%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP243-1 : TPTP v9.2.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:24:55 PM UTC 2026
% Result : Unsatisfiable 11.69s 7.63s
% Output : CNFRefutation 11.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 35
% Syntax : Number of clauses : 237 ( 25 unt; 202 nHn; 211 RR)
% Number of literals : 606 ( 605 equ; 131 neg)
% Maximal clause size : 16 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 97 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_64,negated_conjecture,
( multiply(X1,sk_c12) != sk_c11
| inverse(X1) != sk_c12
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X7) != sk_c11
| multiply(X7,sk_c10) != sk_c11
| multiply(X8,X9) != sk_c11
| inverse(X8) != X9
| multiply(X9,sk_c10) != sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_64) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_36,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_55,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_48,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_62,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_62) ).
cnf(prove_this_47,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_53,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
cnf(prove_this_29,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_54,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_44,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_51,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_25,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_23,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(c_0_35,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_36,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_37,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_38,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_37 ).
cnf(c_0_40,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( multiply(inverse(sk_c3),sk_c12) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c3) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_30 ).
cnf(c_0_43,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_36]),c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( multiply(X1,sk_c12) != sk_c11
| inverse(X1) != sk_c12
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X7) != sk_c11
| multiply(X7,sk_c10) != sk_c11
| multiply(X8,X9) != sk_c11
| inverse(X8) != X9
| multiply(X9,sk_c10) != sk_c11 ),
prove_this_64 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
prove_this_46 ).
cnf(c_0_47,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_43]),c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c7) = sk_c11 ),
prove_this_31 ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c7) = sk_c11 ),
prove_this_10 ).
cnf(c_0_50,negated_conjecture,
( multiply(inverse(sk_c6),sk_c12) = sk_c11
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| inverse(sk_c6) = sk_c12 ),
prove_this_36 ).
cnf(c_0_52,negated_conjecture,
( multiply(inverse(X1),sk_c10) != sk_c11
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c12
| multiply(X6,sk_c11) != sk_c10
| multiply(X7,sk_c12) != sk_c11
| inverse(X3) != sk_c11
| inverse(X4) != sk_c12
| inverse(X5) != sk_c12
| inverse(X6) != sk_c11
| inverse(X7) != sk_c12 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_45])]) ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c8) = sk_c9 ),
prove_this_55 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c8) = sk_c9 ),
prove_this_48 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| inverse(sk_c8) = sk_c9 ),
prove_this_62 ).
cnf(c_0_56,negated_conjecture,
( multiply(inverse(sk_c4),sk_c11) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_46]) ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c7) = sk_c11
| inverse(sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c7) = sk_c11
| inverse(sk_c12) = sk_c1 ),
inference(spm,[status(thm)],[c_0_47,c_0_49]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
prove_this_47 ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c10
| multiply(X6,sk_c12) != sk_c11
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12
| inverse(X4) != sk_c12
| inverse(X5) != sk_c11
| inverse(X6) != sk_c12 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55]) ).
cnf(c_0_62,negated_conjecture,
( multiply(inverse(inverse(sk_c4)),sk_c5) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c11 ),
prove_this_53 ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c12) = sk_c3
| inverse(sk_c11) = sk_c7 ),
inference(spm,[status(thm)],[c_0_47,c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( inverse(sk_c12) = sk_c1
| inverse(sk_c11) = sk_c7 ),
inference(spm,[status(thm)],[c_0_47,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( multiply(inverse(sk_c3),sk_c12) = sk_c11
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c6) = sk_c12 ),
prove_this_29 ).
cnf(c_0_68,negated_conjecture,
( multiply(inverse(sk_c4),sk_c11) = sk_c5
| multiply(sk_c8,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(X1,sk_c10) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c12) != sk_c11
| inverse(X1) != sk_c11
| inverse(X2) != sk_c12
| inverse(X3) != sk_c12
| inverse(X4) != sk_c11
| inverse(X5) != sk_c12 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_53]),c_0_54]),c_0_55]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_36]) ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c11) = sk_c7
| sk_c3 = sk_c1 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c11
| inverse(sk_c6) = sk_c12 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( multiply(inverse(inverse(sk_c4)),sk_c5) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c8,sk_c9) = sk_c11 ),
prove_this_54 ).
