%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP208-1 : TPTP v9.2.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.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 04:24:49 PM UTC 2026
% Result : Unsatisfiable 4.57s 3.37s
% Output : CNFRefutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 28
% Syntax : Number of clauses : 195 ( 25 unt; 139 nHn; 172 RR)
% Number of literals : 517 ( 516 equ; 180 neg)
% Maximal clause size : 16 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 117 ( 12 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_5,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c12
| multiply(sk_c7,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_36,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c12
| inverse(sk_c7) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_40,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c10,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c7) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c7,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c7,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_39,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| inverse(sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c5,sk_c6) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_44,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| inverse(sk_c7) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
cnf(prove_this_54,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c7) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
cnf(prove_this_61,negated_conjecture,
( multiply(X1,X2) != sk_c12
| inverse(X1) != X2
| multiply(X2,sk_c11) != sk_c12
| multiply(sk_c12,X3) != sk_c11
| multiply(X4,sk_c12) != X3
| inverse(X4) != sk_c12
| multiply(X5,X6) != sk_c12
| inverse(X5) != X6
| multiply(X6,sk_c11) != sk_c12
| inverse(X7) != sk_c12
| multiply(X7,sk_c11) != sk_c12
| multiply(X8,X9) != sk_c11
| inverse(X8) != X9
| multiply(X9,sk_c12) != sk_c11
| inverse(X10) != sk_c11
| multiply(X10,sk_c12) != sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
cnf(prove_this_32,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_55,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c7,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c7,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_34,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| inverse(sk_c7) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_52,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
cnf(prove_this_57,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_57) ).
cnf(prove_this_51,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c5,sk_c6) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_56,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_56) ).
cnf(prove_this_43,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_59,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_59) ).
cnf(c_0_28,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_29,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_30,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_31,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c12
| multiply(sk_c7,sk_c11) = sk_c12 ),
prove_this_5 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
prove_this_36 ).
cnf(c_0_34,negated_conjecture,
( multiply(inverse(sk_c7),sk_c12) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c12 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c12
| inverse(sk_c7) = sk_c12 ),
prove_this_4 ).
cnf(c_0_36,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c9
| multiply(sk_c12,sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| inverse(sk_c8) = sk_c9 ),
prove_this_37 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c10,sk_c12) = sk_c11 ),
prove_this_40 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c8,multiply(sk_c9,X1)) = multiply(sk_c11,X1)
| multiply(sk_c12,sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_33]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_31]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c7) = sk_c12 ),
prove_this_14 ).
cnf(c_0_44,negated_conjecture,
( multiply(inverse(sk_c1),sk_c12) = sk_c2
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_31,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c7,sk_c11) = sk_c12 ),
prove_this_15 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c7,sk_c11) = sk_c12 ),
prove_this_45 ).
cnf(c_0_47,negated_conjecture,
( multiply(inverse(sk_c10),sk_c11) = sk_c12
| multiply(sk_c12,sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_31,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| inverse(sk_c10) = sk_c11 ),
prove_this_39 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c8,sk_c9) = multiply(sk_c11,sk_c11)
| multiply(sk_c12,sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_42]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c5,sk_c6) = sk_c12 ),
prove_this_31 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c12,multiply(sk_c7,X1)) = X1
| inverse(sk_c1) = sk_c2 ),
inference(spm,[status(thm)],[c_0_31,c_0_43]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c7,sk_c11) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11
| multiply(sk_c2,sk_c12) = sk_c2 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_54,negated_conjecture,
( multiply(inverse(sk_c7),sk_c12) = sk_c11
| multiply(sk_c3,sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_31,c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| inverse(sk_c7) = sk_c12 ),
prove_this_44 ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c11
| multiply(sk_c12,sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_33,c_0_49]) ).
cnf(c_0_58,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_50]),c_0_50]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c7) = sk_c12 ),
prove_this_54 ).
