%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP383-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:43:26 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.68s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 18
% Syntax : Number of clauses : 102 ( 18 unt; 67 nHn; 93 RR)
% Number of literals : 282 ( 281 equ; 119 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_36,negated_conjecture,
( multiply(X5,sk_c6) != sk_c7
| inverse(X5) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| inverse(X2) != X3
| multiply(X2,X3) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(c_0_18,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_19,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_20,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_21,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
prove_this_18 ).
cnf(c_0_23,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(inverse(sk_c1),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_13 ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(inverse(sk_c4),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
prove_this_17 ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(inverse(sk_c1),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_12 ).
cnf(c_0_31,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
multiply(sk_c8,sk_c8) = sk_c7,
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
prove_this_16 ).
cnf(c_0_34,negated_conjecture,
multiply(inverse(sk_c8),sk_c7) = sk_c8,
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
prove_this_5 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(inverse(sk_c1),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
prove_this_11 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c8
| multiply(inverse(sk_c5),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_21,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
prove_this_4 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(inverse(sk_c8),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
prove_this_1 ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
prove_this_10 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c8
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_34,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(inverse(sk_c5),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_21,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
prove_this_9 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c8
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_21,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c8
| multiply(inverse(sk_c7),sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_21,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
prove_this_6 ).
cnf(c_0_53,negated_conjecture,
multiply(inverse(inverse(sk_c8)),sk_c8) = sk_c7,
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( sk_c8 = sk_c7
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
prove_this_21 ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(inverse(sk_c7),sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_21,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(inverse(sk_c7),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_53,c_0_43]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(inverse(sk_c7),sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_21,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
( sk_c8 = sk_c7
| multiply(inverse(sk_c7),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_21,c_0_55]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(inverse(sk_c2),sk_c7) = sk_c3 ),
inference(spm,[status(thm)],[c_0_21,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
prove_this_26 ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c7,sk_c8) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_19,c_0_43]) ).
cnf(c_0_64,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( sk_c6 = sk_c7
| sk_c8 = sk_c7
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c3
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( identity != sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(ef,[status(thm)],[c_0_63]) ).
cnf(c_0_68,negated_conjecture,
( sk_c6 = sk_c7
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_21,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( sk_c8 = sk_c7
| sk_c6 = sk_c7
| multiply(inverse(sk_c7),sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_21,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( identity = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_66]),c_0_19]) ).
cnf(c_0_71,negated_conjecture,
( identity != sk_c6
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_21,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( sk_c8 = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( identity = sk_c7
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_21,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( identity != sk_c7
| identity = sk_c8
| sk_c8 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_19]) ).
cnf(c_0_75,negated_conjecture,
( multiply(X5,sk_c6) != sk_c7
| inverse(X5) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| inverse(X2) != X3
| multiply(X2,X3) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_36]) ).
cnf(c_0_76,negated_conjecture,
( identity = sk_c8
| sk_c8 = sk_c7 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_72]),c_0_19]),c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( multiply(X5,sk_c6) != sk_c7
| inverse(X5) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| inverse(X2) != X3
| multiply(X2,X3) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c7 ),
c_0_75 ).
cnf(c_0_78,negated_conjecture,
( sk_c8 = sk_c7
| multiply(sk_c8,X1) = X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_76]) ).
cnf(c_0_79,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c7
| inverse(sk_c8) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| multiply(X2,sk_c6) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(X1),sk_c8) != sk_c7 ),
inference(er,[status(thm)],[c_0_77]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c7,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_41]) ).
cnf(c_0_81,negated_conjecture,
sk_c8 = sk_c7,
inference(spm,[status(thm)],[c_0_32,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| multiply(X2,sk_c6) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(X1),sk_c8) != sk_c7
| multiply(sk_c7,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
identity = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_81]),c_0_19]),c_0_81]) ).
cnf(c_0_84,negated_conjecture,
multiply(sk_c7,sk_c7) = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_81]),c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( identity != sk_c6
| inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| multiply(X2,sk_c6) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(inverse(X1),sk_c8) != sk_c7
| multiply(sk_c7,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_82,c_0_67]) ).
cnf(c_0_86,plain,
multiply(sk_c7,X1) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_83]) ).
cnf(c_0_87,negated_conjecture,
sk_c6 = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_81]),c_0_84])]) ).
