%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP260-1 : 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 : n025.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 04:25:01 PM UTC 2026
% Result : Unsatisfiable 4.94s 3.50s
% Output : CNFRefutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 38
% Syntax : Number of clauses : 291 ( 28 unt; 237 nHn; 250 RR)
% Number of literals : 679 ( 678 equ; 122 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 : 100 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_38,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_48,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_49,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_51,negated_conjecture,
( multiply(X1,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| multiply(X2,sk_c10) != sk_c9
| inverse(X2) != sk_c10
| multiply(sk_c9,sk_c11) != 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_16,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_50,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_37,negated_conjecture,
( inverse(sk_c2) = sk_c10
| 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_c9,sk_c11) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c1,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,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_33,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_43,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_44,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(c_0_38,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
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,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_42,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_39]) ).
cnf(c_0_43,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_41]) ).
cnf(c_0_44,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_42,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_c1) = sk_c11
| inverse(sk_c7) = sk_c6 ),
prove_this_18 ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c7) = sk_c6 ),
prove_this_38 ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_19 ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c6 ),
prove_this_8 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c7) = sk_c6 ),
prove_this_28 ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c8 ),
prove_this_39 ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_45,c_0_47]) ).
cnf(c_0_54,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_39,c_0_45]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c1) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c8 ),
prove_this_9 ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_45,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c8 ),
prove_this_29 ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_45,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
( inverse(sk_c2) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c6 ),
prove_this_48 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c2,sk_c10) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_54,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c8 ),
prove_this_49 ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_45,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c10,X1) = X1
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_40,c_0_68]) ).
cnf(c_0_72,negated_conjecture,
( multiply(X1,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| multiply(X2,sk_c10) != sk_c9
| inverse(X2) != sk_c10
| multiply(sk_c9,sk_c11) != 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_73,negated_conjecture,
( multiply(sk_c9,X1) = X1
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_40,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
( multiply(X1,sk_c10) = X1
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_44,c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( multiply(inverse(sk_c9),sk_c10) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c10) = sk_c2
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_45,c_0_60]) ).
cnf(c_0_77,negated_conjecture,
( inverse(sk_c10) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_54,c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c9,sk_c11) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X6,sk_c11) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_72])]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c9) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_54,c_0_73]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c9) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_81,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c2 ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c9,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X6,sk_c11) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11
| identity != sk_c11 ),
inference(rw,[status(thm)],[c_0_78,c_0_54]) ).
cnf(c_0_83,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c2,X1) = X1
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_40,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( sk_c7 = sk_c8
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X6,sk_c11) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_70]) ).
cnf(c_0_86,negated_conjecture,
( inverse(sk_c2) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_54,c_0_84]) ).
cnf(c_0_87,negated_conjecture,
( sk_c7 = sk_c8
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_70,c_0_73]) ).
cnf(c_0_88,negated_conjecture,
( sk_c7 = sk_c8
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| inverse(X5) != identity
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != X5 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_44]),c_0_40]),c_0_44]),c_0_87]) ).
cnf(c_0_89,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_16 ).
cnf(c_0_90,negated_conjecture,
( sk_c7 = sk_c8
| multiply(X1,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| inverse(X4) != identity
| inverse(X1) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| inverse(X4) != X4 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_39]),c_0_45])]),c_0_69]) ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_45,c_0_48]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_45,c_0_89]) ).
cnf(c_0_93,negated_conjecture,
( sk_c7 = sk_c8
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c11) != sk_c10
| inverse(X3) != identity
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != X3 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_39]),c_0_45])]),c_0_68]) ).
cnf(c_0_94,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
prove_this_6 ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_45,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c8) = sk_c5
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_45,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
( sk_c7 = sk_c8
| multiply(X1,sk_c11) != sk_c10
| inverse(X2) != identity
| inverse(X1) != sk_c11
| inverse(X2) != X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_64]),c_0_60]) ).
cnf(c_0_99,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_94]) ).
cnf(c_0_100,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
prove_this_36 ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_45,c_0_56]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_45,c_0_95]) ).