cnf(c_0_60,negated_conjecture,
( multiply(X1,X2) != sk_c12
| inverse(X1) != X2
| multiply(X2,sk_c11) != sk_c12
| multiply(sk_c12,X3) != sk_c11
| multiply(X4,sk_c12) != X3
| inverse(X4) != sk_c12
| multiply(X5,X6) != sk_c12
| inverse(X5) != X6
| multiply(X6,sk_c11) != sk_c12
| inverse(X7) != sk_c12
| multiply(X7,sk_c11) != sk_c12
| multiply(X8,X9) != sk_c11
| inverse(X8) != X9
| multiply(X9,sk_c12) != sk_c11
| inverse(X10) != sk_c11
| multiply(X10,sk_c12) != sk_c11 ),
prove_this_61 ).
cnf(c_0_61,negated_conjecture,
( multiply(inverse(sk_c5),sk_c12) = sk_c6
| multiply(sk_c12,sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_31,c_0_51]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| inverse(sk_c5) = sk_c6 ),
prove_this_32 ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c2
| multiply(sk_c12,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_66,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c12) = sk_c7 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| multiply(inverse(X2),sk_c12) != sk_c11
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(inverse(X4),sk_c11) != sk_c12
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X4,inverse(X4)) != sk_c12
| multiply(X5,sk_c12) != sk_c11
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != sk_c11
| inverse(X6) != sk_c12
| inverse(X1) != sk_c12 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_60])])])]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c6,sk_c12) = sk_c6 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c11
| multiply(sk_c2,sk_c12) = sk_c2 ),
inference(spm,[status(thm)],[c_0_44,c_0_63]) ).
cnf(c_0_70,negated_conjecture,
( multiply(inverse(sk_c3),sk_c4) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_31,c_0_64]) ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c7,sk_c11) = sk_c12 ),
prove_this_55 ).
cnf(c_0_72,negated_conjecture,
( multiply(inverse(sk_c12),sk_c11) = sk_c4
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_31,c_0_65]) ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c12) = sk_c7
| inverse(sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_58,c_0_66]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| multiply(inverse(X2),sk_c12) != sk_c11
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(inverse(X4),sk_c11) != sk_c12
| inverse(inverse(inverse(X1))) != sk_c12
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X4,inverse(X4)) != sk_c12
| multiply(X5,sk_c12) != sk_c11
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != sk_c11
| inverse(X6) != sk_c12 ),
inference(spm,[status(thm)],[c_0_67,c_0_42]) ).
cnf(c_0_75,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| identity = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_68]),c_0_29]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c11
| identity = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_69]),c_0_29]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c12,multiply(sk_c7,X1)) = X1
| inverse(sk_c3) = sk_c12 ),
inference(spm,[status(thm)],[c_0_31,c_0_59]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c7,sk_c11) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11
| multiply(sk_c12,sk_c4) = sk_c12 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
( multiply(inverse(inverse(sk_c7)),sk_c11) = sk_c12
| multiply(sk_c3,sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_31,c_0_54]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c7,sk_c11) = sk_c12
| inverse(sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_58,c_0_71]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c7,sk_c11) = sk_c4
| inverse(sk_c12) = sk_c3
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,negated_conjecture,
( inverse(inverse(inverse(identity))) != sk_c12
| multiply(inverse(X1),sk_c12) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(sk_c12,sk_c12) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| multiply(X5,sk_c11) != sk_c12
| inverse(X4) != sk_c11
| inverse(X5) != sk_c12 ),
inference(spm,[status(thm)],[c_0_74,c_0_30]) ).
cnf(c_0_84,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_75,c_0_50]) ).
cnf(c_0_85,negated_conjecture,
( multiply(inverse(sk_c12),sk_c11) = sk_c4
| identity = sk_c12 ),
inference(spm,[status(thm)],[c_0_31,c_0_76]) ).
cnf(c_0_86,negated_conjecture,
( multiply(inverse(sk_c12),sk_c11) = sk_c12
| identity = sk_c12 ),
inference(spm,[status(thm)],[c_0_31,c_0_77]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11
| inverse(sk_c3) = sk_c12 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_88,negated_conjecture,
( multiply(inverse(sk_c12),sk_c11) = sk_c12
| multiply(sk_c3,sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_80,c_0_55]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c7,sk_c11) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c4
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_72,c_0_81]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c7,sk_c11) = sk_c4
| multiply(sk_c3,sk_c11) = sk_c4
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_72,c_0_82]) ).
