%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP380-1 : 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 : n028.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 04:25:59 PM UTC 2026
% Result : Unsatisfiable 58.68s 34.96s
% Output : CNFRefutation 58.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 37
% Syntax : Number of clauses : 275 ( 39 unt; 203 nHn; 233 RR)
% Number of literals : 625 ( 624 equ; 149 neg)
% Maximal clause size : 15 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 117 ( 8 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(prove_this_15,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
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_17,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_43,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_44,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_51,negated_conjecture,
( inverse(sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c9) != sk_c10
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_50,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
cnf(prove_this_37,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_47,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_49,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(c_0_37,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_15 ).
cnf(c_0_39,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_40,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c11,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_17 ).
cnf(c_0_43,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_39]),c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_11 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c5,sk_c11) = multiply(sk_c11,sk_c10)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_12 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_13 ).
cnf(c_0_49,negated_conjecture,
( multiply(inverse(sk_c5),multiply(sk_c11,sk_c10)) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c10 ),
prove_this_14 ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c6 ),
prove_this_20 ).
cnf(c_0_54,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_38]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_16 ).
cnf(c_0_56,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c7,multiply(sk_c8,X1)) = multiply(sk_c6,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_37,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_56,c_0_55]) ).
cnf(c_0_61,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_43,c_0_43]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| sk_c11 != sk_c10 ),
inference(ef,[status(thm)],[c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c7,sk_c8) = multiply(sk_c6,sk_c11)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c7,sk_c11) = multiply(sk_c6,sk_c10)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_58,c_0_42]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c7,sk_c11) = multiply(sk_c6,sk_c11)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_58,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_19 ).
cnf(c_0_67,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( identity = sk_c9
| sk_c11 != sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_62]),c_0_39]) ).
cnf(c_0_69,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_70,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_60]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_45 ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_3 ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_53,c_0_63]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c6,sk_c11) = multiply(sk_c6,sk_c10)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c8,multiply(sk_c6,X1)) = X1
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_66]) ).
cnf(c_0_76,negated_conjecture,
( multiply(X1,sk_c9) = X1
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_23 ).
cnf(c_0_79,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
prove_this_46 ).
cnf(c_0_81,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_67]),c_0_67]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
prove_this_36 ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_72]) ).
cnf(c_0_84,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_43,c_0_37]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c6 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c6) = sk_c11 ),
inference(spm,[status(thm)],[c_0_75,c_0_73]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c6) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_88,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_78]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_24 ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_43 ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_93,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c10,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_43,c_0_83]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_4 ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c10,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_43]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_98,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_90]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_44 ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_91]),c_0_39]) ).
cnf(c_0_101,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_35 ).
cnf(c_0_102,negated_conjecture,
( inverse(sk_c8) = sk_c5
| inverse(sk_c2) = sk_c1 ),
inference(spm,[status(thm)],[c_0_81,c_0_92]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c10,sk_c11) = identity
| multiply(sk_c10,sk_c9) = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_104,negated_conjecture,
multiply(sk_c10,sk_c9) = sk_c11,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_95]),c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c1,multiply(sk_c2,X1)) = multiply(sk_c10,X1)
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_37,c_0_97]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_107,negated_conjecture,
( multiply(inverse(sk_c2),sk_c10) = sk_c9
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_100]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c1 ),
inference(spm,[status(thm)],[c_0_81,c_0_101]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c2) = sk_c1 ),
inference(spm,[status(thm)],[c_0_39,c_0_102]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c10,sk_c11) = identity
| inverse(sk_c11) = sk_c10
| sk_c11 = sk_c10 ),
inference(rw,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c1,multiply(sk_c2,X1)) = multiply(sk_c10,X1)
| sk_c11 = sk_c10 ),
inference(rw,[status(thm)],[c_0_105,c_0_104]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| sk_c11 = sk_c10 ),
inference(rw,[status(thm)],[c_0_106,c_0_104]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_107,c_0_109]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_22 ).
cnf(c_0_116,plain,
inverse(multiply(inverse(multiply(X1,X2)),X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_39]),c_0_67]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c10,sk_c11) = identity
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_39,c_0_110]) ).
cnf(c_0_118,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_40]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| sk_c11 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_104]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_115]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_42 ).
cnf(c_0_123,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c11 ),
prove_this_32 ).
cnf(c_0_124,negated_conjecture,
inverse(multiply(inverse(sk_c11),sk_c10)) = sk_c9,
inference(spm,[status(thm)],[c_0_116,c_0_104]) ).
