%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP328-1 : 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 : n031.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 04:25:35 PM UTC 2026
% Result : Unsatisfiable 9.33s 6.09s
% Output : CNFRefutation 9.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 23
% Syntax : Number of clauses : 224 ( 22 unt; 178 nHn; 183 RR)
% Number of literals : 479 ( 478 equ; 74 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 : 71 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| multiply(sk_c8,X2) != sk_c7
| multiply(X3,sk_c8) != X2
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
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_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_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_29,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(c_0_23,negated_conjecture,
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| multiply(sk_c8,X2) != sk_c7
| multiply(X3,sk_c8) != X2
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
prove_this_31 ).
cnf(c_0_24,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_25,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c6 ),
prove_this_27 ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,multiply(X2,sk_c8)) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c6
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_23])]) ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
prove_this_26 ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,multiply(X2,sk_c8)) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_3 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c2) = identity
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,multiply(X2,sk_c8)) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_23 ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_28 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_18 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c7 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_37,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_38,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c2) = identity
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_8 ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_13 ).
cnf(c_0_42,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_24]),c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( multiply(inverse(sk_c8),identity) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_45,negated_conjecture,
( multiply(inverse(sk_c8),X1) = multiply(sk_c2,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_44]),c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c2,multiply(sk_c8,X1)) = multiply(sk_c3,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_37,c_0_33]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c2,multiply(sk_c8,X1)) = X1
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c8,multiply(sk_c3,X1)) = multiply(sk_c7,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_37,c_0_35]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c3,X1) = X1 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c7,X1) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_30 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,identity) = sk_c1 ),
inference(spm,[status(thm)],[c_0_47,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c4) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c2,X1) = multiply(sk_c1,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_54]),c_0_38]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_55]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
prove_this_25 ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c3
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c8,multiply(sk_c2,X1)) = X1
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_43]),c_0_38]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
prove_this_20 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c8,multiply(sk_c2,X1)) = X1
| multiply(sk_c8,sk_c4) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_57]),c_0_38]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
( multiply(inverse(sk_c1),sk_c3) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_60,c_0_33]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_42]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_45]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_64,c_0_41]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_65]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_74,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_24]),c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_24 ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_69,c_0_56]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c1,sk_c8) = multiply(sk_c8,sk_c3)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c8) = sk_c4
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_73]),c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_42,c_0_75]) ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_29 ).
cnf(c_0_82,negated_conjecture,
( multiply(inverse(sk_c7),multiply(sk_c8,X1)) = X1
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_51]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
prove_this_6 ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_19 ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c7,multiply(sk_c8,X1)) = multiply(sk_c6,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_37,c_0_30]) ).
cnf(c_0_89,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_74]),c_0_74]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c7) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_74]) ).
cnf(c_0_91,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_84]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
prove_this_11 ).
cnf(c_0_93,negated_conjecture,
( multiply(inverse(sk_c4),sk_c5) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_85]) ).
cnf(c_0_94,negated_conjecture,
( multiply(inverse(sk_c4),sk_c5) = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_86]) ).
cnf(c_0_95,negated_conjecture,
( multiply(inverse(sk_c4),sk_c5) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_87]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c6,sk_c3) = multiply(sk_c7,sk_c8)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_88,c_0_65]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c6,sk_c3) = multiply(sk_c7,sk_c7)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_88,c_0_35]) ).
cnf(c_0_98,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_99,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c3
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_35]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c3,sk_c3) = multiply(sk_c2,sk_c8)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_46,c_0_65]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c3,sk_c3) = multiply(sk_c2,sk_c7)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_46,c_0_35]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(inverse(sk_c3),X1) = X1 ),
inference(spm,[status(thm)],[c_0_42,c_0_49]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c8
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_95,c_0_94]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c7,sk_c7) = multiply(sk_c7,sk_c8)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_98,c_0_41]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(spm,[status(thm)],[c_0_99,c_0_45]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c2,sk_c7) = multiply(sk_c2,sk_c8)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_111,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_89,c_0_25]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,X1) = X1 ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_113,negated_conjecture,
( multiply(inverse(sk_c7),sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_104]) ).
cnf(c_0_114,negated_conjecture,
sk_c7 = sk_c8,
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c7,sk_c8) = multiply(sk_c8,sk_c7)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_107,c_0_51]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c1,sk_c7) = multiply(sk_c8,sk_c8)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_70,c_0_108]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c3
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_109,c_0_56]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c2,sk_c8) = multiply(sk_c1,sk_c7)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_110,c_0_56]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_92]) ).
cnf(c_0_120,negated_conjecture,
( inverse(sk_c8) = sk_c6
| sk_c2 != sk_c6 ),
inference(ef,[status(thm)],[c_0_111]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,identity) = sk_c2 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,identity) = sk_c3 ),
inference(spm,[status(thm)],[c_0_47,c_0_83]) ).