cnf(c_0_91,negated_conjecture,
( multiply(inverse(X1),sk_c12) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(sk_c12,sk_c12) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| multiply(X5,sk_c11) != sk_c12
| inverse(X4) != sk_c11
| inverse(X5) != sk_c12
| identity != sk_c12 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84]),c_0_84]),c_0_84]) ).
cnf(c_0_92,negated_conjecture,
( identity = sk_c12
| sk_c4 = sk_c12 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c11
| multiply(sk_c12,sk_c4) = sk_c12 ),
inference(spm,[status(thm)],[c_0_70,c_0_87]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| sk_c11 = sk_c12
| sk_c4 = sk_c12 ),
inference(spm,[status(thm)],[c_0_72,c_0_88]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c4
| sk_c11 = sk_c12
| sk_c4 = sk_c12 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
( sk_c4 = sk_c12
| multiply(inverse(X1),sk_c12) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(sk_c12,sk_c12) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| multiply(X5,sk_c11) != sk_c12
| inverse(X4) != sk_c11
| inverse(X5) != sk_c12 ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c11
| identity = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_93]),c_0_29]) ).
cnf(c_0_98,negated_conjecture,
( multiply(inverse(sk_c3),sk_c4) = sk_c12
| sk_c4 = sk_c12
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_31,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
( multiply(inverse(sk_c3),sk_c4) = sk_c11
| sk_c4 = sk_c12
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_31,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( identity = sk_c4
| sk_c4 = sk_c12
| multiply(inverse(X1),sk_c12) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| multiply(X5,sk_c11) != sk_c12
| inverse(X4) != sk_c11
| inverse(X5) != sk_c12 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_101,negated_conjecture,
( sk_c4 = sk_c12
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_102,negated_conjecture,
( sk_c4 = sk_c12
| identity = sk_c4
| multiply(inverse(X1),sk_c11) != sk_c12
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(X1,inverse(X1)) != sk_c12
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,sk_c12) != sk_c11
| multiply(X4,sk_c11) != sk_c12
| inverse(X3) != sk_c11
| inverse(X4) != sk_c12
| identity != sk_c11 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_84]),c_0_30]),c_0_30]),c_0_101]) ).
cnf(c_0_103,negated_conjecture,
( sk_c4 = sk_c12
| multiply(inverse(X1),sk_c11) != sk_c12
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(X1,inverse(X1)) != sk_c12
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,sk_c12) != sk_c11
| multiply(X4,sk_c11) != sk_c12
| inverse(X3) != sk_c11
| inverse(X4) != sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_92]),c_0_101]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c12 ),
prove_this_41 ).
cnf(c_0_105,negated_conjecture,
( sk_c4 = sk_c12
| multiply(inverse(X1),sk_c11) != sk_c12
| multiply(X1,inverse(X1)) != sk_c12
| multiply(X2,sk_c12) != sk_c11
| multiply(X3,sk_c11) != sk_c12
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_84]),c_0_30]),c_0_30]),c_0_92]),c_0_101]) ).
cnf(c_0_106,negated_conjecture,
( multiply(inverse(sk_c5),sk_c12) = sk_c6
| multiply(sk_c3,sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_31,c_0_104]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| inverse(sk_c5) = sk_c6 ),
prove_this_42 ).
cnf(c_0_108,negated_conjecture,
( sk_c4 = sk_c12
| multiply(X1,sk_c12) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| inverse(X1) != sk_c11
| inverse(X2) != sk_c12 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_84]),c_0_30]),c_0_30]),c_0_92]),c_0_101]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c6,sk_c12) = sk_c6 ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_110,negated_conjecture,
( inverse(sk_c12) = sk_c3
| sk_c7 != sk_c3 ),
inference(ef,[status(thm)],[c_0_73]) ).