cnf(c_0_103,negated_conjecture,
( inverse(sk_c11) = sk_c1
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( sk_c7 = sk_c8
| inverse(X1) != identity
| inverse(X1) != X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_39]),c_0_45])]),c_0_68]) ).
cnf(c_0_105,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_39,c_0_99]) ).
cnf(c_0_106,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_45,c_0_52]) ).
cnf(c_0_107,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_45,c_0_100]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_39,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c6,sk_c7) = identity
| inverse(sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_39,c_0_47]) ).
cnf(c_0_111,negated_conjecture,
sk_c7 = sk_c8,
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_45,c_0_106]) ).
cnf(c_0_113,negated_conjecture,
( inverse(sk_c8) = sk_c5
| inverse(sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_45,c_0_107]) ).
cnf(c_0_114,negated_conjecture,
( sk_c5 = sk_c6
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c6,sk_c8) = identity
| inverse(sk_c2) = sk_c10 ),
inference(rw,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c6,sk_c7) = identity
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_39,c_0_46]) ).
cnf(c_0_117,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_15 ).
cnf(c_0_118,negated_conjecture,
( inverse(sk_c10) = sk_c2
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c10) = sk_c10
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_105,c_0_114]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c6,sk_c8) = identity
| multiply(sk_c2,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_54,c_0_115]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c6,sk_c7) = identity
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_116]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_117]) ).
cnf(c_0_123,negated_conjecture,
( sk_c5 = sk_c6
| sk_c2 = sk_c10 ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_124,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c6 ),
prove_this_20 ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c2,sk_c10) = identity
| inverse(sk_c6) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_120]),c_0_44]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c6,sk_c8) = identity ),
inference(rw,[status(thm)],[c_0_121,c_0_111]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c6,sk_c8) = sk_c11
| sk_c2 = sk_c10 ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_58]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c2,sk_c10) = identity
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_125]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c6,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_50]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_5 ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| sk_c2 = sk_c10
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[c_0_128,c_0_111]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c8,sk_c6) = identity
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c6,sk_c8) = identity
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[c_0_131,c_0_111]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10
| sk_c2 = sk_c10 ),
inference(spm,[status(thm)],[c_0_132,c_0_123]) ).
cnf(c_0_138,negated_conjecture,
( inverse(sk_c11) = sk_c1
| identity = sk_c11
| sk_c2 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_133]),c_0_44]) ).
cnf(c_0_139,negated_conjecture,
( multiply(inverse(sk_c8),sk_c6) = sk_c8
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_41,c_0_134]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_39,c_0_92]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c11,X1)
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_38,c_0_122]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c6 ),
prove_this_50 ).
cnf(c_0_143,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_45 ).
cnf(c_0_144,negated_conjecture,
( inverse(sk_c8) = sk_c6
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_135]),c_0_44]) ).
cnf(c_0_145,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_37 ).
cnf(c_0_146,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c2 = sk_c10
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| sk_c2 = sk_c10
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_39,c_0_138]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_149,negated_conjecture,
( multiply(sk_c5,sk_c6) = multiply(sk_c11,sk_c8)
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_141,c_0_134]) ).
cnf(c_0_150,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_47 ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c7,multiply(sk_c8,X1)) = multiply(sk_c6,X1)
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_142]) ).
cnf(c_0_152,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_41,c_0_143]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
prove_this_46 ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = X1
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_144]) ).
cnf(c_0_155,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_38,c_0_54]) ).
cnf(c_0_156,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_27 ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_54,c_0_145]) ).
cnf(c_0_158,negated_conjecture,
( identity = sk_c11
| sk_c2 = sk_c10
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_159,negated_conjecture,
( multiply(sk_c11,sk_c8) = sk_c8
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_160,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_2 ).
cnf(c_0_161,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_41,c_0_150]) ).
cnf(c_0_162,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_45,c_0_66]) ).
