%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP318-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:39:16 PM UTC 2026
% Result : Unsatisfiable 5.44s 1.18s
% Output : CNFRefutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 39
% Syntax : Number of clauses : 211 ( 23 unt; 171 nHn; 186 RR)
% Number of literals : 507 ( 506 equ; 131 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 : 99 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_48,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_61,negated_conjecture,
( multiply(X8,X7) != X9
| inverse(X9) != X7
| inverse(X8) != X9
| multiply(X7,sk_c11) != sk_c12
| inverse(X6) != X7
| multiply(X6,X7) != sk_c12
| inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| inverse(X3) != sk_c12
| multiply(X3,sk_c12) != X2
| multiply(sk_c12,X2) != sk_c11
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c12
| multiply(sk_c11,sk_c12) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_29,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_49,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_58,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_58) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_38,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_59,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_59) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_40,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_52,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
cnf(prove_this_42,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_51,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(c_0_39,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_40,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_41,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_42,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_43,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_42]) ).
cnf(c_0_44,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_40]),c_0_43]) ).
cnf(c_0_45,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_44]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c11) = sk_c12 ),
prove_this_18 ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
prove_this_19 ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c11 ),
prove_this_28 ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c12) = sk_c3 ),
prove_this_48 ).
cnf(c_0_51,negated_conjecture,
( multiply(X8,X7) != X9
| inverse(X9) != X7
| inverse(X8) != X9
| multiply(X7,sk_c11) != sk_c12
| inverse(X6) != X7
| multiply(X6,X7) != sk_c12
| inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| inverse(X3) != sk_c12
| multiply(X3,sk_c12) != X2
| multiply(sk_c12,X2) != sk_c11
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c12
| multiply(sk_c11,sk_c12) != sk_c10 ),
inference(fof_simplification,[status(thm)],[prove_this_61]) ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c11,sk_c12) = sk_c10 ),
prove_this_8 ).
cnf(c_0_53,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c11 ),
prove_this_29 ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c2,sk_c12) = sk_c3 ),
prove_this_49 ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_45,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c12 ),
prove_this_58 ).
cnf(c_0_59,negated_conjecture,
( multiply(X8,X7) != X9
| inverse(X9) != X7
| inverse(X8) != X9
| multiply(X7,sk_c11) != sk_c12
| inverse(X6) != X7
| multiply(X6,X7) != sk_c12
| inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| inverse(X3) != sk_c12
| multiply(X3,sk_c12) != X2
| multiply(sk_c12,X2) != sk_c11
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c12
| multiply(sk_c11,sk_c12) != sk_c10 ),
c_0_51 ).
cnf(c_0_60,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
prove_this_9 ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_45,c_0_52]) ).
cnf(c_0_62,negated_conjecture,
( sk_c8 = sk_c9
| multiply(inverse(sk_c1),sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_53]) ).
cnf(c_0_63,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c12,sk_c3) = sk_c11 ),
prove_this_38 ).
cnf(c_0_65,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_66,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c2) = sk_c12 ),
prove_this_59 ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c12 ),
inference(spm,[status(thm)],[c_0_45,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X1) != sk_c12
| inverse(X5) != sk_c12
| inverse(X4) != sk_c11
| multiply(X6,sk_c11) != sk_c12
| multiply(X5,sk_c12) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,inverse(X3)) != sk_c12
| multiply(sk_c11,sk_c12) != sk_c10
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c11) != sk_c12
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_59])])]) ).
cnf(c_0_69,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_41]) ).
cnf(c_0_71,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c11,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
prove_this_39 ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
( sk_c8 = sk_c9
| multiply(inverse(sk_c2),sk_c3) = sk_c12 ),
inference(spm,[status(thm)],[c_0_42,c_0_65]) ).
cnf(c_0_75,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c2) = sk_c12 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X1) != sk_c12
| inverse(X5) != sk_c12
| inverse(X4) != sk_c11
| multiply(X6,sk_c11) != sk_c12
| multiply(X5,sk_c12) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c11) != sk_c12
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_77,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_70,c_0_44]) ).
cnf(c_0_78,negated_conjecture,
( sk_c10 = sk_c11
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_69,c_0_71]) ).
cnf(c_0_79,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_80,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c12,sk_c3) = sk_c12 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_81,negated_conjecture,
( identity != sk_c11
| inverse(X5) != sk_c11
| inverse(X1) != sk_c12
| inverse(X4) != sk_c12
| multiply(X5,sk_c11) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c11) != sk_c12
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| sk_c8 = sk_c9 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_41]),c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( identity = sk_c12
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_71]),c_0_40]) ).