cnf(c_0_75,negated_conjecture,
( inverse(sk_c8) = sk_c9
| identity = sk_c11
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,sk_c11) != sk_c12
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c12) != sk_c11
| inverse(sk_c7) != sk_c11
| inverse(X1) != sk_c12
| inverse(X2) != sk_c12
| inverse(X3) != sk_c11
| inverse(X4) != sk_c12 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c7) = sk_c11
| sk_c3 = sk_c1 ),
inference(spm,[status(thm)],[c_0_47,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
multiply(sk_c12,sk_c12) = sk_c11,
inference(spm,[status(thm)],[c_0_50,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_36]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c3 = sk_c1
| identity = sk_c11
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,sk_c11) != sk_c12
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c12) != sk_c11
| inverse(X1) != sk_c12
| inverse(X2) != sk_c12
| inverse(X3) != sk_c11
| inverse(X4) != sk_c12 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
multiply(inverse(sk_c12),sk_c11) = sk_c12,
inference(spm,[status(thm)],[c_0_38,c_0_77]) ).
cnf(c_0_81,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c9
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c8) = sk_c9
| identity = sk_c11
| sk_c3 = sk_c1
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c12) != sk_c11
| inverse(X1) != sk_c12
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_47])]) ).
cnf(c_0_83,negated_conjecture,
( multiply(inverse(inverse(sk_c8)),sk_c9) = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c8) = sk_c9 ),
prove_this_20 ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_44 ).
cnf(c_0_86,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c3 = sk_c1
| identity = sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(X2,sk_c12) != sk_c11
| inverse(X1) != sk_c11
| inverse(X2) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_80]),c_0_47])]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| identity = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_36])]) ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c8) = sk_c9 ),
prove_this_27 ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| inverse(sk_c8) = sk_c9 ),
prove_this_6 ).
cnf(c_0_90,negated_conjecture,
( multiply(inverse(sk_c4),sk_c11) = sk_c5
| multiply(sk_c6,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_38,c_0_85]) ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c3) = sk_c12
| inverse(sk_c8) = sk_c9 ),
prove_this_34 ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c8) = sk_c9
| identity = sk_c11
| sk_c3 = sk_c1
| multiply(X1,sk_c12) != sk_c11
| inverse(X1) != sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| identity = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_89]),c_0_36])]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c8) = sk_c9 ),
prove_this_13 ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c11,sk_c2) = identity
| inverse(sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_88]) ).
cnf(c_0_96,negated_conjecture,
( multiply(inverse(inverse(sk_c4)),sk_c5) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_38,c_0_90]) ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_51 ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c12,sk_c3) = identity
| inverse(sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_91]) ).
cnf(c_0_99,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c3 = sk_c1
| identity = sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_100,negated_conjecture,
multiply(inverse(sk_c12),multiply(sk_c11,X1)) = multiply(sk_c12,X1),
inference(spm,[status(thm)],[c_0_35,c_0_80]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c11,sk_c2) = identity
| identity = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_95]),c_0_36])]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_36]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c12,sk_c3) = identity
| multiply(sk_c9,sk_c11) = sk_c9
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_81,c_0_98]) ).
cnf(c_0_104,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c9
| sk_c3 = sk_c1
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_81,c_0_99]) ).
cnf(c_0_106,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c6) = sk_c12 ),
prove_this_8 ).
cnf(c_0_107,negated_conjecture,
( inverse(sk_c12) = multiply(sk_c12,sk_c2)
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_43]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c6,multiply(sk_c11,X1)) = multiply(sk_c12,X1)
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_35,c_0_102]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c12,sk_c3) = identity
| identity = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_103]),c_0_36])]) ).
cnf(c_0_110,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_104,c_0_43]) ).
cnf(c_0_111,negated_conjecture,
( sk_c3 = sk_c1
| identity = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_105]),c_0_36])]) ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c6) = sk_c12
| inverse(sk_c12) = sk_c1 ),
inference(spm,[status(thm)],[c_0_47,c_0_106]) ).
cnf(c_0_113,negated_conjecture,
( inverse(multiply(sk_c12,sk_c2)) = sk_c12
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_107]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c12,sk_c2) = sk_c6
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_101]),c_0_43]) ).
cnf(c_0_115,negated_conjecture,
( inverse(sk_c12) = sk_c3
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_109]),c_0_43]) ).