cnf(c_0_88,negated_conjecture,
( inverse(X4) != sk_c7
| inverse(X3) != sk_c7
| inverse(X2) != sk_c7
| multiply(X4,sk_c7) != sk_c7
| multiply(X3,sk_c7) != sk_c7
| multiply(X2,sk_c7) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(inverse(X1),sk_c7) != sk_c7
| sk_c5 = sk_c7 ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_86]),c_0_83]),c_0_87]),c_0_86]),c_0_87]),c_0_83]),c_0_87])]) ).
cnf(c_0_89,negated_conjecture,
( sk_c5 = sk_c7
| inverse(sk_c7) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_86]),c_0_83]) ).
cnf(c_0_90,negated_conjecture,
( inverse(X3) != sk_c7
| inverse(X2) != sk_c7
| inverse(X1) != sk_c7
| multiply(X3,sk_c7) != sk_c7
| multiply(X2,sk_c7) != sk_c7
| multiply(X1,sk_c7) != sk_c7
| sk_c5 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_86])]) ).
cnf(c_0_91,negated_conjecture,
( inverse(X2) != sk_c7
| inverse(X1) != sk_c7
| multiply(X2,sk_c7) != sk_c7
| multiply(X1,sk_c7) != sk_c7
| sk_c5 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_86]),c_0_89]) ).
cnf(c_0_92,negated_conjecture,
( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c7
| sk_c5 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_86]),c_0_89]) ).
cnf(c_0_93,negated_conjecture,
( inverse(sk_c7) = sk_c7
| inverse(sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[c_0_41,c_0_81]) ).
cnf(c_0_94,negated_conjecture,
sk_c5 = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_89]),c_0_86])]) ).
cnf(c_0_95,negated_conjecture,
( inverse(X4) != sk_c7
| inverse(X3) != sk_c7
| inverse(X2) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(X4,sk_c7) != sk_c7
| multiply(X3,sk_c7) != sk_c7
| multiply(X2,sk_c7) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(inverse(X1),sk_c7) != sk_c7 ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_86]),c_0_87]),c_0_87]),c_0_86]),c_0_87])]) ).
cnf(c_0_96,negated_conjecture,
inverse(sk_c7) = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
cnf(c_0_97,negated_conjecture,
( inverse(X4) != sk_c7
| inverse(X3) != sk_c7
| inverse(X2) != sk_c7
| multiply(X4,sk_c7) != sk_c7
| multiply(X3,sk_c7) != sk_c7
| multiply(X2,sk_c7) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(inverse(X1),sk_c7) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]) ).
cnf(c_0_98,negated_conjecture,
( inverse(X3) != sk_c7
| inverse(X2) != sk_c7
| inverse(X1) != sk_c7
| multiply(X3,sk_c7) != sk_c7
| multiply(X2,sk_c7) != sk_c7
| multiply(X1,sk_c7) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_96]),c_0_86])]) ).
cnf(c_0_99,negated_conjecture,
( inverse(X2) != sk_c7
| inverse(X1) != sk_c7
| multiply(X2,sk_c7) != sk_c7
| multiply(X1,sk_c7) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_86]),c_0_96])]) ).
cnf(c_0_100,negated_conjecture,
( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_86]),c_0_96])]) ).
cnf(c_0_101,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_96]),c_0_86])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP383-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.57 % Computer : n017.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Sun Sep 20 20:05:57 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.63 Running first-order theorem proving
% 0.14/0.63 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.68 % Version: 3.5.1
% 0.14/0.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.14/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.14/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.68 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.68 % Starting sh5l with 300s (1) cores
% 0.14/0.68 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 522919 completed with status 0
% 0.14/0.68 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.14/0.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.14/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.14/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.68 % No SInE strategy applied
% 0.14/0.68 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.14/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.68 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.14/0.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.68 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.68 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.68 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 522926 completed with status 0
% 0.14/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.14/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.14/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.68 % No SInE strategy applied
% 0.14/0.68 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.14/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.68 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.14/0.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.68 % Preprocessing time : 0.001 s
% 0.14/0.68 % Presaturation interreduction done
% 0.14/0.68
% 0.14/0.68 % Proof found!
