%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP237-1 : 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 : n014.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 04:24:54 PM UTC 2026
% Result : Unsatisfiable 101.92s 51.19s
% Output : CNFRefutation 102.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 29
% Syntax : Number of clauses : 272 ( 25 unt; 224 nHn; 235 RR)
% Number of literals : 623 ( 622 equ; 109 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 87 ( 3 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,
( inverse(sk_c9) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c9,X2) != sk_c8
| multiply(X3,sk_c9) != X2
| inverse(X3) != sk_c9
| multiply(X4,X5) != sk_c9
| inverse(X4) != X5
| multiply(X5,sk_c8) != sk_c9
| multiply(sk_c9,X6) != sk_c8
| multiply(X7,sk_c9) != X6
| inverse(X7) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(c_0_29,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_30,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_31,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_32,negated_conjecture,
( inverse(sk_c9) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c9,X2) != sk_c8
| multiply(X3,sk_c9) != X2
| inverse(X3) != sk_c9
| multiply(X4,X5) != sk_c9
| inverse(X4) != X5
| multiply(X5,sk_c8) != sk_c9
| multiply(sk_c9,X6) != sk_c8
| multiply(X7,sk_c9) != X6
| inverse(X7) != sk_c9 ),
prove_this_37 ).
cnf(c_0_33,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c4,sk_c5) = sk_c9 ),
prove_this_19 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c7) = sk_c8 ),
prove_this_28 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(X2,sk_c9)) != sk_c8
| multiply(inverse(X3),sk_c8) != sk_c9
| multiply(X3,inverse(X3)) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| inverse(X4) != sk_c9 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_32])])]) ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
prove_this_4 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
prove_this_16 ).
cnf(c_0_39,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c5 ),
prove_this_20 ).
cnf(c_0_41,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
prove_this_34 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
prove_this_23 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(X2,sk_c9)) != sk_c8
| multiply(inverse(X3),sk_c8) != sk_c9
| multiply(X3,inverse(X3)) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| inverse(X4) != sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
prove_this_22 ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c4,multiply(sk_c5,X1)) = multiply(sk_c9,X1)
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c5 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c6) = sk_c9 ),
prove_this_24 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X3) != sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_42]),c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( multiply(inverse(inverse(sk_c1)),sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
prove_this_10 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c4,sk_c5) = multiply(sk_c9,sk_c9)
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_45,c_0_49]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_35]),c_0_42]),c_0_45]) ).
cnf(c_0_59,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_46,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_34,c_0_55]) ).
cnf(c_0_62,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_33,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c3
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_33,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,inverse(sk_c9)) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c3
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_33,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| sk_c8 = sk_c9
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9 ),
inference(spm,[status(thm)],[c_0_64,c_0_37]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c9
| multiply(sk_c9,sk_c9) = sk_c8
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
( sk_c3 = sk_c7
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_56,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_54]),c_0_38]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c9
| sk_c3 = sk_c7 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_69]),c_0_70]) ).
cnf(c_0_73,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(spm,[status(thm)],[c_0_33,c_0_71]) ).
cnf(c_0_74,negated_conjecture,
( sk_c3 = sk_c7
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_72]),c_0_30]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| sk_c3 = sk_c7
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(spm,[status(thm)],[c_0_63,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c9,X1) = X1
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_31,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| sk_c3 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_70]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c9,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_71]) ).
cnf(c_0_79,negated_conjecture,
( sk_c3 = sk_c7
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_77]),c_0_30]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c7,X1) = multiply(sk_c8,X1)
| sk_c3 = sk_c7
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(spm,[status(thm)],[c_0_76,c_0_78]) ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
prove_this_12 ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c7,X1) = X1
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_31,c_0_79]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c7,X1) = multiply(sk_c8,X1)
| sk_c3 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_76]),c_0_70]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c8,X1) = X1
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_84]) ).
cnf(c_0_87,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_33]) ).
cnf(c_0_88,negated_conjecture,
( multiply(inverse(sk_c8),X1) = X1
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c9,sk_c6) = identity
| sk_c3 = sk_c7
| identity = sk_c1 ),
inference(spm,[status(thm)],[c_0_76,c_0_86]) ).
cnf(c_0_90,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( sk_c3 = sk_c7
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( identity = sk_c1
| sk_c3 = sk_c7
| identity = sk_c6 ),
inference(spm,[status(thm)],[c_0_76,c_0_89]) ).
cnf(c_0_93,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c9 ),
prove_this_36 ).
cnf(c_0_94,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_90]),c_0_90]) ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
prove_this_6 ).