cnf(c_0_116,negated_conjecture,
( inverse(sk_c11) = sk_c11
| sk_c3 = sk_c1 ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_117,negated_conjecture,
( inverse(sk_c6) = sk_c12
| inverse(sk_c12) = sk_c3 ),
inference(spm,[status(thm)],[c_0_47,c_0_67]) ).
cnf(c_0_118,negated_conjecture,
( inverse(sk_c12) = sk_c1
| inverse(sk_c12) = sk_c6 ),
inference(spm,[status(thm)],[c_0_47,c_0_112]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c6) = sk_c12
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_120,negated_conjecture,
( inverse(sk_c3) = sk_c12
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_115]) ).
cnf(c_0_121,negated_conjecture,
( sk_c3 = sk_c1
| sk_c7 = sk_c11 ),
inference(spm,[status(thm)],[c_0_71,c_0_116]) ).
cnf(c_0_122,negated_conjecture,
multiply(sk_c12,multiply(sk_c12,X1)) = multiply(sk_c11,X1),
inference(spm,[status(thm)],[c_0_35,c_0_77]) ).
cnf(c_0_123,negated_conjecture,
( multiply(sk_c1,multiply(sk_c12,X1)) = multiply(sk_c11,X1)
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_35,c_0_93]) ).
cnf(c_0_124,negated_conjecture,
( inverse(sk_c12) = sk_c3
| inverse(sk_c12) = sk_c6 ),
inference(spm,[status(thm)],[c_0_47,c_0_117]) ).
cnf(c_0_125,negated_conjecture,
( inverse(sk_c12) = sk_c6
| sk_c1 != sk_c6 ),
inference(ef,[status(thm)],[c_0_118]) ).
cnf(c_0_126,negated_conjecture,
( inverse(sk_c12) = sk_c6
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_119]) ).
cnf(c_0_127,negated_conjecture,
( inverse(sk_c1) = sk_c12
| sk_c7 = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c12
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_109]),c_0_43]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c1
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_109]),c_0_43]) ).
cnf(c_0_130,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c7) = sk_c11 ),
prove_this_24 ).
cnf(c_0_131,negated_conjecture,
( inverse(sk_c12) = sk_c6
| sk_c3 = sk_c1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_118]),c_0_125]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c11 ),
prove_this_17 ).
cnf(c_0_133,negated_conjecture,
( identity = sk_c11
| sk_c3 = sk_c6 ),
inference(spm,[status(thm)],[c_0_126,c_0_115]) ).
cnf(c_0_134,negated_conjecture,
( inverse(sk_c12) = sk_c1
| identity = sk_c11
| sk_c7 = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_127]) ).
cnf(c_0_135,negated_conjecture,
( identity = sk_c11
| sk_c1 = sk_c12 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_136,negated_conjecture,
( inverse(sk_c7) = sk_c11
| inverse(sk_c11) = sk_c2 ),
inference(spm,[status(thm)],[c_0_47,c_0_130]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| sk_c3 = sk_c1 ),
inference(spm,[status(thm)],[c_0_80,c_0_131]) ).
cnf(c_0_138,negated_conjecture,
( multiply(X1,sk_c11) = X1
| sk_c3 = sk_c1 ),
inference(spm,[status(thm)],[c_0_43,c_0_111]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c7 ),
inference(spm,[status(thm)],[c_0_47,c_0_132]) ).
cnf(c_0_140,negated_conjecture,
( inverse(sk_c11) = sk_c11
| sk_c3 = sk_c6 ),
inference(spm,[status(thm)],[c_0_110,c_0_133]) ).
cnf(c_0_141,negated_conjecture,
( sk_c7 = sk_c11
| identity = sk_c11
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_126,c_0_134]) ).
cnf(c_0_142,negated_conjecture,
( inverse(sk_c11) = sk_c11
| sk_c1 = sk_c12 ),
inference(spm,[status(thm)],[c_0_110,c_0_135]) ).
cnf(c_0_143,negated_conjecture,
( inverse(sk_c11) = sk_c2
| inverse(sk_c11) = sk_c7 ),
inference(spm,[status(thm)],[c_0_47,c_0_136]) ).
cnf(c_0_144,negated_conjecture,
( sk_c3 = sk_c1
| sk_c6 = sk_c12 ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c11 ),
prove_this_18 ).