cnf(c_0_125,negated_conjecture,
( inverse(sk_c10) = sk_c11
| sk_c11 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_117]),c_0_67]) ).
cnf(c_0_126,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_118,c_0_67]) ).
cnf(c_0_127,negated_conjecture,
( identity = sk_c11
| sk_c11 = sk_c10
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_128,negated_conjecture,
( inverse(sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c9) != sk_c10
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
prove_this_51 ).
cnf(c_0_129,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_2 ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c1,multiply(sk_c2,X1)) = multiply(sk_c10,X1)
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_121]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_122]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(sk_c1) = sk_c2 ),
inference(spm,[status(thm)],[c_0_39,c_0_123]) ).
cnf(c_0_133,negated_conjecture,
multiply(inverse(sk_c11),sk_c10) = inverse(sk_c9),
inference(spm,[status(thm)],[c_0_81,c_0_124]) ).
cnf(c_0_134,negated_conjecture,
( inverse(sk_c11) = sk_c10
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_81,c_0_125]) ).
cnf(c_0_135,negated_conjecture,
( inverse(sk_c11) = sk_c11
| sk_c9 = sk_c11
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_136,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_128])])]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_39,c_0_129]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_47]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c1,sk_c10) = multiply(sk_c10,sk_c9)
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_140,negated_conjecture,
( multiply(inverse(sk_c2),sk_c10) = sk_c9
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_43,c_0_131]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(sk_c2) = sk_c1 ),
inference(spm,[status(thm)],[c_0_81,c_0_132]) ).
cnf(c_0_142,negated_conjecture,
multiply(sk_c11,inverse(sk_c9)) = sk_c10,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_133]),c_0_81]) ).
cnf(c_0_143,negated_conjecture,
( sk_c9 = sk_c11
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_144,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_39,c_0_81]) ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138]) ).
cnf(c_0_146,negated_conjecture,
( inverse(sk_c9) = sk_c9
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_126,c_0_68]) ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c9,X1) = X1
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_68]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(rw,[status(thm)],[c_0_139,c_0_104]) ).
cnf(c_0_149,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_150,negated_conjecture,
( sk_c11 = sk_c10
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]) ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(inverse(X2),sk_c9) != sk_c10
| inverse(inverse(X1)) != inverse(X1)
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c10
| inverse(X1) != inverse(identity)
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11 ),
inference(spm,[status(thm)],[c_0_145,c_0_40]) ).
cnf(c_0_152,negated_conjecture,
( multiply(inverse(sk_c1),sk_c10) = sk_c2
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_43,c_0_121]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c9,sk_c9) = identity
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_39,c_0_146]) ).
cnf(c_0_154,negated_conjecture,
( multiply(inverse(X1),multiply(sk_c9,multiply(X1,X2))) = X2
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_84,c_0_147]) ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_156,negated_conjecture,
( inverse(sk_c10) = sk_c10
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_126,c_0_150]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(inverse(identity)) != inverse(identity)
| multiply(inverse(X1),sk_c9) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| inverse(identity) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| sk_c11 != sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_118]),c_0_40]) ).
cnf(c_0_158,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(sk_c2,sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_152,c_0_132]) ).
cnf(c_0_159,negated_conjecture,
( multiply(inverse(multiply(X1,sk_c9)),X1) = sk_c9
| sk_c11 != sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_153]),c_0_67]) ).
cnf(c_0_160,negated_conjecture,
( multiply(inverse(sk_c11),sk_c9) = sk_c3
| sk_c9 = sk_c11
| sk_c11 != sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_67]) ).
cnf(c_0_161,negated_conjecture,
sk_c11 = sk_c10,
inference(spm,[status(thm)],[c_0_125,c_0_156]) ).
cnf(c_0_162,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(inverse(X1),sk_c9) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| identity != sk_c11
| sk_c11 != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_126]),c_0_126]),c_0_126]),c_0_126])]) ).
cnf(c_0_163,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_158]),c_0_39]) ).
cnf(c_0_164,negated_conjecture,
( multiply(inverse(sk_c11),sk_c10) = sk_c9
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_159,c_0_104]) ).
cnf(c_0_165,negated_conjecture,
( multiply(inverse(sk_c10),sk_c9) = sk_c3
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_161]),c_0_161]),c_0_161])]) ).
cnf(c_0_166,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(inverse(X1),sk_c9) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| identity != sk_c11
| sk_c11 != sk_c10 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_144]),c_0_163]) ).
cnf(c_0_167,negated_conjecture,
identity = sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_161]),c_0_39]),c_0_161])]) ).