cnf(c_0_83,negated_conjecture,
( sk_c11 = sk_c12
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X1) != sk_c12
| inverse(X4) != sk_c12
| multiply(X5,sk_c11) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c11) != sk_c12
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| sk_c8 = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_85,negated_conjecture,
( identity != sk_c11
| inverse(X4) != sk_c11
| inverse(X1) != sk_c12
| multiply(X4,sk_c11) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c11) != sk_c12
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_45])]),c_0_40]) ).
cnf(c_0_86,negated_conjecture,
( inverse(X4) != sk_c11
| inverse(X1) != sk_c12
| multiply(X4,sk_c11) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c11) != sk_c12
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| sk_c8 = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_82]),c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c12
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X2),sk_c11) != sk_c12
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| sk_c8 = sk_c9 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_45])]),c_0_40]),c_0_44]),c_0_83]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c11 ),
prove_this_30 ).
cnf(c_0_89,negated_conjecture,
( multiply(X2,inverse(X2)) != sk_c12
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X2),sk_c11) != sk_c12
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| sk_c8 = sk_c9 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_45])]),c_0_40]),c_0_82]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_40,c_0_88]) ).
cnf(c_0_91,negated_conjecture,
( inverse(X1) != X1
| inverse(X1) != identity
| sk_c8 = sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_77]),c_0_44]),c_0_41]),c_0_44]),c_0_44]),c_0_82]),c_0_83]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c11 ),
prove_this_26 ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c11 ),
prove_this_25 ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(inverse(sk_c8),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_90]) ).
cnf(c_0_95,negated_conjecture,
sk_c8 = sk_c9,
inference(spm,[status(thm)],[c_0_91,c_0_77]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c9) = sk_c6
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c6,sk_c9) = sk_c12 ),
inference(spm,[status(thm)],[c_0_40,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
prove_this_17 ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(inverse(sk_c9),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( inverse(sk_c9) = sk_c6
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_40,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c6,multiply(sk_c9,X1)) = multiply(sk_c12,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_97]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c7
| multiply(sk_c11,sk_c1) = identity ),
inference(rw,[status(thm)],[c_0_90,c_0_95]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(inverse(sk_c1),sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_98]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
prove_this_15 ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c6,sk_c7) = multiply(sk_c12,sk_c9) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c12,sk_c3) = sk_c11 ),
prove_this_40 ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
prove_this_35 ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(inverse(inverse(sk_c1)),sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_42,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c11 ),
prove_this_27 ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(inverse(sk_c6),sk_c12) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_104]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c12,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(inverse(sk_c8),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_107]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(inverse(sk_c6),sk_c12) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_108]) ).
cnf(c_0_115,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
prove_this_36 ).
cnf(c_0_116,negated_conjecture,
( identity = sk_c12
| multiply(sk_c9,sk_c11) = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_40]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(inverse(inverse(sk_c6)),sk_c9) = sk_c12 ),
inference(spm,[status(thm)],[c_0_42,c_0_111]) ).
cnf(c_0_118,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
prove_this_16 ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c11) = sk_c1
| multiply(sk_c12,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_112]),c_0_44]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(inverse(sk_c8),multiply(sk_c7,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_113]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c7,sk_c8) = identity
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_40,c_0_64]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
prove_this_37 ).
cnf(c_0_123,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c8,multiply(sk_c9,X1)) = multiply(sk_c7,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_107]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c9,sk_c12) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_125,negated_conjecture,
( identity = sk_c12
| multiply(inverse(sk_c9),sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_116]) ).
cnf(c_0_126,negated_conjecture,
( identity = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_40]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| multiply(sk_c12,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_40,c_0_119]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c8) = multiply(sk_c9,sk_c8) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_44]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(inverse(sk_c9),sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_122]) ).
cnf(c_0_130,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_72]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c8,sk_c9) = multiply(sk_c7,sk_c12) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_132,negated_conjecture,
( identity = sk_c12
| multiply(inverse(sk_c9),multiply(sk_c12,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_125]) ).
cnf(c_0_133,negated_conjecture,
( identity = sk_c12
| multiply(sk_c12,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c9) = multiply(sk_c9,sk_c9) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_95]),c_0_95]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c7,sk_c12) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c7,sk_c12) = multiply(sk_c9,sk_c9) ),
inference(rw,[status(thm)],[c_0_131,c_0_95]) ).