cnf(c_0_146,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| sk_c3 = sk_c6
| sk_c7 = sk_c11 ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_147,negated_conjecture,
( multiply(X1,sk_c11) = X1
| sk_c1 = sk_c6
| sk_c7 = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_141]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| sk_c1 = sk_c12
| sk_c7 = sk_c11 ),
inference(spm,[status(thm)],[c_0_139,c_0_142]) ).
cnf(c_0_149,negated_conjecture,
( sk_c1 = sk_c12
| sk_c7 = sk_c11
| sk_c2 = sk_c11 ),
inference(spm,[status(thm)],[c_0_143,c_0_142]) ).
cnf(c_0_150,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_16 ).
cnf(c_0_151,negated_conjecture,
( inverse(sk_c1) = sk_c12
| sk_c6 = sk_c12
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_120,c_0_144]) ).
cnf(c_0_152,negated_conjecture,
( multiply(inverse(sk_c2),sk_c10) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_145]) ).
cnf(c_0_153,negated_conjecture,
( sk_c3 = sk_c6
| sk_c7 = sk_c11
| sk_c2 = sk_c11 ),
inference(spm,[status(thm)],[c_0_143,c_0_140]) ).
cnf(c_0_154,negated_conjecture,
( sk_c1 = sk_c6
| sk_c7 = sk_c11
| sk_c3 = sk_c6
| sk_c2 = sk_c10 ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c11,sk_c11) = identity
| sk_c1 = sk_c12 ),
inference(spm,[status(thm)],[c_0_36,c_0_142]) ).
cnf(c_0_156,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| sk_c7 = sk_c11
| sk_c1 = sk_c12 ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_157,negated_conjecture,
( multiply(inverse(sk_c2),sk_c10) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_38,c_0_150]) ).
cnf(c_0_158,negated_conjecture,
( inverse(sk_c12) = sk_c1
| identity = sk_c11
| sk_c6 = sk_c12 ),
inference(spm,[status(thm)],[c_0_47,c_0_151]) ).
cnf(c_0_159,negated_conjecture,
( multiply(inverse(inverse(sk_c2)),sk_c11) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_152]) ).
cnf(c_0_160,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
prove_this_25 ).
cnf(c_0_161,negated_conjecture,
( sk_c2 = sk_c11
| sk_c7 = sk_c11
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_121,c_0_153]) ).
cnf(c_0_162,negated_conjecture,
( sk_c2 = sk_c10
| sk_c7 = sk_c11
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_121,c_0_154]) ).
cnf(c_0_163,negated_conjecture,
( sk_c7 = sk_c11
| sk_c1 = sk_c12
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_164,negated_conjecture,
( multiply(inverse(inverse(sk_c2)),sk_c11) = sk_c10
| multiply(sk_c6,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_38,c_0_157]) ).
cnf(c_0_165,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_23 ).
cnf(c_0_166,negated_conjecture,
( sk_c6 = sk_c12
| identity = sk_c11
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_126,c_0_158]) ).
cnf(c_0_167,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_36]) ).
cnf(c_0_168,negated_conjecture,
( sk_c1 = sk_c6
| sk_c7 = sk_c11
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_169,negated_conjecture,
( sk_c7 = sk_c11
| sk_c1 = sk_c12
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_135,c_0_163]) ).
cnf(c_0_170,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_36]) ).
cnf(c_0_171,negated_conjecture,
( multiply(X1,sk_c11) = X1
| sk_c1 = sk_c6
| sk_c6 = sk_c12 ),
inference(spm,[status(thm)],[c_0_43,c_0_166]) ).
cnf(c_0_172,negated_conjecture,
( multiply(inverse(sk_c7),sk_c11) = sk_c10
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_167]) ).
cnf(c_0_173,negated_conjecture,
( sk_c10 = sk_c11
| sk_c7 = sk_c11
| sk_c6 = sk_c12 ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_174,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c11 ),
prove_this_19 ).
cnf(c_0_175,negated_conjecture,
( sk_c1 = sk_c6
| identity = sk_c10
| sk_c6 = sk_c12 ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_176,negated_conjecture,
( sk_c6 = sk_c12
| sk_c10 = sk_c11
| identity = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_36])]) ).
cnf(c_0_177,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
prove_this_21 ).
cnf(c_0_178,negated_conjecture,
( multiply(inverse(sk_c2),sk_c10) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_174]) ).