cnf(c_0_96,negated_conjecture,
( identity = sk_c6
| sk_c1 = sk_c8
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c9,sk_c2) = identity
| inverse(sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
prove_this_35 ).
cnf(c_0_99,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( sk_c1 = sk_c8
| sk_c6 = sk_c8
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_91,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c9) = sk_c1 ),
inference(spm,[status(thm)],[c_0_94,c_0_81]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c9,multiply(sk_c6,X1)) = X1
| multiply(sk_c9,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_33,c_0_97]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_98]) ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
prove_this_11 ).
cnf(c_0_105,negated_conjecture,
( inverse(sk_c9) = sk_c8
| sk_c6 != sk_c8 ),
inference(ef,[status(thm)],[c_0_99]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c1 ),
inference(spm,[status(thm)],[c_0_94,c_0_54]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c6 = sk_c8
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_45,c_0_100]) ).
cnf(c_0_108,negated_conjecture,
( inverse(sk_c9) = sk_c1
| inverse(sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_94,c_0_101]) ).
cnf(c_0_109,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c5 ),
prove_this_8 ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_42]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c9,sk_c2) = identity
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c9,multiply(sk_c6,X1)) = X1
| multiply(sk_c9,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_33,c_0_84]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_104]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c1 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_115,negated_conjecture,
( inverse(sk_c9) = sk_c6
| sk_c1 != sk_c6 ),
inference(ef,[status(thm)],[c_0_108]) ).
cnf(c_0_116,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c4) = sk_c5 ),
prove_this_2 ).
cnf(c_0_117,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c9) = sk_c1 ),
inference(spm,[status(thm)],[c_0_94,c_0_109]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c9,sk_c2) = identity
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_54]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_121,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_114]) ).
cnf(c_0_122,negated_conjecture,
( inverse(sk_c9) = sk_c6
| sk_c1 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_108]),c_0_115]) ).
cnf(c_0_123,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
prove_this_5 ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c9) = sk_c1 ),
inference(spm,[status(thm)],[c_0_94,c_0_104]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c6) = sk_c9 ),
prove_this_30 ).
cnf(c_0_126,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
prove_this_7 ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c5,sk_c4) = identity
| inverse(sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_116]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c5,sk_c4) = identity
| inverse(sk_c9) = sk_c1 ),
inference(spm,[status(thm)],[c_0_30,c_0_117]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c6,sk_c9) = sk_c7 ),
prove_this_29 ).
cnf(c_0_130,negated_conjecture,
( inverse(sk_c9) = sk_c2
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_118]),c_0_90]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c9,sk_c1) = identity
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_125]) ).
cnf(c_0_135,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c4,sk_c5) = sk_c9 ),
prove_this_1 ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c9) = sk_c1 ),
inference(spm,[status(thm)],[c_0_94,c_0_126]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c5,sk_c4) = identity
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_138,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_129]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_62,c_0_130]) ).
cnf(c_0_140,negated_conjecture,
( inverse(sk_c9) = sk_c1
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_131]),c_0_90]) ).
cnf(c_0_141,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_132]) ).
cnf(c_0_142,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c9
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_133]) ).
cnf(c_0_143,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_33,c_0_134]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_145,negated_conjecture,
( inverse(sk_c5) = sk_c4
| sk_c1 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_137]),c_0_90]) ).
cnf(c_0_146,negated_conjecture,
( inverse(sk_c6) = sk_c9
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_94,c_0_122]) ).
cnf(c_0_147,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_138,c_0_70]) ).
cnf(c_0_148,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_33,c_0_139]) ).
cnf(c_0_149,negated_conjecture,
( inverse(sk_c1) = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_94,c_0_140]) ).
cnf(c_0_150,negated_conjecture,
( sk_c1 = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_151,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c9
| multiply(sk_c9,sk_c6) = identity
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_143,c_0_70]) ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c3 = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_60,c_0_76]) ).
cnf(c_0_153,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c5
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_144]) ).
cnf(c_0_154,negated_conjecture,
( inverse(sk_c4) = sk_c5
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_94,c_0_145]) ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_142,c_0_146]) ).
cnf(c_0_156,negated_conjecture,
( multiply(sk_c6,sk_c9) = identity
| sk_c1 != sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_115]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_158,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_159,negated_conjecture,
( multiply(sk_c9,sk_c6) = identity
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_151,c_0_148]) ).
cnf(c_0_160,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c9
| sk_c7 = sk_c8
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_152]) ).
