a5,a11),f21(a27,a5,a11))),f32(a11))),
% 0.91/0.98 inference(scs_inference,[],[128,126,124,87,86,85,84,83,82,81,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,99,91,90,89,88,80,94,92])).
% 0.91/0.98 cnf(236,plain,
% 0.91/0.98 (P4(f31(a11,f31(a11,f21(a27,a5,a11),f21(a27,a5,a11)),f31(a11,f21(a27,a5,a11),f21(a27,a5,a11))),a11)),
% 0.91/0.98 inference(scs_inference,[],[79,67,76,75,128,126,124,87,86,85,84,83,82,81,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,99,91,90,89,88,80,94,92,109,105,100])).
% 0.91/0.98 cnf(255,plain,
% 0.91/0.98 (~P4(f31(a5,f17(f21(a27,a5,a11)),f18(f21(a27,a5,a11))),a5)),
% 0.91/0.98 inference(scs_inference,[],[75,216,79,105])).
% 0.91/0.98 cnf(270,plain,
% 0.91/0.98 (~E(f17(f31(a11,f21(a27,a5,a11),f21(a27,a5,a11))),f31(a5,f17(f21(a27,a5,a11)),f18(f21(a27,a5,a11))))),
% 0.91/0.98 inference(scs_inference,[],[159,255,54])).
% 0.91/0.98 cnf(281,plain,
% 0.91/0.98 (P4(f32(a11),a11)),
% 0.91/0.98 inference(scs_inference,[],[230,236,54])).
% 0.91/0.98 cnf(312,plain,
% 0.91/0.98 (P4(f12(f32(a11)),a30)),
% 0.91/0.98 inference(scs_inference,[],[76,73,270,165,281,255,93,108,54,2,55,87,85,82,81])).
% 0.91/0.98 cnf(382,plain,
% 0.91/0.98 ($false),
% 0.91/0.98 inference(scs_inference,[],[67,121,76,124,179,167,312,255,281,86,84,83,47,46,45,44,43,42,41,40,37,36,34,33,30,29,27,26,24,17,16,13,10,8,6,4,91,88,94,92,109,100,54,2,87]),
% 0.91/0.98 ['proof']).
% 0.91/0.98 % SZS output end Proof
% 0.91/0.98 % Total time :0.310000s
%------------------------------------------------------------------------------