cnf(c_0_179,negated_conjecture,
( sk_c1 = sk_c6
| sk_c10 = sk_c11
| sk_c6 = sk_c12 ),
inference(spm,[status(thm)],[c_0_166,c_0_175]) ).
cnf(c_0_180,negated_conjecture,
( sk_c6 = sk_c12
| sk_c1 = sk_c12
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_135,c_0_176]) ).
cnf(c_0_181,negated_conjecture,
( multiply(inverse(sk_c2),sk_c10) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_177]) ).
cnf(c_0_182,negated_conjecture,
( multiply(inverse(inverse(sk_c2)),sk_c11) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_178]) ).
cnf(c_0_183,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c11 ),
prove_this_26 ).
cnf(c_0_184,negated_conjecture,
( multiply(inverse(sk_c6),sk_c12) = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_102]) ).
cnf(c_0_185,negated_conjecture,
( sk_c10 = sk_c11
| sk_c6 = sk_c12 ),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_186,negated_conjecture,
( multiply(inverse(inverse(sk_c2)),sk_c11) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_181]) ).
cnf(c_0_187,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
prove_this_28 ).
cnf(c_0_188,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_183]),c_0_36]) ).
cnf(c_0_189,negated_conjecture,
( sk_c10 = sk_c11
| identity = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_36])]) ).
cnf(c_0_190,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_36]) ).
cnf(c_0_191,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c9
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_188]) ).
cnf(c_0_192,negated_conjecture,
( multiply(X1,sk_c11) = X1
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_189]) ).
cnf(c_0_193,negated_conjecture,
( multiply(inverse(sk_c9),sk_c11) = sk_c10
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_190]) ).
cnf(c_0_194,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c10 = sk_c11
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_195,negated_conjecture,
( inverse(sk_c9) = sk_c10
| sk_c10 = sk_c11
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_193,c_0_192]) ).
cnf(c_0_196,negated_conjecture,
( inverse(sk_c7) = sk_c10
| sk_c10 = sk_c11
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_172,c_0_192]) ).
cnf(c_0_197,negated_conjecture,
( inverse(sk_c9) = sk_c8
| identity = sk_c10
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_194]) ).
cnf(c_0_198,negated_conjecture,
( inverse(sk_c10) = sk_c9
| identity = sk_c10
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_195]) ).
cnf(c_0_199,negated_conjecture,
( inverse(sk_c10) = sk_c7
| identity = sk_c10
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_196]) ).
cnf(c_0_200,negated_conjecture,
( identity = sk_c10
| sk_c10 = sk_c11
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_195,c_0_197]) ).
cnf(c_0_201,negated_conjecture,
( sk_c10 = sk_c11
| identity = sk_c10
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_202,negated_conjecture,
( inverse(sk_c8) = sk_c9
| inverse(sk_c11) = sk_c2 ),
inference(spm,[status(thm)],[c_0_47,c_0_88]) ).
cnf(c_0_203,negated_conjecture,
( sk_c8 = sk_c10
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_189,c_0_200]) ).
cnf(c_0_204,negated_conjecture,
( sk_c7 = sk_c9
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_189,c_0_201]) ).
cnf(c_0_205,negated_conjecture,
( inverse(sk_c11) = sk_c2
| inverse(sk_c10) = sk_c9
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
cnf(c_0_206,negated_conjecture,
( multiply(sk_c11,X1) = X1
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_37,c_0_189]) ).
cnf(c_0_207,negated_conjecture,
( inverse(sk_c11) = sk_c2
| inverse(sk_c9) = sk_c11
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_136,c_0_204]) ).
cnf(c_0_208,negated_conjecture,
( inverse(sk_c11) = sk_c2
| inverse(sk_c9) = sk_c10
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_205]) ).
cnf(c_0_209,negated_conjecture,
( multiply(inverse(sk_c11),X1) = X1
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_206]) ).
cnf(c_0_210,negated_conjecture,
( inverse(sk_c11) = sk_c2
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_207,c_0_208]) ).
cnf(c_0_211,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c11,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_132]) ).
cnf(c_0_212,negated_conjecture,
( multiply(sk_c2,X1) = X1
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_213,negated_conjecture,
( multiply(sk_c11,sk_c7) = identity
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_214,negated_conjecture,
( sk_c10 = sk_c11
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_206,c_0_213]) ).
