%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP236-1 : 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 : n002.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 04:24:53 PM UTC 2026
% Result : Unsatisfiable 1.60s 1.81s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 25
% Syntax : Number of clauses : 154 ( 43 unt; 86 nHn; 130 RR)
% Number of literals : 389 ( 388 equ; 155 neg)
% Maximal clause size : 11 ( 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 : 101 ( 1 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_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,X3) != sk_c7
| inverse(X2) != X3
| multiply(X3,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| multiply(sk_c8,X5) != sk_c7
| multiply(X6,sk_c8) != X5
| inverse(X6) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_1,negated_conjecture,
inverse(sk_c8) = sk_c7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_21,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(c_0_25,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_26,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_27,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_28,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
prove_this_8 ).
cnf(c_0_30,negated_conjecture,
( multiply(inverse(sk_c4),sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_7 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
prove_this_3 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
prove_this_14 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c3
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c8,sk_c6) = sk_c7 ),
prove_this_19 ).
cnf(c_0_39,negated_conjecture,
( multiply(inverse(sk_c4),sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_2 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c3 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,X3) != sk_c7
| inverse(X2) != X3
| multiply(X3,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| multiply(sk_c8,X5) != sk_c7
| multiply(X6,sk_c8) != X5
| inverse(X6) != sk_c8 ),
prove_this_27 ).
cnf(c_0_44,negated_conjecture,
inverse(sk_c8) = sk_c7,
prove_this_1 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_41]),c_0_26]) ).
cnf(c_0_46,negated_conjecture,
multiply(sk_c8,sk_c8) = sk_c7,
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(inverse(X2),sk_c8) != sk_c7
| multiply(X2,inverse(X2)) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X3) != sk_c8
| inverse(X4) != sk_c8 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])])])]) ).
cnf(c_0_48,negated_conjecture,
multiply(sk_c7,sk_c8) = identity,
inference(spm,[status(thm)],[c_0_26,c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_45]),c_0_44]) ).
cnf(c_0_50,negated_conjecture,
multiply(sk_c7,sk_c7) = sk_c8,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_46]),c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c8,multiply(X1,multiply(X2,sk_c8))) != sk_c7
| multiply(inverse(X3),sk_c8) != sk_c7
| multiply(X3,inverse(X3)) != sk_c7
| inverse(multiply(X1,X2)) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| multiply(X5,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| inverse(X5) != sk_c8 ),
inference(spm,[status(thm)],[c_0_47,c_0_25]) ).
cnf(c_0_52,negated_conjecture,
multiply(inverse(sk_c7),identity) = sk_c8,
inference(spm,[status(thm)],[c_0_28,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( identity = sk_c7
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c8,multiply(X1,identity)) != sk_c7
| multiply(inverse(X2),sk_c8) != sk_c7
| inverse(multiply(X1,sk_c7)) != sk_c8
| multiply(X2,inverse(X2)) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| inverse(X4) != sk_c8 ),
inference(spm,[status(thm)],[c_0_51,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( sk_c6 = sk_c8
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_26]) ).
cnf(c_0_56,negated_conjecture,
multiply(inverse(sk_c7),sk_c8) = sk_c7,
inference(spm,[status(thm)],[c_0_28,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( inverse(multiply(inverse(identity),sk_c7)) != sk_c8
| multiply(inverse(X1),sk_c8) != sk_c7
| multiply(sk_c8,identity) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8 ),
inference(spm,[status(thm)],[c_0_54,c_0_26]) ).
cnf(c_0_58,negated_conjecture,
( sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_55]),c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( sk_c6 = sk_c8
| multiply(inverse(X1),sk_c8) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_55]),c_0_44]),c_0_50]),c_0_44]),c_0_46])]),c_0_58]) ).
cnf(c_0_60,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c8 ),
prove_this_17 ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
prove_this_12 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
prove_this_22 ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c4) = sk_c8
| sk_c6 = sk_c8
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_62]) ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c4) = sk_c8
| sk_c6 = sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(identity) != sk_c8
| inverse(X1) != sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_27]),c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( inverse(sk_c4) = sk_c8
| sk_c6 = sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_55]),c_0_44]),c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( inverse(sk_c4) = sk_c8
| sk_c6 = sk_c8
| inverse(identity) != sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_27]),c_0_58]) ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c4) = sk_c8
| sk_c6 = sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_55]),c_0_44]),c_0_58]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_67]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c7,identity) = sk_c4
| sk_c6 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_68]),c_0_44]) ).
