%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP372-1 : TPTP v9.2.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 : Tue May 5 04:25:57 PM UTC 2026
% Result : Unsatisfiable 1.36s 1.76s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 23
% Syntax : Number of clauses : 107 ( 25 unt; 66 nHn; 93 RR)
% Number of literals : 268 ( 267 equ; 99 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 : 60 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_37,negated_conjecture,
( inverse(sk_c8) != sk_c7
| multiply(X1,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(c_0_23,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_24,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_25,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_26,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
prove_this_8 ).
cnf(c_0_28,negated_conjecture,
( multiply(inverse(sk_c1),sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
prove_this_14 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_7 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( multiply(inverse(sk_c1),sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_13 ).
cnf(c_0_34,negated_conjecture,
( multiply(inverse(sk_c3),sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
prove_this_9 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_25 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
prove_this_3 ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( multiply(inverse(sk_c2),sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_31 ).
cnf(c_0_42,negated_conjecture,
( multiply(inverse(sk_c8),sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_34,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( multiply(inverse(sk_c1),sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
prove_this_15 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_23 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_46]),c_0_24]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_47]),c_0_24]) ).
cnf(c_0_52,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c8,
inference(spm,[status(thm)],[c_0_34,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c8) != sk_c7
| multiply(X1,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
prove_this_37 ).
cnf(c_0_54,negated_conjecture,
( multiply(inverse(sk_c4),sk_c5) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c8 ),
prove_this_24 ).
cnf(c_0_56,negated_conjecture,
( identity = sk_c6
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
identity = sk_c7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_52]),c_0_24]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_28 ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X4,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7
| inverse(X4) != sk_c8 ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_4 ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_22 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( sk_c6 = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
( multiply(inverse(sk_c2),sk_c6) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_34 ).
cnf(c_0_66,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X4,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7
| inverse(X4) != sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| sk_c6 != sk_c8 ),
inference(ef,[status(thm)],[c_0_37]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,negated_conjecture,
( sk_c6 = sk_c8
| sk_c7 != sk_c8 ),
inference(ef,[status(thm)],[c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X4,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7
| inverse(X4) != sk_c8
| sk_c6 != sk_c8 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
sk_c6 = sk_c8,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_63]),c_0_52])]),c_0_70]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_71]),c_0_24]) ).
cnf(c_0_76,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( identity = sk_c7
| sk_c6 != sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_68]),c_0_24]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7
| inverse(X4) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74]),c_0_74])]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_10 ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_57]),c_0_74]) ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_16 ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c6 != sk_c8 ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(X1,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c7
| inverse(X3) != sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_52]),c_0_80]),c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c7,sk_c7) = identity
| sk_c6 != sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_82]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_79]),c_0_81]) ).
cnf(c_0_86,negated_conjecture,
multiply(sk_c7,sk_c7) = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_57]),c_0_74])]) ).
cnf(c_0_87,plain,
inverse(sk_c7) = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_57]),c_0_57]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(X1,sk_c8) != sk_c7
| inverse(X1) != sk_c8 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]),c_0_80]) ).
cnf(c_0_89,negated_conjecture,
multiply(sk_c8,sk_c5) = sk_c7,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_81]),c_0_79]) ).
cnf(c_0_90,negated_conjecture,
multiply(inverse(sk_c8),sk_c7) = sk_c5,
inference(spm,[status(thm)],[c_0_26,c_0_89]) ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_5 ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| sk_c5 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_86]) ).
cnf(c_0_93,negated_conjecture,
( multiply(inverse(sk_c4),sk_c5) = sk_c8
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_92]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
prove_this_6 ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c8) = sk_c7
| sk_c5 = sk_c7
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_89]) ).
cnf(c_0_96,negated_conjecture,
( sk_c7 = sk_c8
| sk_c5 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_95]),c_0_86])]) ).
cnf(c_0_97,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_98,negated_conjecture,
sk_c7 = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_96]),c_0_52])]) ).
cnf(c_0_99,plain,
multiply(inverse(inverse(X1)),sk_c8) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_57]),c_0_98]) ).
cnf(c_0_100,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_57]),c_0_98]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X4,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7
| inverse(X4) != sk_c8
| sk_c6 != sk_c8 ),
inference(rw,[status(thm)],[c_0_59,c_0_52]) ).
cnf(c_0_102,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_99]),c_0_100]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7
| inverse(X4) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_74]),c_0_74]),c_0_74])]) ).
cnf(c_0_104,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_99,c_0_102]) ).
cnf(c_0_105,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_98]),c_0_98]) ).
cnf(c_0_106,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[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)],[inference(rw,[status(thm)],[c_0_103,c_0_98]),c_0_98]),c_0_98]),c_0_98]),c_0_98]),c_0_98]),c_0_98]),c_0_100]),c_0_104]),c_0_100]),c_0_104]),c_0_104]),c_0_104]),c_0_105])])])])])]),c_0_105])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP372-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:33:29 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.36/1.76 % Version : CSE_E---1.7
% 1.36/1.76 % Problem : theBenchmark.p
% 1.36/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.36/1.76 % SZS output start CNFRefutation
% See solution above
% 1.36/1.76 % Total time : 1.371s
%------------------------------------------------------------------------------