cnf(c_0_215,negated_conjecture,
( sk_c7 = sk_c11
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_189,c_0_214]) ).
cnf(c_0_216,negated_conjecture,
( multiply(sk_c2,multiply(sk_c11,X1)) = multiply(sk_c10,X1)
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_35,c_0_87]) ).
cnf(c_0_217,negated_conjecture,
( sk_c10 = sk_c11
| identity = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_215]),c_0_36])]) ).
cnf(c_0_218,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c2
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_101]),c_0_43]) ).
cnf(c_0_219,negated_conjecture,
sk_c10 = sk_c11,
inference(spm,[status(thm)],[c_0_189,c_0_217]) ).
cnf(c_0_220,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c2
| identity = sk_c11 ),
inference(rw,[status(thm)],[c_0_218,c_0_219]) ).
cnf(c_0_221,negated_conjecture,
( inverse(sk_c11) = sk_c2
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_101]),c_0_43]) ).
cnf(c_0_222,negated_conjecture,
( identity = sk_c11
| identity = sk_c2 ),
inference(spm,[status(thm)],[c_0_101,c_0_220]) ).
cnf(c_0_223,negated_conjecture,
( inverse(sk_c2) = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_221]) ).
cnf(c_0_224,negated_conjecture,
( inverse(sk_c2) = sk_c2
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_110,c_0_222]) ).
cnf(c_0_225,negated_conjecture,
( identity = sk_c11
| sk_c2 != sk_c11 ),
inference(ef,[status(thm)],[c_0_222]) ).
cnf(c_0_226,negated_conjecture,
identity = sk_c11,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_225]) ).
cnf(c_0_227,negated_conjecture,
( multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c10
| multiply(X6,sk_c12) != sk_c11
| inverse(identity) != sk_c11
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12
| inverse(X4) != sk_c12
| inverse(X5) != sk_c11
| inverse(X6) != sk_c12
| sk_c10 != sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_104]),c_0_37]) ).
cnf(c_0_228,plain,
multiply(inverse(X1),X1) = sk_c11,
inference(rw,[status(thm)],[c_0_36,c_0_226]) ).
cnf(c_0_229,plain,
multiply(X1,sk_c11) = X1,
inference(rw,[status(thm)],[c_0_43,c_0_226]) ).
cnf(c_0_230,negated_conjecture,
( multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c10
| multiply(X6,sk_c12) != sk_c11
| inverse(X2) != sk_c11
| inverse(X3) != sk_c12
| inverse(X4) != sk_c12
| inverse(X5) != sk_c11
| inverse(X6) != sk_c12
| identity != sk_c11
| sk_c10 != sk_c11 ),
inference(rw,[status(thm)],[c_0_227,c_0_110]) ).
cnf(c_0_231,plain,
multiply(X1,inverse(X1)) = sk_c11,
inference(spm,[status(thm)],[c_0_228,c_0_47]) ).
cnf(c_0_232,plain,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_226]),c_0_226]) ).
cnf(c_0_233,negated_conjecture,
inverse(sk_c12) = sk_c12,
inference(rw,[status(thm)],[c_0_80,c_0_229]) ).
cnf(c_0_234,negated_conjecture,
( multiply(X1,sk_c12) != sk_c11
| inverse(X2) != sk_c11
| inverse(X1) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_230,c_0_219]),c_0_219]),c_0_219]),c_0_219])]),c_0_229]),c_0_231]),c_0_229]),c_0_229]),c_0_229]),c_0_229]),c_0_226])])])])])]),c_0_232]),c_0_233])]) ).
cnf(c_0_235,negated_conjecture,
inverse(X1) != sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_77]),c_0_233])]) ).
cnf(c_0_236,plain,
$false,
inference(sr,[status(thm)],[c_0_232,c_0_235]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP243-1 : TPTP v9.2.1. Released v2.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon May 4 18:30:41 EDT 2026
% 0.17/0.35 % CPUTime :
% 0.20/0.36 % start to proof: theBenchmark
% 11.69/7.63 % Version : CSE_E---1.7
% 11.69/7.63 % Problem : theBenchmark.p
% 11.69/7.63 % SZS status Unsatisfiable for theBenchmark.p
% 11.69/7.63 % SZS output start CNFRefutation
% See solution above
% 11.69/7.68 % Total time : 5.369s
%------------------------------------------------------------------------------