cnf(c_0_161,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c5
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_162,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_30,c_0_90]) ).
cnf(c_0_163,negated_conjecture,
( sk_c1 = sk_c8
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_155]),c_0_30]) ).
cnf(c_0_164,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_30,c_0_94]) ).
cnf(c_0_165,negated_conjecture,
( sk_c8 = sk_c9
| identity = sk_c7
| sk_c1 != sk_c6 ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_166,negated_conjecture,
( inverse(sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_94,c_0_158]) ).
cnf(c_0_167,negated_conjecture,
( inverse(sk_c9) = sk_c6
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_159]),c_0_90]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c3 = sk_c7
| sk_c7 = sk_c8
| multiply(sk_c9,inverse(sk_c9)) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9 ),
inference(spm,[status(thm)],[c_0_58,c_0_160]) ).
cnf(c_0_169,negated_conjecture,
( sk_c1 = sk_c8
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_161]),c_0_30]) ).
cnf(c_0_170,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_171,negated_conjecture,
( multiply(inverse(sk_c9),multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_62]) ).
cnf(c_0_172,negated_conjecture,
( multiply(sk_c8,sk_c9) = identity
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_164,c_0_158]) ).
cnf(c_0_173,negated_conjecture,
( identity = sk_c7
| sk_c8 = sk_c9
| sk_c6 != sk_c8 ),
inference(spm,[status(thm)],[c_0_165,c_0_150]) ).
cnf(c_0_174,negated_conjecture,
( sk_c8 = sk_c9
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c7 = sk_c8
| sk_c3 = sk_c7
| multiply(X1,sk_c8) != sk_c9
| inverse(sk_c9) != sk_c9
| inverse(X1) != sk_c9 ),
inference(spm,[status(thm)],[c_0_168,c_0_76]) ).
cnf(c_0_176,negated_conjecture,
( sk_c7 = sk_c9
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_163,c_0_169]) ).
cnf(c_0_177,negated_conjecture,
( multiply(sk_c7,sk_c7) = identity
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_170]) ).
cnf(c_0_178,negated_conjecture,
( inverse(sk_c9) = multiply(sk_c7,sk_c9)
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_90]) ).
cnf(c_0_179,negated_conjecture,
( sk_c8 = sk_c9
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c3 = sk_c7
| sk_c7 = sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_37]),c_0_56]) ).
cnf(c_0_181,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_60,c_0_176]) ).
cnf(c_0_182,negated_conjecture,
( multiply(sk_c9,sk_c9) = identity
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_177,c_0_176]) ).
cnf(c_0_183,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
prove_this_17 ).
cnf(c_0_184,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_185,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_49]),c_0_30]) ).
cnf(c_0_186,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_166,c_0_178]) ).
cnf(c_0_187,negated_conjecture,
( multiply(sk_c7,X1) = X1
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_31,c_0_179]) ).
cnf(c_0_188,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c7 = sk_c8
| sk_c3 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_38]),c_0_54]) ).
cnf(c_0_189,negated_conjecture,
( sk_c1 = sk_c8
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_190,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_183]) ).
cnf(c_0_191,negated_conjecture,
( multiply(inverse(multiply(X1,sk_c9)),multiply(X1,sk_c8)) = sk_c7
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_192,negated_conjecture,
sk_c8 = sk_c9,
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_193,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_33,c_0_185]) ).
cnf(c_0_194,negated_conjecture,
( sk_c3 = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_76,c_0_188]) ).
cnf(c_0_195,negated_conjecture,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_30,c_0_109]) ).
cnf(c_0_196,negated_conjecture,
( sk_c7 = sk_c8
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_163,c_0_189]) ).
cnf(c_0_197,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_190,c_0_104]) ).
cnf(c_0_198,negated_conjecture,
( identity = sk_c3
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_191,c_0_192]),c_0_30]) ).
cnf(c_0_199,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(sk_c2,sk_c9) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9 ),
inference(spm,[status(thm)],[c_0_58,c_0_42]) ).
cnf(c_0_200,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| identity = sk_c3
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_193,c_0_63]) ).
cnf(c_0_201,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_45,c_0_194]) ).
cnf(c_0_202,negated_conjecture,
( multiply(sk_c5,multiply(sk_c4,X1)) = X1
| multiply(sk_c9,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_33,c_0_195]) ).
cnf(c_0_203,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_126]) ).
cnf(c_0_204,negated_conjecture,
( multiply(inverse(sk_c9),multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_73]) ).
cnf(c_0_205,negated_conjecture,
( multiply(sk_c8,sk_c8) = identity
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_177,c_0_196]) ).