cnf(c_0_111,negated_conjecture,
( sk_c4 = sk_c12
| multiply(X1,sk_c11) != sk_c12
| inverse(X1) != sk_c12
| identity != sk_c11 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_29]),c_0_58]),c_0_101]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c5,multiply(sk_c6,X1)) = multiply(sk_c12,X1)
| multiply(sk_c3,sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_28,c_0_104]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| identity = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_109]),c_0_29]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c3,sk_c12) = identity
| sk_c7 != sk_c3 ),
inference(spm,[status(thm)],[c_0_29,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
( sk_c4 = sk_c12
| identity != sk_c11 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_84]),c_0_30]),c_0_92]),c_0_101]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c7,sk_c11) = sk_c12 ),
prove_this_35 ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c5,sk_c6) = multiply(sk_c12,sk_c12)
| multiply(sk_c3,sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_112,c_0_109]) ).
cnf(c_0_118,negated_conjecture,
( identity = sk_c12
| identity = sk_c4
| sk_c7 != sk_c3 ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_119,negated_conjecture,
sk_c4 = sk_c12,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_92]),c_0_101]) ).
cnf(c_0_120,negated_conjecture,
( multiply(inverse(sk_c7),sk_c12) = sk_c11
| multiply(sk_c12,sk_c4) = sk_c11 ),
inference(spm,[status(thm)],[c_0_31,c_0_116]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| inverse(sk_c7) = sk_c12 ),
prove_this_34 ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c12,sk_c12) = sk_c12 ),
inference(spm,[status(thm)],[c_0_104,c_0_117]) ).
cnf(c_0_123,negated_conjecture,
( identity = sk_c12
| sk_c7 != sk_c3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119])]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c12,sk_c4) = sk_c11
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_125,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c5) = sk_c6 ),
prove_this_52 ).
cnf(c_0_126,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c8) = sk_c9 ),
prove_this_57 ).
cnf(c_0_127,negated_conjecture,
( multiply(inverse(sk_c3),sk_c4) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c12 ),
inference(spm,[status(thm)],[c_0_31,c_0_122]) ).
cnf(c_0_128,negated_conjecture,
( inverse(sk_c12) = sk_c12
| sk_c7 != sk_c3 ),
inference(spm,[status(thm)],[c_0_84,c_0_123]) ).
cnf(c_0_129,negated_conjecture,
multiply(sk_c12,sk_c12) = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_119])]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c6,sk_c5) = identity
| inverse(sk_c3) = sk_c12 ),
inference(spm,[status(thm)],[c_0_29,c_0_125]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c9,sk_c8) = identity
| inverse(sk_c3) = sk_c12 ),
inference(spm,[status(thm)],[c_0_29,c_0_126]) ).
cnf(c_0_132,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c5,sk_c6) = sk_c12 ),
prove_this_51 ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c12
| multiply(sk_c12,sk_c4) = sk_c12
| inverse(sk_c12) = sk_c7 ),
inference(spm,[status(thm)],[c_0_127,c_0_66]) ).
cnf(c_0_134,negated_conjecture,
( identity = sk_c11
| sk_c7 != sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_128]),c_0_129]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c12,multiply(sk_c3,X1)) = X1
| multiply(sk_c6,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_130]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c12
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_119]),c_0_129]) ).
cnf(c_0_137,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c8,sk_c9) = sk_c11 ),
prove_this_56 ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c12,multiply(sk_c3,X1)) = X1
| multiply(sk_c9,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_131]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c12
| inverse(sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_58,c_0_132]) ).
cnf(c_0_140,negated_conjecture,
( inverse(sk_c12) = sk_c7
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_119])]),c_0_129]) ).
cnf(c_0_141,negated_conjecture,
( sk_c11 = sk_c12
| sk_c7 != sk_c3 ),
inference(spm,[status(thm)],[c_0_123,c_0_134]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c6,sk_c5) = identity
| sk_c11 = sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_129])]) ).