cnf(c_0_70,negated_conjecture,
( sk_c6 = sk_c8
| identity = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_55]),c_0_48]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c4,X1) = X1
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_70]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c4,X1) = multiply(sk_c7,X1)
| sk_c6 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_69]),c_0_27]) ).
cnf(c_0_73,negated_conjecture,
multiply(sk_c7,multiply(sk_c8,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_48]),c_0_27]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c7,X1) = X1
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( sk_c6 = sk_c8
| multiply(sk_c8,sk_c7) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_44]),c_0_48]),c_0_53]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c8,X1) = X1
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
prove_this_25 ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
prove_this_26 ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
prove_this_24 ).
cnf(c_0_80,negated_conjecture,
( sk_c6 = sk_c8
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(inverse(X1),sk_c8) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_77]),c_0_78]),c_0_79]) ).
cnf(c_0_82,negated_conjecture,
( sk_c6 = sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_76]),c_0_44])]),c_0_58]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c5,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(spm,[status(thm)],[c_0_81,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
( sk_c6 = sk_c8
| multiply(sk_c4,sk_c7) != sk_c8 ),
inference(spm,[status(thm)],[c_0_82,c_0_67]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
prove_this_10 ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
prove_this_11 ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
prove_this_9 ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_46])]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_84,c_0_78]) ).
cnf(c_0_91,negated_conjecture,
sk_c6 = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_72]),c_0_50])]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(inverse(X1),sk_c8) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_86]),c_0_87]),c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| sk_c6 != sk_c7 ),
inference(spm,[status(thm)],[c_0_89,c_0_77]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91]),c_0_46]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c5,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(spm,[status(thm)],[c_0_92,c_0_87]) ).
cnf(c_0_96,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_86]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_91]),c_0_94]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
prove_this_23 ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_46])]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_96,c_0_87]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_62]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| sk_c6 != sk_c7 ),
inference(spm,[status(thm)],[c_0_99,c_0_86]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_91]),c_0_46]) ).
cnf(c_0_104,negated_conjecture,
multiply(sk_c3,sk_c8) = sk_c7,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_62]),c_0_98]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
prove_this_15 ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_91]),c_0_103]) ).
cnf(c_0_107,negated_conjecture,
multiply(sk_c3,multiply(sk_c8,X1)) = multiply(sk_c7,X1),
inference(spm,[status(thm)],[c_0_25,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_29]),c_0_31]) ).
cnf(c_0_110,negated_conjecture,
multiply(sk_c3,sk_c7) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_46]),c_0_48]) ).
cnf(c_0_111,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c8 ),
inference(rw,[status(thm)],[c_0_108,c_0_91]) ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c6 ),
prove_this_20 ).
cnf(c_0_113,negated_conjecture,
multiply(sk_c1,sk_c7) = sk_c8,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_31]),c_0_29]) ).
cnf(c_0_114,negated_conjecture,
multiply(inverse(sk_c3),identity) = sk_c7,
inference(spm,[status(thm)],[c_0_28,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
( multiply(inverse(inverse(sk_c2)),sk_c3) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(rw,[status(thm)],[c_0_112,c_0_91]) ).
cnf(c_0_117,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c8 ),
prove_this_21 ).
cnf(c_0_118,negated_conjecture,
multiply(sk_c3,multiply(sk_c7,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_110]),c_0_27]) ).
cnf(c_0_119,negated_conjecture,
multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c8,X1),
inference(spm,[status(thm)],[c_0_25,c_0_113]) ).
cnf(c_0_120,negated_conjecture,
multiply(inverse(sk_c3),X1) = multiply(sk_c7,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_114]),c_0_27]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c8
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_26]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c3,sk_c2) = identity
| inverse(sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_117]) ).
cnf(c_0_123,negated_conjecture,
multiply(sk_c3,X1) = multiply(sk_c8,X1),
inference(spm,[status(thm)],[c_0_118,c_0_73]) ).