cnf(c_0_206,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_155,c_0_196]) ).
cnf(c_0_207,negated_conjecture,
( multiply(sk_c6,multiply(sk_c9,X1)) = multiply(sk_c7,X1)
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_29,c_0_197]) ).
cnf(c_0_208,negated_conjecture,
identity = sk_c7,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_198]),c_0_79]) ).
cnf(c_0_209,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(sk_c2,sk_c9) != sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_54]),c_0_38]) ).
cnf(c_0_210,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c9,sk_c9) = sk_c8
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_65,c_0_63]) ).
cnf(c_0_211,negated_conjecture,
( sk_c3 = sk_c7
| identity = sk_c3
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_200]),c_0_30]) ).
cnf(c_0_212,negated_conjecture,
( multiply(inverse(multiply(X1,sk_c9)),multiply(X1,sk_c8)) = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_184,c_0_201]) ).
cnf(c_0_213,negated_conjecture,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c5,sk_c9) = sk_c5 ),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
cnf(c_0_214,negated_conjecture,
( inverse(sk_c9) = multiply(sk_c7,sk_c8)
| sk_c1 = sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_90]),c_0_206]) ).
cnf(c_0_215,negated_conjecture,
( multiply(inverse(sk_c1),multiply(sk_c9,X1)) = multiply(sk_c8,X1)
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_29,c_0_190]) ).
cnf(c_0_216,negated_conjecture,
( multiply(sk_c7,sk_c7) = multiply(sk_c6,sk_c8)
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_207,c_0_60]) ).
cnf(c_0_217,plain,
multiply(X1,sk_c7) = X1,
inference(rw,[status(thm)],[c_0_90,c_0_208]) ).
cnf(c_0_218,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c8) != sk_c9
| sk_c3 != sk_c9 ),
inference(spm,[status(thm)],[c_0_209,c_0_35]) ).
cnf(c_0_219,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c3 = sk_c7
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_210,c_0_76]) ).
cnf(c_0_220,negated_conjecture,
( identity = sk_c7
| sk_c3 = sk_c9
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_74,c_0_211]) ).
cnf(c_0_221,negated_conjecture,
( multiply(sk_c9,sk_c1) = identity
| sk_c7 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_33])]) ).
cnf(c_0_222,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_122,c_0_214]) ).
cnf(c_0_223,negated_conjecture,
( multiply(inverse(sk_c1),multiply(sk_c8,X1)) = multiply(sk_c8,multiply(sk_c7,X1))
| multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(spm,[status(thm)],[c_0_215,c_0_78]) ).
cnf(c_0_224,plain,
multiply(sk_c7,X1) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_208]) ).
cnf(c_0_225,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_216,c_0_192]),c_0_192]),c_0_217]) ).
cnf(c_0_226,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| multiply(sk_c9,sk_c8) != sk_c9
| sk_c3 != sk_c9 ),
inference(spm,[status(thm)],[c_0_33,c_0_218]) ).
cnf(c_0_227,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c9
| sk_c7 = sk_c9
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_219]) ).
cnf(c_0_228,negated_conjecture,
( sk_c3 = sk_c9
| sk_c7 = sk_c9
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_74,c_0_220]) ).
cnf(c_0_229,negated_conjecture,
( inverse(sk_c9) = sk_c1
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_221]),c_0_90]) ).
cnf(c_0_230,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c8
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_114,c_0_196]) ).
cnf(c_0_231,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c6
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_222,c_0_176]) ).
cnf(c_0_232,negated_conjecture,
( multiply(inverse(sk_c1),multiply(sk_c9,X1)) = multiply(sk_c9,X1)
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_223,c_0_192]),c_0_192]),c_0_192]),c_0_224]),c_0_225]) ).
cnf(c_0_233,plain,
multiply(X1,inverse(X1)) = sk_c7,
inference(rw,[status(thm)],[c_0_164,c_0_208]) ).
cnf(c_0_234,negated_conjecture,
( sk_c3 = sk_c7
| sk_c7 = sk_c9
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_228]) ).
cnf(c_0_235,negated_conjecture,
( inverse(sk_c1) = sk_c9
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_94,c_0_229]) ).
cnf(c_0_236,negated_conjecture,
( sk_c1 = sk_c8
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_237,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c6 != sk_c8 ),
inference(spm,[status(thm)],[c_0_94,c_0_105]) ).
cnf(c_0_238,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_217]) ).