cnf(c_0_163,negated_conjecture,
( multiply(sk_c8,multiply(sk_c8,X1)) = multiply(sk_c6,X1)
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[c_0_151,c_0_111]) ).
cnf(c_0_164,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_165,negated_conjecture,
( multiply(X1,inverse(multiply(sk_c8,X1))) = sk_c6
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_44]) ).
cnf(c_0_166,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_167,negated_conjecture,
( multiply(sk_c11,X1) = X1
| identity = sk_c10
| sk_c2 = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_158]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c11,sk_c8) = sk_c8
| inverse(sk_c11) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_159]),c_0_44]) ).
cnf(c_0_169,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_170,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_54,c_0_160]) ).
cnf(c_0_171,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c6,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_172,negated_conjecture,
( multiply(sk_c6,sk_c11) = multiply(sk_c8,sk_c8)
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_173,negated_conjecture,
( multiply(sk_c10,inverse(sk_c11)) = sk_c6
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_174,negated_conjecture,
( inverse(sk_c11) = identity
| sk_c2 = sk_c10
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_54,c_0_167]) ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c11,sk_c8) = sk_c8
| multiply(sk_c1,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_168]) ).
cnf(c_0_176,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_177,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c6
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[c_0_142,c_0_111]) ).
cnf(c_0_178,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_179,negated_conjecture,
( identity = sk_c10
| sk_c2 = sk_c10
| identity = sk_c9
| sk_c6 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_44]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c11,sk_c8) = sk_c8
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_181,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| sk_c6 = sk_c10 ),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_182,negated_conjecture,
( multiply(X1,sk_c11) = X1
| identity = sk_c10
| sk_c2 = sk_c10 ),
inference(spm,[status(thm)],[c_0_44,c_0_158]) ).
cnf(c_0_183,negated_conjecture,
( sk_c6 = sk_c10
| sk_c2 = sk_c10
| identity = sk_c10
| sk_c9 != sk_c10 ),
inference(ef,[status(thm)],[c_0_179]) ).
cnf(c_0_184,negated_conjecture,
( identity = sk_c10
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_180]),c_0_54]),c_0_44]) ).
cnf(c_0_185,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_34 ).
cnf(c_0_186,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_33 ).
cnf(c_0_187,negated_conjecture,
( sk_c2 = sk_c10
| identity = sk_c10
| sk_c6 = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_183]) ).
cnf(c_0_188,negated_conjecture,
( multiply(sk_c11,X1) = X1
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_184]) ).
cnf(c_0_189,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_45,c_0_185]) ).
cnf(c_0_190,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_45,c_0_186]) ).
cnf(c_0_191,negated_conjecture,
( inverse(sk_c10) = sk_c10
| sk_c6 = sk_c10
| sk_c2 = sk_c10 ),
inference(spm,[status(thm)],[c_0_105,c_0_187]) ).
cnf(c_0_192,negated_conjecture,
( inverse(sk_c11) = identity
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_54,c_0_188]) ).
cnf(c_0_193,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_45,c_0_189]) ).
cnf(c_0_194,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| sk_c6 = sk_c10
| sk_c2 = sk_c10 ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_195,negated_conjecture,
( multiply(X1,sk_c10) = X1
| sk_c6 = sk_c10
| sk_c2 = sk_c10 ),
inference(spm,[status(thm)],[c_0_44,c_0_187]) ).
cnf(c_0_196,negated_conjecture,
( identity = sk_c10
| identity = sk_c9
| sk_c6 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_192]),c_0_44]) ).
cnf(c_0_197,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c10
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_154,c_0_166]) ).
cnf(c_0_198,negated_conjecture,
( sk_c6 = sk_c10
| sk_c2 = sk_c10
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_193,c_0_191]) ).
cnf(c_0_199,negated_conjecture,
( sk_c2 = sk_c10
| sk_c6 = sk_c10
| sk_c4 = sk_c9 ),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_200,negated_conjecture,
( multiply(X1,sk_c11) = X1
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_44,c_0_184]) ).