cnf(c_0_168,negated_conjecture,
multiply(X1,sk_c9) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_161])]) ).
cnf(c_0_169,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_165]),c_0_81]) ).
cnf(c_0_170,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c10) != sk_c10
| inverse(X3) != sk_c10
| inverse(X1) != sk_c10
| inverse(X2) != sk_c10 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_161]),c_0_161]),c_0_161]),c_0_161]),c_0_161])]),c_0_167]),c_0_168]),c_0_167]),c_0_169]) ).
cnf(c_0_171,plain,
multiply(inverse(multiply(X1,inverse(X2))),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_39]),c_0_67]) ).
cnf(c_0_172,negated_conjecture,
inverse(sk_c9) = sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_161])]) ).
cnf(c_0_173,negated_conjecture,
( multiply(sk_c11,multiply(sk_c3,X1)) = X1
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_129]) ).
cnf(c_0_174,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_81,c_0_94]) ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(X1,sk_c10) != sk_c10
| inverse(X2) != sk_c10
| inverse(X1) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_81])]),c_0_172]),c_0_168])]) ).
cnf(c_0_176,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c9
| inverse(sk_c11) = sk_c10
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_173,c_0_76]) ).
cnf(c_0_177,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_81,c_0_174]) ).
cnf(c_0_178,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_179,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(X1) != sk_c10 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_171]),c_0_81])]),c_0_144]),c_0_167]),c_0_169]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(sk_c10) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_176,c_0_161]),c_0_161]),c_0_161])]) ).
cnf(c_0_181,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
prove_this_6 ).
cnf(c_0_182,negated_conjecture,
( inverse(sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
inference(spm,[status(thm)],[c_0_81,c_0_177]) ).
cnf(c_0_183,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_81,c_0_178]) ).
cnf(c_0_184,negated_conjecture,
multiply(sk_c10,sk_c3) = sk_c9,
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_185,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_81,c_0_181]) ).
cnf(c_0_186,negated_conjecture,
( multiply(inverse(sk_c9),X1) = X1
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_147]) ).
cnf(c_0_187,negated_conjecture,
multiply(inverse(sk_c10),sk_c11) = sk_c9,
inference(spm,[status(thm)],[c_0_43,c_0_104]) ).
cnf(c_0_188,negated_conjecture,
( inverse(sk_c10) = sk_c11
| sk_c4 != sk_c11 ),
inference(ef,[status(thm)],[c_0_177]) ).
cnf(c_0_189,negated_conjecture,
( multiply(sk_c10,multiply(sk_c4,X1)) = X1
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_182]) ).
cnf(c_0_190,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c10
| inverse(sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_161]),c_0_161]) ).
cnf(c_0_191,negated_conjecture,
inverse(sk_c10) = sk_c3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_184]),c_0_168]) ).
cnf(c_0_192,negated_conjecture,
( multiply(sk_c5,multiply(sk_c8,X1)) = X1
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_185]) ).
cnf(c_0_193,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_5 ).
cnf(c_0_194,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_27 ).
cnf(c_0_195,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_21 ).
cnf(c_0_196,negated_conjecture,
( multiply(inverse(X1),multiply(inverse(sk_c9),multiply(X1,X2))) = X2
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_84,c_0_186]) ).
cnf(c_0_197,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c9
| sk_c4 != sk_c11 ),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_198,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c10) = sk_c11
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_189,c_0_76]) ).
cnf(c_0_199,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c10
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_200,negated_conjecture,
inverse(sk_c3) = sk_c10,
inference(spm,[status(thm)],[c_0_81,c_0_191]) ).
cnf(c_0_201,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c11) = sk_c10
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_192,c_0_76]) ).
cnf(c_0_202,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_81,c_0_193]) ).
cnf(c_0_203,negated_conjecture,
( multiply(inverse(sk_c1),sk_c10) = sk_c2
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_194]) ).
cnf(c_0_204,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_195]) ).
cnf(c_0_205,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c6 ),
prove_this_50 ).
cnf(c_0_206,negated_conjecture,
( inverse(sk_c11) = sk_c11
| sk_c11 != sk_c10
| sk_c4 != sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_39]),c_0_67]) ).
cnf(c_0_207,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c10) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_161]),c_0_161])]) ).
cnf(c_0_208,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c10
| sk_c3 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_199]),c_0_200]) ).
cnf(c_0_209,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c10) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_161]),c_0_161])]) ).
cnf(c_0_210,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_202,c_0_161]),c_0_161]) ).