cnf(c_0_123,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_112]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c8
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114]),c_0_24]),c_0_114]),c_0_114]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_115]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_93,c_0_61]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_51]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_69,c_0_118]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_65]),c_0_24]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c7,multiply(sk_c1,X1)) = X1
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_119]),c_0_38]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_37,c_0_84]) ).
cnf(c_0_133,negated_conjecture,
( inverse(sk_c6) = sk_c8
| sk_c2 != sk_c6 ),
inference(spm,[status(thm)],[c_0_89,c_0_120]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_35,c_0_83]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
prove_this_2 ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c7,multiply(sk_c6,X1)) = multiply(sk_c8,X1)
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_37,c_0_104]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c6,sk_c8) = identity
| sk_c2 != sk_c6 ),
inference(spm,[status(thm)],[c_0_24,c_0_120]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c7,multiply(sk_c1,X1)) = X1
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_50]),c_0_38]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c1,identity) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_121,c_0_56]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_141,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_123]) ).
cnf(c_0_142,negated_conjecture,
( identity = sk_c6
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_124]),c_0_24]) ).
cnf(c_0_143,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_42,c_0_125]) ).
cnf(c_0_144,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| multiply(sk_c8,sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_42,c_0_126]) ).
cnf(c_0_145,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c3
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_127]) ).
cnf(c_0_146,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_42,c_0_128]) ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_116,c_0_129]) ).
cnf(c_0_148,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_42,c_0_130]) ).
cnf(c_0_149,negated_conjecture,
( multiply(sk_c7,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_150,negated_conjecture,
( multiply(sk_c8,sk_c6) = identity
| sk_c2 != sk_c6 ),
inference(spm,[status(thm)],[c_0_24,c_0_133]) ).
cnf(c_0_151,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_134]) ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_135]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7
| sk_c2 != sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_74]) ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_155,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_42,c_0_140]) ).
cnf(c_0_156,negated_conjecture,
( sk_c6 = sk_c8
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_114]),c_0_24]) ).
cnf(c_0_157,negated_conjecture,
( identity = sk_c8
| sk_c6 != sk_c8 ),
inference(ef,[status(thm)],[c_0_142]) ).
cnf(c_0_158,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c6
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_114]),c_0_24]),c_0_114]) ).
cnf(c_0_159,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c3
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_114]),c_0_24]) ).
cnf(c_0_160,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c8
| sk_c3 = sk_c5 ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_161,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| multiply(sk_c8,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_147]) ).
cnf(c_0_162,negated_conjecture,
( identity = sk_c3
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_114]),c_0_24]) ).
cnf(c_0_163,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c8) = sk_c6 ),
prove_this_12 ).
cnf(c_0_164,negated_conjecture,
( multiply(sk_c7,multiply(sk_c6,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_166,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c7
| sk_c2 != sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_74]) ).
cnf(c_0_167,negated_conjecture,
( identity = sk_c8
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_114]),c_0_24]),c_0_114]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = X1
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_152]),c_0_38]) ).
cnf(c_0_169,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_170,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c8
| sk_c2 != sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_114]),c_0_114]),c_0_114])]) ).
cnf(c_0_171,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| identity = sk_c2 ),
inference(spm,[status(thm)],[c_0_154,c_0_112]) ).
cnf(c_0_172,negated_conjecture,
( sk_c3 = sk_c2
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_114]),c_0_24]) ).
cnf(c_0_173,negated_conjecture,
( identity = sk_c8
| sk_c5 = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_142]),c_0_157]) ).
cnf(c_0_174,negated_conjecture,
( identity = sk_c5
| sk_c3 = sk_c6 ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c6
| sk_c3 = sk_c5
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_160]),c_0_24]) ).
cnf(c_0_176,negated_conjecture,
( multiply(sk_c8,sk_c8) = identity
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_114]),c_0_24]) ).
cnf(c_0_177,negated_conjecture,
( identity = sk_c5
| sk_c3 != sk_c5 ),
inference(ef,[status(thm)],[c_0_162]) ).
cnf(c_0_178,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_89,c_0_163]) ).
cnf(c_0_179,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_74]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c8
| sk_c2 != sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_114]),c_0_114]),c_0_114])]) ).
cnf(c_0_181,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_74]) ).
cnf(c_0_182,negated_conjecture,
( identity = sk_c8
| sk_c5 != sk_c8 ),
inference(ef,[status(thm)],[c_0_167]) ).
cnf(c_0_183,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_168,c_0_125]) ).
cnf(c_0_184,negated_conjecture,
( multiply(sk_c8,X1) = X1
| sk_c2 != sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_42]) ).
cnf(c_0_185,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c8
| identity = sk_c2 ),
inference(rw,[status(thm)],[c_0_171,c_0_114]) ).
cnf(c_0_186,negated_conjecture,
( sk_c5 = sk_c6
| sk_c5 = sk_c8
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_187,negated_conjecture,
( sk_c5 = sk_c6
| sk_c3 = sk_c6
| sk_c5 = sk_c8 ),
inference(spm,[status(thm)],[c_0_174,c_0_173]) ).