cnf(c_0_201,negated_conjecture,
( sk_c6 = sk_c10
| identity = sk_c10
| sk_c9 != sk_c10 ),
inference(ef,[status(thm)],[c_0_196]) ).
cnf(c_0_202,negated_conjecture,
( multiply(inverse(sk_c6),sk_c10) = sk_c11
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_197]) ).
cnf(c_0_203,negated_conjecture,
( sk_c9 = sk_c10
| sk_c2 = sk_c10
| sk_c6 = sk_c10 ),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_204,negated_conjecture,
( inverse(sk_c10) = sk_c2
| sk_c4 != sk_c2 ),
inference(ef,[status(thm)],[c_0_193]) ).
cnf(c_0_205,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_23 ).
cnf(c_0_206,negated_conjecture,
( identity = sk_c10
| sk_c6 = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_200]),c_0_201]) ).
cnf(c_0_207,negated_conjecture,
( sk_c2 = sk_c10
| sk_c9 = sk_c10
| identity = sk_c9
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_39]) ).
cnf(c_0_208,negated_conjecture,
( inverse(sk_c2) = sk_c10
| sk_c4 != sk_c2 ),
inference(spm,[status(thm)],[c_0_45,c_0_204]) ).
cnf(c_0_209,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_205]) ).
cnf(c_0_210,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
prove_this_24 ).
cnf(c_0_211,negated_conjecture,
( multiply(sk_c10,X1) = X1
| sk_c6 = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_206]) ).
cnf(c_0_212,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_43 ).
cnf(c_0_213,negated_conjecture,
( identity = sk_c11
| sk_c9 = sk_c10
| sk_c2 = sk_c10
| sk_c9 != sk_c11 ),
inference(ef,[status(thm)],[c_0_207]) ).
cnf(c_0_214,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_41 ).
cnf(c_0_215,negated_conjecture,
( multiply(sk_c10,multiply(sk_c2,X1)) = X1
| sk_c4 != sk_c2 ),
inference(spm,[status(thm)],[c_0_41,c_0_208]) ).
cnf(c_0_216,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_217,negated_conjecture,
( inverse(sk_c10) = identity
| sk_c6 = sk_c10 ),
inference(spm,[status(thm)],[c_0_54,c_0_211]) ).
cnf(c_0_218,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_54,c_0_210]) ).
cnf(c_0_219,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_41,c_0_212]) ).
cnf(c_0_220,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_44 ).
cnf(c_0_221,negated_conjecture,
( identity = sk_c11
| sk_c9 = sk_c10
| sk_c2 = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_207]),c_0_213]) ).
cnf(c_0_222,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_41,c_0_214]) ).
cnf(c_0_223,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_42 ).
cnf(c_0_224,negated_conjecture,
( multiply(sk_c2,multiply(sk_c10,X1)) = X1
| sk_c4 != sk_c2 ),
inference(spm,[status(thm)],[c_0_41,c_0_204]) ).
cnf(c_0_225,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| sk_c4 != sk_c2 ),
inference(spm,[status(thm)],[c_0_215,c_0_216]) ).
cnf(c_0_226,negated_conjecture,
( sk_c6 = sk_c10
| identity = sk_c2
| identity = sk_c4 ),
inference(spm,[status(thm)],[c_0_193,c_0_217]) ).
cnf(c_0_227,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_205,c_0_218]) ).
cnf(c_0_228,negated_conjecture,
( multiply(X1,sk_c10) = X1
| sk_c6 = sk_c10 ),
inference(spm,[status(thm)],[c_0_44,c_0_206]) ).
cnf(c_0_229,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_219,c_0_220]) ).
cnf(c_0_230,negated_conjecture,
( multiply(X1,sk_c11) = X1
| sk_c2 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_44,c_0_221]) ).
cnf(c_0_231,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_222,c_0_223]) ).
cnf(c_0_232,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| sk_c4 != sk_c2 ),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_233,negated_conjecture,
( identity = sk_c2
| sk_c6 = sk_c10
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_206,c_0_226]) ).