cnf(c_0_137,negated_conjecture,
( identity = sk_c12
| multiply(sk_c11,sk_c9) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_40]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c11,sk_c12) = sk_c10 ),
prove_this_10 ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
prove_this_5 ).
cnf(c_0_140,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
prove_this_32 ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(multiply(sk_c9,sk_c9)) = sk_c9 ),
inference(spm,[status(thm)],[c_0_45,c_0_134]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c9,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_143,negated_conjecture,
( identity = sk_c12
| inverse(sk_c11) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_137]),c_0_44]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(inverse(sk_c8),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_138]) ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(inverse(sk_c6),sk_c12) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_139]) ).
cnf(c_0_146,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
prove_this_6 ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(inverse(sk_c9),multiply(sk_c12,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_129]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c12,sk_c4) = identity
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_40,c_0_140]) ).
cnf(c_0_149,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_150,negated_conjecture,
( identity = sk_c12
| multiply(sk_c9,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_40,c_0_143]) ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(inverse(sk_c8),multiply(sk_c7,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_144]) ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c7,sk_c8) = identity
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_52]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
prove_this_7 ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c8,multiply(sk_c9,X1)) = multiply(sk_c7,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_138]) ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c9,sk_c12) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_156,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c12 ),
prove_this_52 ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c9) = multiply(sk_c11,sk_c4) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_44]) ).
cnf(c_0_158,negated_conjecture,
( inverse(sk_c9) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_149]) ).
cnf(c_0_159,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
prove_this_42 ).
cnf(c_0_160,negated_conjecture,
identity = sk_c12,
inference(spm,[status(thm)],[c_0_116,c_0_150]) ).
cnf(c_0_161,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(sk_c8) = multiply(sk_c9,sk_c8) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_44]) ).
cnf(c_0_162,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(inverse(sk_c9),sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_153]) ).
cnf(c_0_163,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_45,c_0_60]) ).
cnf(c_0_164,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c8,sk_c9) = multiply(sk_c7,sk_c12) ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_165,negated_conjecture,
( inverse(sk_c12) = sk_c4
| inverse(sk_c2) = sk_c12 ),
inference(spm,[status(thm)],[c_0_45,c_0_156]) ).
cnf(c_0_166,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c12 ),
prove_this_51 ).
cnf(c_0_167,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c11,sk_c4) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_169,negated_conjecture,
( inverse(sk_c12) = sk_c4
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_45,c_0_159]) ).
cnf(c_0_170,plain,
multiply(X1,sk_c12) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_160]) ).
cnf(c_0_171,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c11,sk_c12) = sk_c10 ),
prove_this_3 ).
cnf(c_0_172,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(sk_c9) = multiply(sk_c9,sk_c9) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_95]),c_0_95]) ).
cnf(c_0_173,negated_conjecture,
( multiply(sk_c7,sk_c12) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_174,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c7,sk_c12) = multiply(sk_c9,sk_c9) ),
inference(rw,[status(thm)],[c_0_164,c_0_95]) ).
cnf(c_0_175,negated_conjecture,
( inverse(sk_c12) = sk_c2
| inverse(sk_c12) = sk_c4 ),
inference(spm,[status(thm)],[c_0_45,c_0_165]) ).
cnf(c_0_176,negated_conjecture,
( inverse(sk_c12) = sk_c2
| multiply(sk_c4,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_166]) ).
cnf(c_0_177,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
prove_this_31 ).
cnf(c_0_178,negated_conjecture,
( multiply(sk_c4,X1) = X1
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_42]) ).
cnf(c_0_179,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c12) = sk_c3 ),
prove_this_41 ).
cnf(c_0_180,plain,
inverse(sk_c12) = sk_c12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_160]),c_0_160]) ).
cnf(c_0_181,negated_conjecture,
( sk_c3 = sk_c2
| inverse(sk_c12) = sk_c4 ),
inference(rw,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_182,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(inverse(sk_c5),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_171]) ).
cnf(c_0_183,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
prove_this_4 ).
cnf(c_0_184,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(multiply(sk_c9,sk_c9)) = sk_c9 ),
inference(spm,[status(thm)],[c_0_45,c_0_172]) ).
cnf(c_0_185,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c9,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_186,negated_conjecture,
( sk_c4 != sk_c2
| inverse(sk_c12) = sk_c2 ),
inference(ef,[status(thm)],[c_0_175]) ).
cnf(c_0_187,negated_conjecture,
( sk_c4 = sk_c11
| inverse(sk_c12) = sk_c2 ),
inference(rw,[status(thm)],[c_0_176,c_0_170]) ).