cnf(c_0_188,negated_conjecture,
( identity = sk_c5
| identity = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_177]) ).
cnf(c_0_189,negated_conjecture,
( inverse(sk_c8) = sk_c1
| inverse(sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[c_0_178,c_0_114]) ).
cnf(c_0_190,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_179]),c_0_74]) ).
cnf(c_0_191,negated_conjecture,
( identity = sk_c8
| sk_c2 != sk_c6 ),
inference(spm,[status(thm)],[c_0_150,c_0_180]) ).
cnf(c_0_192,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c5 != sk_c8 ),
inference(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_193,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c5
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_114]),c_0_114]),c_0_114])]) ).
cnf(c_0_194,negated_conjecture,
( multiply(X1,sk_c8) = X1
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_74,c_0_173]) ).
cnf(c_0_195,negated_conjecture,
( identity = sk_c2
| sk_c5 = sk_c8
| sk_c2 != sk_c6 ),
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_196,negated_conjecture,
( sk_c2 = sk_c6
| sk_c5 = sk_c8
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_197,negated_conjecture,
( identity = sk_c6
| sk_c5 != sk_c6 ),
inference(ef,[status(thm)],[c_0_188]) ).
cnf(c_0_198,negated_conjecture,
( inverse(sk_c8) = sk_c6
| sk_c1 != sk_c6 ),
inference(ef,[status(thm)],[c_0_189]) ).
cnf(c_0_199,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c8
| inverse(sk_c8) = sk_c2 ),
inference(rw,[status(thm)],[c_0_190,c_0_114]) ).
cnf(c_0_200,negated_conjecture,
( multiply(X1,sk_c8) = X1
| sk_c2 != sk_c6 ),
inference(spm,[status(thm)],[c_0_74,c_0_191]) ).
cnf(c_0_201,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c6 ),
prove_this_7 ).
cnf(c_0_202,negated_conjecture,
( multiply(sk_c8,sk_c8) = identity
| sk_c5 != sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_192]) ).
cnf(c_0_203,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c6
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_204,negated_conjecture,
( sk_c5 = sk_c8
| identity = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_197]) ).
cnf(c_0_205,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c8
| sk_c1 != sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_199]),c_0_200]) ).
cnf(c_0_206,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_201]) ).
cnf(c_0_207,negated_conjecture,
identity = sk_c6,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_204]),c_0_197]) ).
cnf(c_0_208,negated_conjecture,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_24,c_0_163]) ).
cnf(c_0_209,negated_conjecture,
( identity = sk_c8
| sk_c1 != sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_205]),c_0_24]) ).
cnf(c_0_210,negated_conjecture,
( multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_206]) ).
cnf(c_0_211,plain,
multiply(sk_c6,X1) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_207]) ).
cnf(c_0_212,negated_conjecture,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_208]) ).
cnf(c_0_213,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c1 != sk_c6 ),
inference(spm,[status(thm)],[c_0_181,c_0_209]) ).
cnf(c_0_214,negated_conjecture,
( multiply(sk_c1,multiply(sk_c8,X1)) = multiply(sk_c8,X1)
| sk_c6 = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_210,c_0_114]),c_0_211]),c_0_207]) ).
cnf(c_0_215,negated_conjecture,
( multiply(sk_c8,sk_c1) = sk_c6
| sk_c6 = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_212,c_0_114]),c_0_207]),c_0_211]),c_0_207]) ).
cnf(c_0_216,plain,
multiply(X1,sk_c6) = X1,
inference(rw,[status(thm)],[c_0_74,c_0_207]) ).
cnf(c_0_217,negated_conjecture,
( sk_c6 = sk_c8
| sk_c1 != sk_c6 ),
inference(spm,[status(thm)],[c_0_198,c_0_213]) ).
cnf(c_0_218,negated_conjecture,
sk_c6 = sk_c8,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_216]),c_0_217]) ).
cnf(c_0_219,plain,
inverse(sk_c6) = sk_c6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_207]),c_0_207]) ).
cnf(c_0_220,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_216,c_0_218]) ).
cnf(c_0_221,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[c_0_211,c_0_218]) ).
cnf(c_0_222,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_219,c_0_218]),c_0_218]) ).
cnf(c_0_223,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_114]),c_0_114]),c_0_114]),c_0_114]),c_0_114]),c_0_114]),c_0_220]),c_0_221]),c_0_220]),c_0_221]),c_0_221]),c_0_218]),c_0_216]),c_0_220]),c_0_222]),c_0_218])])])])]),c_0_222])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP328-1 : 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
% 0.13/0.33 % Computer : n031.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 May 4 18:34:23 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 9.33/6.09 % Version : CSE_E---1.7
% 9.33/6.09 % Problem : theBenchmark.p
% 9.33/6.09 % SZS status Unsatisfiable for theBenchmark.p
% 9.33/6.09 % SZS output start CNFRefutation
% See solution above
% 9.44/6.13 % Total time : 4.371s
%------------------------------------------------------------------------------