% 0.14/0.68 % SZS status Unsatisfiable
% 0.14/0.68 % SZS output start CNFRefutation
% See solution above
% 0.14/0.69 % Parsed axioms : 39
% 0.14/0.69 % Removed by relevancy pruning/SinE : 0
% 0.14/0.69 % Initial clauses : 39
% 0.14/0.69 % Removed in clause preprocessing : 0
% 0.14/0.69 % Initial clauses in saturation : 39
% 0.14/0.69 % Processed clauses : 778
% 0.14/0.69 % ...of these trivial : 157
% 0.14/0.69 % ...subsumed : 180
% 0.14/0.69 % ...remaining for further processing : 441
% 0.14/0.69 % Other redundant clauses eliminated : 1
% 0.14/0.69 % Clauses deleted for lack of memory : 0
% 0.14/0.69 % Backward-subsumed : 53
% 0.14/0.69 % Backward-rewritten : 326
% 0.14/0.69 % Generated clauses : 2228
% 0.14/0.69 % ...of the previous two non-redundant : 2382
% 0.14/0.69 % ...aggressively subsumed : 0
% 0.14/0.69 % Contextual simplify-reflections : 16
% 0.14/0.69 % Paramodulations : 2223
% 0.14/0.69 % Factorizations : 4
% 0.14/0.69 % NegExts : 0
% 0.14/0.69 % Equation resolutions : 1
% 0.14/0.69 % Disequality decompositions : 0
% 0.14/0.69 % Total rewrite steps : 1837
% 0.14/0.69 % ...of those cached : 1715
% 0.14/0.69 % Propositional unsat checks : 0
% 0.14/0.69 % Propositional check models : 0
% 0.14/0.69 % Propositional check unsatisfiable : 0
% 0.14/0.69 % Propositional clauses : 0
% 0.14/0.69 % Propositional clauses after purity: 0
% 0.14/0.69 % Propositional unsat core size : 0
% 0.14/0.69 % Propositional preprocessing time : 0.000
% 0.14/0.69 % Propositional encoding time : 0.000
% 0.14/0.69 % Propositional solver time : 0.000
% 0.14/0.69 % Success case prop preproc time : 0.000
% 0.14/0.69 % Success case prop encoding time : 0.000
% 0.14/0.69 % Success case prop solver time : 0.000
% 0.14/0.69 % Current number of processed clauses : 22
% 0.14/0.69 % Positive orientable unit clauses : 13
% 0.14/0.69 % Positive unorientable unit clauses: 0
% 0.14/0.69 % Negative unit clauses : 0
% 0.14/0.69 % Non-unit-clauses : 9
% 0.14/0.69 % Current number of unprocessed clauses: 981
% 0.14/0.69 % ...number of literals in the above : 3341
% 0.14/0.69 % Current number of archived formulas : 0
% 0.14/0.69 % Current number of archived clauses : 418
% 0.14/0.69 % Clause-clause subsumption calls (NU) : 5220
% 0.14/0.69 % Rec. Clause-clause subsumption calls : 1461
% 0.14/0.69 % Non-unit clause-clause subsumptions : 241
% 0.14/0.69 % Unit Clause-clause subsumption calls : 142
% 0.14/0.69 % Rewrite failures with RHS unbound : 0
% 0.14/0.69 % BW rewrite match attempts : 25
% 0.14/0.69 % BW rewrite match successes : 24
% 0.14/0.69 % Condensation attempts : 0
% 0.14/0.69 % Condensation successes : 0
% 0.14/0.69 % Termbank termtop insertions : 40249
% 0.14/0.69 % Search garbage collected termcells : 32
% 0.14/0.69
% 0.14/0.69 % -------------------------------------------------
% 0.14/0.69 % User time : 0.035 s
% 0.14/0.69 % System time : 0.004 s
% 0.14/0.69 % Total time : 0.039 s
% 0.14/0.69 % Maximum resident set size: 3652 pages
% 0.14/0.69
% 0.14/0.69 % -------------------------------------------------
% 0.14/0.69 % User time : 0.182 s
% 0.14/0.69 % System time : 0.015 s
% 0.14/0.69 % Total time : 0.196 s
% 0.14/0.69 % Maximum resident set size: 4608 pages
% 0.14/0.69 % E exiting
%------------------------------------------------------------------------------