cnf(c_0_211,negated_conjecture,
( multiply(inverse(inverse(sk_c1)),sk_c2) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_203]) ).
cnf(c_0_212,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_37 ).
cnf(c_0_213,negated_conjecture,
( multiply(inverse(inverse(sk_c3)),sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_204]) ).
cnf(c_0_214,negated_conjecture,
( multiply(sk_c7,multiply(sk_c8,X1)) = multiply(sk_c6,X1)
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_37,c_0_205]) ).
cnf(c_0_215,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_47 ).
cnf(c_0_216,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c6) = sk_c8 ),
prove_this_49 ).
cnf(c_0_217,negated_conjecture,
( inverse(sk_c10) = sk_c10
| sk_c4 != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_206,c_0_161]),c_0_161]),c_0_161]),c_0_161])]) ).
cnf(c_0_218,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_207,c_0_191]) ).
cnf(c_0_219,negated_conjecture,
( multiply(sk_c10,X1) = X1
| sk_c3 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_208]),c_0_43]) ).
cnf(c_0_220,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_209,c_0_191]) ).
cnf(c_0_221,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_210,c_0_191]) ).
cnf(c_0_222,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_39]) ).
cnf(c_0_223,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_115]),c_0_39]) ).
cnf(c_0_224,negated_conjecture,
( multiply(sk_c7,sk_c8) = multiply(sk_c6,sk_c11)
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_214,c_0_91]) ).
cnf(c_0_225,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_215]) ).
cnf(c_0_226,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_81,c_0_216]) ).
cnf(c_0_227,negated_conjecture,
inverse(multiply(sk_c9,inverse(sk_c11))) = sk_c10,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_133]),c_0_81]) ).
cnf(c_0_228,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_81,c_0_129]) ).
cnf(c_0_229,negated_conjecture,
( sk_c3 = sk_c10
| sk_c4 != sk_c10 ),
inference(spm,[status(thm)],[c_0_217,c_0_191]) ).
cnf(c_0_230,negated_conjecture,
( sk_c3 = sk_c10
| sk_c4 = sk_c9 ),
inference(spm,[status(thm)],[c_0_218,c_0_219]) ).
cnf(c_0_231,negated_conjecture,
( sk_c3 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_220,c_0_221]) ).
cnf(c_0_232,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c10
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_222]) ).
cnf(c_0_233,negated_conjecture,
( multiply(inverse(sk_c1),sk_c10) = sk_c2
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_223]) ).
cnf(c_0_234,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c6) = sk_c8 ),
prove_this_39 ).
cnf(c_0_235,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c6,sk_c11) = sk_c6 ),
inference(spm,[status(thm)],[c_0_205,c_0_224]) ).
cnf(c_0_236,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c6,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_225,c_0_226]) ).
cnf(c_0_237,negated_conjecture,
multiply(sk_c9,inverse(sk_c11)) = inverse(sk_c10),
inference(spm,[status(thm)],[c_0_81,c_0_227]) ).
cnf(c_0_238,negated_conjecture,
( inverse(sk_c11) = sk_c10
| sk_c3 != sk_c10 ),
inference(ef,[status(thm)],[c_0_228]) ).
cnf(c_0_239,negated_conjecture,
( multiply(sk_c10,multiply(sk_c11,X1)) = X1
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_178]) ).
cnf(c_0_240,negated_conjecture,
sk_c3 = sk_c10,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_231]) ).
cnf(c_0_241,negated_conjecture,
( multiply(inverse(sk_c8),multiply(sk_c11,X1)) = multiply(sk_c10,X1)
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_37,c_0_232]) ).
cnf(c_0_242,negated_conjecture,
( multiply(inverse(multiply(X1,inverse(sk_c1))),multiply(X1,sk_c2)) = sk_c10
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_84,c_0_233]) ).
cnf(c_0_243,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_81,c_0_234]) ).
cnf(c_0_244,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| sk_c6 = sk_c10 ),
inference(spm,[status(thm)],[c_0_235,c_0_236]) ).
cnf(c_0_245,negated_conjecture,
multiply(sk_c9,inverse(sk_c10)) = inverse(sk_c10),
inference(rw,[status(thm)],[c_0_237,c_0_161]) ).
cnf(c_0_246,negated_conjecture,
( multiply(inverse(sk_c1),multiply(sk_c10,X1)) = multiply(sk_c2,X1)
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_37,c_0_233]) ).
cnf(c_0_247,negated_conjecture,
( multiply(sk_c10,sk_c11) = identity
| sk_c3 != sk_c10 ),
inference(spm,[status(thm)],[c_0_39,c_0_238]) ).