cnf(c_0_143,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| inverse(sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_58,c_0_137]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c9,sk_c8) = identity
| sk_c11 = sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_136]),c_0_129])]) ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c12
| sk_c11 = sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]) ).
cnf(c_0_146,negated_conjecture,
( inverse(sk_c6) = sk_c5
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_142]),c_0_50]) ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| sk_c11 = sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_140]),c_0_141]) ).
cnf(c_0_148,negated_conjecture,
( inverse(sk_c9) = sk_c8
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_144]),c_0_50]) ).
cnf(c_0_149,negated_conjecture,
( multiply(inverse(sk_c5),sk_c12) = sk_c6
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_31,c_0_145]) ).
cnf(c_0_150,negated_conjecture,
( inverse(sk_c5) = sk_c6
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_58,c_0_146]) ).
cnf(c_0_151,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c9
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_31,c_0_147]) ).
cnf(c_0_152,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_58,c_0_148]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c6,sk_c12) = sk_c6
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c9
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_155,negated_conjecture,
( sk_c11 = sk_c12
| identity = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_153]),c_0_29]) ).
cnf(c_0_156,negated_conjecture,
( sk_c11 = sk_c12
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_154]),c_0_29]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_43 ).
cnf(c_0_158,negated_conjecture,
multiply(inverse(sk_c12),sk_c11) = sk_c12,
inference(spm,[status(thm)],[c_0_31,c_0_129]) ).
cnf(c_0_159,negated_conjecture,
sk_c11 = sk_c12,
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_160,negated_conjecture,
( multiply(inverse(sk_c6),sk_c12) = sk_c11
| multiply(sk_c3,sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_31,c_0_157]) ).
cnf(c_0_161,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| inverse(sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_58,c_0_107]) ).
cnf(c_0_162,negated_conjecture,
identity = sk_c12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_159]),c_0_29]) ).
cnf(c_0_163,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c10) = sk_c11 ),
prove_this_59 ).
cnf(c_0_164,negated_conjecture,
( multiply(sk_c5,sk_c12) = multiply(sk_c12,sk_c11)
| multiply(sk_c3,sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_112,c_0_157]) ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c5,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_166,negated_conjecture,
( inverse(sk_c12) = sk_c3
| inverse(sk_c7) = sk_c12 ),
inference(spm,[status(thm)],[c_0_58,c_0_73]) ).
cnf(c_0_167,plain,
inverse(sk_c12) = sk_c12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_162]),c_0_162]) ).
cnf(c_0_168,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_58,c_0_163]) ).
cnf(c_0_169,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(inverse(X1),sk_c12) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(sk_c12,sk_c11) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| inverse(inverse(sk_c7)) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| multiply(X5,sk_c11) != sk_c12
| inverse(X4) != sk_c11
| inverse(X5) != sk_c12 ),
inference(spm,[status(thm)],[c_0_67,c_0_54]) ).
cnf(c_0_170,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(sk_c12,sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_171,plain,
multiply(inverse(X1),X1) = sk_c12,
inference(rw,[status(thm)],[c_0_29,c_0_162]) ).
cnf(c_0_172,negated_conjecture,
( inverse(sk_c7) = sk_c12
| sk_c3 = sk_c12 ),
inference(rw,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_173,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_58,c_0_168]) ).
cnf(c_0_174,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c4
| multiply(inverse(X1),sk_c12) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| multiply(X5,sk_c11) != sk_c12
| inverse(X4) != sk_c11
| inverse(X5) != sk_c12
| sk_c7 != sk_c12 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_58]),c_0_170]) ).
cnf(c_0_175,plain,
multiply(X1,sk_c12) = X1,
inference(rw,[status(thm)],[c_0_50,c_0_162]) ).
cnf(c_0_176,plain,
multiply(X1,inverse(X1)) = sk_c12,
inference(spm,[status(thm)],[c_0_171,c_0_58]) ).
cnf(c_0_177,negated_conjecture,
( sk_c3 = sk_c12
| sk_c7 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_172]),c_0_167]) ).