cnf(c_0_239,plain,
inverse(sk_c7) = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_208]),c_0_208]) ).
cnf(c_0_240,negated_conjecture,
( sk_c7 = sk_c9
| sk_c3 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_76]),c_0_70]) ).
cnf(c_0_241,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c5 ),
prove_this_14 ).
cnf(c_0_242,negated_conjecture,
( inverse(sk_c8) = sk_c9
| sk_c7 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_237]) ).
cnf(c_0_243,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| sk_c7 = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_238]),c_0_239]) ).
cnf(c_0_244,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_45,c_0_240]) ).
cnf(c_0_245,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_201]) ).
cnf(c_0_246,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_94,c_0_241]) ).
cnf(c_0_247,negated_conjecture,
( inverse(sk_c9) = sk_c8
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_94,c_0_242]) ).
cnf(c_0_248,negated_conjecture,
( inverse(sk_c6) = sk_c9
| sk_c7 = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_243]),c_0_217]) ).
cnf(c_0_249,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_33,c_0_244]) ).
cnf(c_0_250,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_245,c_0_229]) ).
cnf(c_0_251,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_246]) ).
cnf(c_0_252,negated_conjecture,
( inverse(sk_c9) = sk_c9
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_247,c_0_192]),c_0_192]) ).
cnf(c_0_253,negated_conjecture,
( inverse(sk_c9) = sk_c6
| sk_c7 = sk_c1 ),
inference(spm,[status(thm)],[c_0_94,c_0_248]) ).
cnf(c_0_254,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
prove_this_13 ).
cnf(c_0_255,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_249,c_0_136]) ).
cnf(c_0_256,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c7
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_192]),c_0_192]) ).
cnf(c_0_257,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_251,c_0_192]),c_0_208]) ).
cnf(c_0_258,negated_conjecture,
( sk_c7 = sk_c1
| sk_c7 = sk_c9
| sk_c6 = sk_c9 ),
inference(spm,[status(thm)],[c_0_252,c_0_253]) ).
cnf(c_0_259,negated_conjecture,
( sk_c1 = sk_c9
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_192]),c_0_192]) ).
cnf(c_0_260,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_254,c_0_255]) ).
cnf(c_0_261,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_256,c_0_257]) ).
cnf(c_0_262,negated_conjecture,
( multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(X2,sk_c9)) != sk_c8
| multiply(inverse(X3),sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| inverse(X4) != sk_c9
| identity != sk_c9 ),
inference(rw,[status(thm)],[c_0_36,c_0_164]) ).
cnf(c_0_263,negated_conjecture,
( sk_c6 = sk_c9
| sk_c7 = sk_c9 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_258]),c_0_259]) ).
cnf(c_0_264,negated_conjecture,
( inverse(sk_c9) = sk_c9
| sk_c6 != sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_192]),c_0_192]) ).
cnf(c_0_265,negated_conjecture,
sk_c7 = sk_c9,
inference(spm,[status(thm)],[c_0_260,c_0_261]) ).
cnf(c_0_266,negated_conjecture,
( multiply(sk_c9,multiply(X1,sk_c9)) != sk_c9
| multiply(sk_c9,multiply(X2,sk_c9)) != sk_c9
| multiply(inverse(X3),sk_c9) != sk_c9
| multiply(X4,sk_c9) != sk_c9
| inverse(sk_c9) != sk_c9
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| inverse(X4) != sk_c9
| sk_c7 != sk_c9 ),
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_262,c_0_192]),c_0_192]),c_0_192]),c_0_192]),c_0_192]),c_0_208]) ).
cnf(c_0_267,negated_conjecture,
inverse(sk_c9) = sk_c9,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_263]),c_0_264]) ).
cnf(c_0_268,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_224,c_0_265]) ).
cnf(c_0_269,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_217,c_0_265]) ).
cnf(c_0_270,negated_conjecture,
inverse(X1) != sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_266,c_0_267])]),c_0_268]),c_0_269]),c_0_268]),c_0_269]),c_0_269]),c_0_269]),c_0_265])])])])]),c_0_267])]) ).
cnf(c_0_271,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_81,c_0_270]),c_0_270]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP237-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n014.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 18:30:36 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 101.92/51.19 % Version : CSE_E---1.7
% 101.92/51.19 % Problem : theBenchmark.p
% 101.92/51.19 % SZS status Unsatisfiable for theBenchmark.p
% 101.92/51.19 % SZS output start CNFRefutation
% See solution above
% 102.30/51.59 % Total time : 36.925s
%------------------------------------------------------------------------------