cnf(c_0_234,negated_conjecture,
( sk_c6 = sk_c10
| identity = sk_c9
| sk_c2 = sk_c9 ),
inference(spm,[status(thm)],[c_0_227,c_0_228]) ).
cnf(c_0_235,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| sk_c2 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_229,c_0_230]) ).
cnf(c_0_236,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| sk_c2 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_231,c_0_230]) ).
cnf(c_0_237,negated_conjecture,
( sk_c6 = sk_c10
| sk_c2 = sk_c9
| sk_c4 != sk_c2 ),
inference(spm,[status(thm)],[c_0_232,c_0_228]) ).
cnf(c_0_238,negated_conjecture,
( sk_c4 = sk_c10
| sk_c6 = sk_c10
| sk_c2 = sk_c9 ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_239,negated_conjecture,
( sk_c9 = sk_c10
| sk_c2 = sk_c10
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_235]),c_0_39]) ).
cnf(c_0_240,negated_conjecture,
( sk_c9 = sk_c10
| sk_c2 = sk_c10
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_236]),c_0_39]) ).
cnf(c_0_241,negated_conjecture,
( sk_c2 = sk_c9
| sk_c6 = sk_c10
| sk_c2 != sk_c10 ),
inference(spm,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_242,negated_conjecture,
( sk_c2 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_239,c_0_240]) ).
cnf(c_0_243,negated_conjecture,
( multiply(sk_c8,multiply(sk_c6,X1)) = X1
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_41,c_0_66]) ).
cnf(c_0_244,negated_conjecture,
( multiply(sk_c6,inverse(sk_c8)) = sk_c8
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_54]),c_0_44]) ).
cnf(c_0_245,negated_conjecture,
( sk_c6 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_246,negated_conjecture,
( inverse(sk_c8) = multiply(sk_c8,sk_c8)
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_243,c_0_244]) ).
cnf(c_0_247,negated_conjecture,
( sk_c9 = sk_c10
| identity = sk_c9
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_245]),c_0_39]) ).
cnf(c_0_248,negated_conjecture,
( inverse(multiply(sk_c8,sk_c8)) = sk_c8
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_45,c_0_246]) ).
cnf(c_0_249,negated_conjecture,
( identity = sk_c11
| sk_c9 = sk_c10
| sk_c9 != sk_c11 ),
inference(ef,[status(thm)],[c_0_247]) ).
cnf(c_0_250,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_248,c_0_178]) ).
cnf(c_0_251,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_54,c_0_220]) ).
cnf(c_0_252,negated_conjecture,
( identity = sk_c11
| sk_c9 = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_247]),c_0_249]) ).
cnf(c_0_253,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c8,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_250]) ).
cnf(c_0_254,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_212,c_0_251]) ).
cnf(c_0_255,negated_conjecture,
( multiply(X1,sk_c11) = X1
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_44,c_0_252]) ).
cnf(c_0_256,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_150,c_0_253]) ).
cnf(c_0_257,negated_conjecture,
( identity = sk_c10
| sk_c11 != sk_c10 ),
inference(ef,[status(thm)],[c_0_184]) ).
cnf(c_0_258,negated_conjecture,
( identity = sk_c9
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_254,c_0_255]) ).
cnf(c_0_259,negated_conjecture,
( multiply(inverse(sk_c9),sk_c10) = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_41,c_0_256]) ).
cnf(c_0_260,negated_conjecture,
( sk_c9 = sk_c10
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_257,c_0_258]) ).
cnf(c_0_261,negated_conjecture,
( identity = sk_c11
| sk_c11 != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_260]),c_0_39])]) ).
cnf(c_0_262,negated_conjecture,
( multiply(sk_c11,X1) = X1
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_252]) ).
cnf(c_0_263,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_231,c_0_255]) ).
cnf(c_0_264,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_12 ).
cnf(c_0_265,negated_conjecture,
( multiply(sk_c11,X1) = X1
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_261]) ).