cnf(c_0_248,negated_conjecture,
( multiply(inverse(X1),multiply(sk_c10,multiply(sk_c11,multiply(X1,X2)))) = X2
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_239]),c_0_37]) ).
cnf(c_0_249,negated_conjecture,
multiply(sk_c10,sk_c10) = sk_c9,
inference(rw,[status(thm)],[c_0_184,c_0_240]) ).
cnf(c_0_250,negated_conjecture,
( inverse(sk_c8) = multiply(sk_c10,sk_c3)
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_163]),c_0_67]) ).
cnf(c_0_251,negated_conjecture,
( inverse(sk_c8) = sk_c6
| identity = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_39])]) ).
cnf(c_0_252,negated_conjecture,
( multiply(sk_c2,multiply(sk_c9,X1)) = multiply(sk_c10,X1)
| sk_c6 = sk_c10 ),
inference(spm,[status(thm)],[c_0_37,c_0_244]) ).
cnf(c_0_253,negated_conjecture,
multiply(sk_c9,sk_c3) = sk_c3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_245,c_0_191]),c_0_191]) ).
cnf(c_0_254,negated_conjecture,
( inverse(sk_c1) = multiply(sk_c2,sk_c11)
| identity = sk_c10
| sk_c3 != sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_247]),c_0_67]) ).
cnf(c_0_255,negated_conjecture,
( multiply(inverse(X1),multiply(sk_c10,multiply(sk_c10,multiply(X1,X2)))) = X2
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_248,c_0_161]),c_0_161]),c_0_240]),c_0_249]) ).
cnf(c_0_256,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_161]),c_0_167]) ).
cnf(c_0_257,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c6
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_250,c_0_251]) ).
cnf(c_0_258,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| sk_c6 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_184]) ).
cnf(c_0_259,negated_conjecture,
( inverse(sk_c1) = multiply(sk_c2,sk_c10)
| sk_c9 = sk_c10 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_254,c_0_161]),c_0_167]),c_0_231]) ).
cnf(c_0_260,negated_conjecture,
( inverse(sk_c1) = sk_c10
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_256]),c_0_168]),c_0_249]),c_0_168]) ).
cnf(c_0_261,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c6
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[c_0_257,c_0_167]) ).
cnf(c_0_262,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| sk_c6 = sk_c10 ),
inference(rw,[status(thm)],[c_0_258,c_0_240]) ).
cnf(c_0_263,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_259,c_0_260]) ).
cnf(c_0_264,negated_conjecture,
( sk_c9 = sk_c10
| sk_c6 = sk_c9 ),
inference(spm,[status(thm)],[c_0_261,c_0_169]) ).
cnf(c_0_265,negated_conjecture,
( sk_c6 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_262,c_0_263]) ).
cnf(c_0_266,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_104])]) ).
cnf(c_0_267,negated_conjecture,
sk_c9 = sk_c10,
inference(spm,[status(thm)],[c_0_264,c_0_265]) ).
cnf(c_0_268,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11
| identity != sk_c11
| identity != sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_266,c_0_144]),c_0_144]) ).
cnf(c_0_269,negated_conjecture,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_168,c_0_267]) ).
cnf(c_0_270,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(X2) != sk_c10
| inverse(X3) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_161]),c_0_161]),c_0_161]),c_0_161]),c_0_161])]),c_0_269]),c_0_267]),c_0_269]),c_0_269]),c_0_267]),c_0_269]),c_0_191]),c_0_240]),c_0_167]),c_0_267])])])]),c_0_191]),c_0_240])]) ).
cnf(c_0_271,negated_conjecture,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[c_0_191,c_0_240]) ).
cnf(c_0_272,negated_conjecture,
( inverse(X1) != sk_c10
| inverse(X2) != sk_c10
| inverse(X1) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_270,c_0_271]),c_0_269]),c_0_269]) ).
cnf(c_0_273,negated_conjecture,
inverse(X1) != sk_c10,
inference(spm,[status(thm)],[c_0_272,c_0_271]) ).
cnf(c_0_274,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_271,c_0_273]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP380-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n028.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:33:30 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 58.68/34.96 % Version : CSE_E---1.7
% 58.68/34.96 % Problem : theBenchmark.p
% 58.68/34.96 % SZS status Unsatisfiable for theBenchmark.p
% 58.68/34.96 % SZS output start CNFRefutation
% See solution above
% 58.98/35.24 % Total time : 25.411s
%------------------------------------------------------------------------------