cnf(c_0_188,negated_conjecture,
( sk_c11 = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_189,plain,
multiply(sk_c12,X1) = X1,
inference(rw,[status(thm)],[c_0_41,c_0_160]) ).
cnf(c_0_190,negated_conjecture,
( sk_c4 = sk_c11
| sk_c3 = sk_c2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_170]),c_0_170]) ).
cnf(c_0_191,negated_conjecture,
( sk_c4 = sk_c12
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_180,c_0_181]) ).
cnf(c_0_192,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c9,multiply(sk_c11,X1)) = multiply(sk_c12,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_153]) ).
cnf(c_0_193,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_194,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_195,negated_conjecture,
( sk_c4 != sk_c2
| sk_c2 = sk_c12 ),
inference(rw,[status(thm)],[c_0_186,c_0_180]) ).
cnf(c_0_196,negated_conjecture,
( sk_c2 = sk_c12
| sk_c4 = sk_c11 ),
inference(spm,[status(thm)],[c_0_180,c_0_187]) ).
cnf(c_0_197,negated_conjecture,
( sk_c3 = sk_c11
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_198,negated_conjecture,
( sk_c3 = sk_c2
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_199,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c9,sk_c11) = multiply(sk_c12,sk_c10) ),
inference(spm,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_200,negated_conjecture,
( multiply(sk_c9,sk_c11) = identity
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_194]) ).
cnf(c_0_201,negated_conjecture,
( sk_c2 != sk_c11
| sk_c2 = sk_c12 ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_202,negated_conjecture,
( sk_c11 = sk_c12
| sk_c2 = sk_c11 ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_203,negated_conjecture,
( multiply(sk_c12,sk_c10) = identity
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_204,negated_conjecture,
sk_c11 = sk_c12,
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_205,plain,
multiply(inverse(X1),X1) = sk_c12,
inference(rw,[status(thm)],[c_0_40,c_0_160]) ).
cnf(c_0_206,negated_conjecture,
sk_c10 = sk_c12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_203,c_0_160]),c_0_170]),c_0_189]),c_0_204])]) ).
cnf(c_0_207,plain,
multiply(X1,inverse(X1)) = sk_c12,
inference(spm,[status(thm)],[c_0_205,c_0_45]) ).
cnf(c_0_208,negated_conjecture,
( inverse(X2) != sk_c12
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
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)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_170]),c_0_170]),c_0_170])]),c_0_189]),c_0_204]),c_0_204]),c_0_170]),c_0_206]),c_0_204]),c_0_207]),c_0_204]),c_0_170]),c_0_206]),c_0_204]),c_0_170]),c_0_204]),c_0_204]),c_0_180]),c_0_204])])])])]),c_0_180])]) ).
cnf(c_0_209,negated_conjecture,
( inverse(X1) != X1
| inverse(X1) != sk_c12 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_180]),c_0_170]),c_0_170]) ).
cnf(c_0_210,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_209,c_0_180]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP318-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:08:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.44/1.18 % Version: 3.5.1
% 5.44/1.18 % Preprocessing class: FSMSSMSMSSSNFFN.
% 5.44/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.44/1.18 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 5.44/1.18 % Starting new_bool_3 with 300s (1) cores
% 5.44/1.18 % Starting new_bool_1 with 300s (1) cores
% 5.44/1.18 % Starting sh5l with 300s (1) cores
% 5.44/1.18 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3306167 completed with status 0
% 5.44/1.18 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 5.44/1.18 % Preprocessing class: FSMSSMSMSSSNFFN.
% 5.44/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.44/1.18 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 5.44/1.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.44/1.18 % No SInE strategy applied
% 5.44/1.18 % Search class: FGHPS-FFMM21-SFFFFFNN
% 5.44/1.18 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.44/1.18 % Starting SubtermCWHack with 136s (1) cores
% 5.44/1.18 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 5.44/1.18 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 5.44/1.18 % Starting new_bool_3 with 136s (1) cores
% 5.44/1.18 % Starting new_bool_1 with 136s (1) cores
% 5.44/1.18 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3306172 completed with status 0
% 5.44/1.18 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 5.44/1.18 % Preprocessing class: FSMSSMSMSSSNFFN.
% 5.44/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.44/1.18 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 5.44/1.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.44/1.18 % No SInE strategy applied
% 5.44/1.18 % Search class: FGHPS-FFMM21-SFFFFFNN
% 5.44/1.18 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.44/1.18 % Starting SubtermCWHack with 136s (1) cores
% 5.44/1.18 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 5.44/1.18 % Preprocessing time : 0.001 s
% 5.44/1.18 % Presaturation interreduction done
% 5.44/1.18
% 5.44/1.18 % Proof found!