cnf(c_0_266,negated_conjecture,
sk_c9 = sk_c10,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_263]),c_0_260]) ).
cnf(c_0_267,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_45,c_0_264]) ).
cnf(c_0_268,negated_conjecture,
( inverse(sk_c11) = identity
| sk_c11 != sk_c10 ),
inference(spm,[status(thm)],[c_0_54,c_0_265]) ).
cnf(c_0_269,negated_conjecture,
identity = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_259,c_0_266]),c_0_39])]) ).
cnf(c_0_270,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_11 ).
cnf(c_0_271,negated_conjecture,
( inverse(sk_c11) = sk_c3
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_45,c_0_267]) ).
cnf(c_0_272,negated_conjecture,
( inverse(sk_c11) = sk_c11
| sk_c11 != sk_c10 ),
inference(rw,[status(thm)],[c_0_268,c_0_269]) ).
cnf(c_0_273,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_45,c_0_270]) ).
cnf(c_0_274,plain,
multiply(X1,sk_c11) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_269]) ).
cnf(c_0_275,negated_conjecture,
( inverse(sk_c11) = sk_c1
| sk_c3 != sk_c1 ),
inference(ef,[status(thm)],[c_0_271]) ).
cnf(c_0_276,plain,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_269]),c_0_269]) ).
cnf(c_0_277,negated_conjecture,
inverse(sk_c11) = sk_c11,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_269]),c_0_269]),c_0_272]) ).
cnf(c_0_278,negated_conjecture,
( inverse(sk_c11) = sk_c1
| sk_c3 = sk_c10 ),
inference(rw,[status(thm)],[c_0_273,c_0_274]) ).
cnf(c_0_279,negated_conjecture,
( sk_c1 = sk_c11
| sk_c3 != sk_c1 ),
inference(spm,[status(thm)],[c_0_275,c_0_276]) ).
cnf(c_0_280,negated_conjecture,
( sk_c3 = sk_c10
| sk_c1 = sk_c11 ),
inference(spm,[status(thm)],[c_0_277,c_0_278]) ).
cnf(c_0_281,negated_conjecture,
( identity = sk_c10
| sk_c1 = sk_c10 ),
inference(spm,[status(thm)],[c_0_176,c_0_200]) ).
cnf(c_0_282,negated_conjecture,
( sk_c1 = sk_c11
| sk_c1 != sk_c10 ),
inference(spm,[status(thm)],[c_0_279,c_0_280]) ).
cnf(c_0_283,negated_conjecture,
( sk_c1 = sk_c10
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_281,c_0_269]) ).
cnf(c_0_284,negated_conjecture,
sk_c11 = sk_c10,
inference(spm,[status(thm)],[c_0_282,c_0_283]) ).
cnf(c_0_285,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_274,c_0_284]) ).
cnf(c_0_286,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_276,c_0_284]),c_0_284]) ).
cnf(c_0_287,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(X2) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[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(rw,[status(thm)],[c_0_82,c_0_266]),c_0_266]),c_0_266]),c_0_285]),c_0_284]),c_0_274]),c_0_285]),c_0_284]),c_0_285]),c_0_285]),c_0_284]),c_0_285]),c_0_284]),c_0_284]),c_0_269]),c_0_284]),c_0_284])])])])])]),c_0_286])]) ).
cnf(c_0_288,plain,
multiply(inverse(X1),X1) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_269]),c_0_284]) ).
cnf(c_0_289,negated_conjecture,
inverse(X1) != sk_c10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_288]),c_0_286]),c_0_45])]) ).
cnf(c_0_290,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_185,c_0_289]),c_0_289]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP260-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:29:43 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.94/3.50 % Version : CSE_E---1.7
% 4.94/3.50 % Problem : theBenchmark.p
% 4.94/3.50 % SZS status Unsatisfiable for theBenchmark.p
% 4.94/3.50 % SZS output start CNFRefutation
% See solution above
% 4.94/3.52 % Total time : 2.374s
%------------------------------------------------------------------------------