cnf(c_0_178,negated_conjecture,
( inverse(sk_c12) = sk_c3
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_58,c_0_173]) ).
cnf(c_0_179,negated_conjecture,
( multiply(sk_c12,X1) = X1
| sk_c7 != sk_c3 ),
inference(spm,[status(thm)],[c_0_30,c_0_123]) ).
cnf(c_0_180,negated_conjecture,
( sk_c3 = sk_c12
| inverse(X1) != sk_c12
| inverse(X2) != sk_c12
| inverse(X3) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[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(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_174,c_0_119]),c_0_175]),c_0_175]),c_0_159]),c_0_159]),c_0_175]),c_0_159]),c_0_175]),c_0_176]),c_0_159]),c_0_176]),c_0_176]),c_0_175]),c_0_159]),c_0_159]),c_0_175]),c_0_159])]),c_0_177])])]),c_0_167])]) ).
cnf(c_0_181,negated_conjecture,
( inverse(sk_c10) = sk_c12
| sk_c3 = sk_c12 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_178,c_0_159]),c_0_167]) ).
cnf(c_0_182,negated_conjecture,
( multiply(X1,sk_c11) = X1
| sk_c7 != sk_c3 ),
inference(spm,[status(thm)],[c_0_50,c_0_134]) ).
cnf(c_0_183,negated_conjecture,
( multiply(inverse(sk_c12),X1) = X1
| sk_c7 != sk_c3 ),
inference(spm,[status(thm)],[c_0_31,c_0_179]) ).
cnf(c_0_184,negated_conjecture,
( sk_c3 = sk_c12
| inverse(X1) != sk_c12
| inverse(X2) != sk_c12 ),
inference(spm,[status(thm)],[c_0_180,c_0_181]) ).
cnf(c_0_185,negated_conjecture,
( inverse(sk_c12) = sk_c11
| sk_c7 != sk_c3 ),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_186,negated_conjecture,
( sk_c3 = sk_c12
| inverse(X1) != sk_c12 ),
inference(spm,[status(thm)],[c_0_184,c_0_181]) ).
cnf(c_0_187,negated_conjecture,
( inverse(sk_c12) = sk_c12
| sk_c7 != sk_c3 ),
inference(rw,[status(thm)],[c_0_185,c_0_159]) ).
cnf(c_0_188,negated_conjecture,
sk_c3 = sk_c12,
inference(spm,[status(thm)],[c_0_186,c_0_181]) ).
cnf(c_0_189,negated_conjecture,
( inverse(sk_c12) = sk_c12
| sk_c7 != sk_c12 ),
inference(rw,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_190,negated_conjecture,
( inverse(X1) != sk_c12
| inverse(X2) != sk_c12
| inverse(X3) != sk_c12 ),
inference(cn,[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(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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_129])]),c_0_175]),c_0_159]),c_0_159]),c_0_175]),c_0_159]),c_0_175]),c_0_176]),c_0_159]),c_0_176]),c_0_176]),c_0_175]),c_0_159]),c_0_159]),c_0_175]),c_0_159]),c_0_162])])])]),c_0_167])]) ).
cnf(c_0_191,negated_conjecture,
inverse(sk_c12) = sk_c12,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_159]),c_0_175]),c_0_188]),c_0_189]) ).
cnf(c_0_192,negated_conjecture,
( inverse(X1) != sk_c12
| inverse(X2) != sk_c12 ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_193,negated_conjecture,
inverse(X1) != sk_c12,
inference(spm,[status(thm)],[c_0_192,c_0_191]) ).
cnf(c_0_194,plain,
$false,
inference(sr,[status(thm)],[c_0_167,c_0_193]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP208-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n020.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 18:29:05 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 4.57/3.37 % Version : CSE_E---1.7
% 4.57/3.37 % Problem : theBenchmark.p
% 4.57/3.37 % SZS status Unsatisfiable for theBenchmark.p
% 4.57/3.37 % SZS output start CNFRefutation
% See solution above
% 4.57/3.39 % Total time : 2.370s
%------------------------------------------------------------------------------