% 5.44/1.18 % SZS status Unsatisfiable
% 5.44/1.18 % SZS output start CNFRefutation
% See solution above
% 5.44/1.19 % Parsed axioms : 64
% 5.44/1.19 % Removed by relevancy pruning/SinE : 0
% 5.44/1.19 % Initial clauses : 64
% 5.44/1.19 % Removed in clause preprocessing : 0
% 5.44/1.19 % Initial clauses in saturation : 64
% 5.44/1.19 % Processed clauses : 14860
% 5.44/1.19 % ...of these trivial : 420
% 5.44/1.19 % ...subsumed : 11701
% 5.44/1.19 % ...remaining for further processing : 2739
% 5.44/1.19 % Other redundant clauses eliminated : 46
% 5.44/1.19 % Clauses deleted for lack of memory : 0
% 5.44/1.19 % Backward-subsumed : 157
% 5.44/1.19 % Backward-rewritten : 1969
% 5.44/1.19 % Generated clauses : 76884
% 5.44/1.19 % ...of the previous two non-redundant : 77635
% 5.44/1.19 % ...aggressively subsumed : 0
% 5.44/1.19 % Contextual simplify-reflections : 21
% 5.44/1.19 % Paramodulations : 76826
% 5.44/1.19 % Factorizations : 27
% 5.44/1.19 % NegExts : 0
% 5.44/1.19 % Equation resolutions : 46
% 5.44/1.19 % Disequality decompositions : 0
% 5.44/1.19 % Total rewrite steps : 18224
% 5.44/1.19 % ...of those cached : 17602
% 5.44/1.19 % Propositional unsat checks : 0
% 5.44/1.19 % Propositional check models : 0
% 5.44/1.19 % Propositional check unsatisfiable : 0
% 5.44/1.19 % Propositional clauses : 0
% 5.44/1.19 % Propositional clauses after purity: 0
% 5.44/1.19 % Propositional unsat core size : 0
% 5.44/1.19 % Propositional preprocessing time : 0.000
% 5.44/1.19 % Propositional encoding time : 0.000
% 5.44/1.19 % Propositional solver time : 0.000
% 5.44/1.19 % Success case prop preproc time : 0.000
% 5.44/1.19 % Success case prop encoding time : 0.000
% 5.44/1.19 % Success case prop solver time : 0.000
% 5.44/1.19 % Current number of processed clauses : 542
% 5.44/1.19 % Positive orientable unit clauses : 13
% 5.44/1.19 % Positive unorientable unit clauses: 0
% 5.44/1.19 % Negative unit clauses : 0
% 5.44/1.19 % Non-unit-clauses : 529
% 5.44/1.19 % Current number of unprocessed clauses: 60921
% 5.44/1.19 % ...number of literals in the above : 262636
% 5.44/1.19 % Current number of archived formulas : 0
% 5.44/1.19 % Current number of archived clauses : 2190
% 5.44/1.19 % Clause-clause subsumption calls (NU) : 397273
% 5.44/1.19 % Rec. Clause-clause subsumption calls : 187996
% 5.44/1.19 % Non-unit clause-clause subsumptions : 11865
% 5.44/1.19 % Unit Clause-clause subsumption calls : 3041
% 5.44/1.19 % Rewrite failures with RHS unbound : 0
% 5.44/1.19 % BW rewrite match attempts : 66
% 5.44/1.19 % BW rewrite match successes : 57
% 5.44/1.19 % Condensation attempts : 0
% 5.44/1.19 % Condensation successes : 0
% 5.44/1.19 % Termbank termtop insertions : 968044
% 5.44/1.19 % Search garbage collected termcells : 46
% 5.44/1.19
% 5.44/1.19 % -------------------------------------------------
% 5.44/1.19 % User time : 0.711 s
% 5.44/1.19 % System time : 0.033 s
% 5.44/1.19 % Total time : 0.744 s
% 5.44/1.19 % Maximum resident set size: 3664 pages
% 5.44/1.19
% 5.44/1.19 % -------------------------------------------------
% 5.44/1.19 % User time : 3.310 s
% 5.44/1.19 % System time : 0.147 s
% 5.44/1.19 % Total time : 3.457 s
% 5.44/1.19 % Maximum resident set size: 4608 pages
% 5.44/1.19 % E exiting
%------------------------------------------------------------------------------