cnf(c_0_124,negated_conjecture,
multiply(sk_c1,identity) = sk_c7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_48]),c_0_46]) ).
cnf(c_0_125,negated_conjecture,
multiply(sk_c7,sk_c3) = identity,
inference(spm,[status(thm)],[c_0_26,c_0_120]) ).
cnf(c_0_126,negated_conjecture,
( multiply(inverse(sk_c5),sk_c8) = sk_c8
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_121]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c5) = sk_c8 ),
inference(rw,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_128,negated_conjecture,
multiply(sk_c1,X1) = multiply(sk_c7,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_124]),c_0_27]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c8 ),
prove_this_16 ).
cnf(c_0_130,negated_conjecture,
sk_c3 = sk_c8,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_125]),c_0_52]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| identity = sk_c7
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_46]) ).
cnf(c_0_132,negated_conjecture,
multiply(sk_c7,identity) = sk_c7,
inference(rw,[status(thm)],[c_0_124,c_0_128]) ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
inference(rw,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_134,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c7
| sk_c2 = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_131]),c_0_44]),c_0_132]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| identity = sk_c7
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_133]),c_0_46]) ).
cnf(c_0_136,negated_conjecture,
( sk_c2 = sk_c7
| sk_c7 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_134]),c_0_50])]) ).
cnf(c_0_137,negated_conjecture,
multiply(sk_c7,multiply(sk_c7,X1)) = multiply(sk_c8,X1),
inference(rw,[status(thm)],[c_0_119,c_0_128]) ).
cnf(c_0_138,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_48])]) ).
cnf(c_0_139,negated_conjecture,
multiply(sk_c8,sk_c7) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_50]),c_0_48]) ).
cnf(c_0_140,negated_conjecture,
sk_c7 = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_138]),c_0_50])]) ).
cnf(c_0_141,negated_conjecture,
identity = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140]),c_0_46]),c_0_140]) ).
cnf(c_0_142,plain,
multiply(inverse(X1),X1) = sk_c8,
inference(rw,[status(thm)],[c_0_26,c_0_141]) ).
cnf(c_0_143,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_28]) ).
cnf(c_0_144,negated_conjecture,
multiply(inverse(inverse(sk_c7)),sk_c8) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_52]) ).
cnf(c_0_145,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_142]),c_0_143]) ).
cnf(c_0_146,negated_conjecture,
( inverse(inverse(inverse(sk_c7))) != sk_c8
| multiply(inverse(X1),sk_c8) != sk_c7
| multiply(sk_c8,identity) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8 ),
inference(spm,[status(thm)],[c_0_47,c_0_144]) ).
cnf(c_0_147,negated_conjecture,
multiply(sk_c8,identity) = sk_c8,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_132]),c_0_50]) ).
cnf(c_0_148,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_145]),c_0_145]) ).
cnf(c_0_149,negated_conjecture,
( inverse(inverse(inverse(sk_c7))) != sk_c8
| multiply(inverse(X1),sk_c8) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8
| sk_c7 != sk_c8 ),
inference(rw,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_150,plain,
multiply(X1,inverse(X1)) = sk_c8,
inference(spm,[status(thm)],[c_0_142,c_0_148]) ).
cnf(c_0_151,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(rw,[status(thm)],[c_0_117,c_0_130]) ).
cnf(c_0_152,negated_conjecture,
inverse(X1) != sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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(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)],[c_0_149,c_0_140]),c_0_44]),c_0_140]),c_0_44]),c_0_140]),c_0_44]),c_0_140]),c_0_140]),c_0_140]),c_0_140]),c_0_140]),c_0_140])]),c_0_145]),c_0_150]),c_0_145]),c_0_145])])])]),c_0_44]),c_0_140])]) ).
cnf(c_0_153,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_151,c_0_152]),c_0_152]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP236-1 : 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 : n002.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 18:30:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.60/1.81 % Version : CSE_E---1.7
% 1.60/1.81 % Problem : theBenchmark.p
% 1.60/1.81 % SZS status Unsatisfiable for theBenchmark.p
% 1.60/1.81 % SZS output start CNFRefutation
% See solution above
% 1.60/1.81 % Total time : 1.369s
%------------------------------------------------------------------------------