%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP305-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:39:14 PM UTC 2026
% Result : Unsatisfiable 1.95s 0.69s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 24
% Syntax : Number of clauses : 208 ( 25 unt; 159 nHn; 186 RR)
% Number of literals : 484 ( 483 equ; 102 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c3) = sk_c5
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_26,negated_conjecture,
( multiply(X3,sk_c4) != sk_c5
| inverse(X3) != sk_c5
| multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c4
| inverse(sk_c6) != sk_c4
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c3) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(c_0_24,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_25,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_26,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_27,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c4 ),
prove_this_5 ).
cnf(c_0_29,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(inverse(sk_c3),sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c4 ),
prove_this_4 ).
cnf(c_0_32,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c4 ),
prove_this_1 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c5,sk_c5) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
prove_this_22 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(inverse(sk_c5),sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(inverse(sk_c5),sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c6) = sk_c1
| inverse(sk_c2) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c3) = sk_c5
| inverse(sk_c6) = sk_c4 ),
prove_this_14 ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c4 ),
prove_this_12 ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c6) = sk_c2
| inverse(sk_c6) = sk_c1 ),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( sk_c5 = sk_c6
| multiply(inverse(sk_c6),sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c6) = sk_c4 ),
prove_this_11 ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c6) = sk_c4
| multiply(sk_c5,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( multiply(X3,sk_c4) != sk_c5
| inverse(X3) != sk_c5
| multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c4
| inverse(sk_c6) != sk_c4
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c4 ),
inference(fof_simplification,[status(thm)],[prove_this_26]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c6) = sk_c2
| inverse(sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( sk_c1 != sk_c2
| inverse(sk_c6) = sk_c2 ),
inference(ef,[status(thm)],[c_0_43]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
prove_this_7 ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
prove_this_2 ).
cnf(c_0_52,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c4,sk_c4) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c4,sk_c4) = sk_c5
| multiply(sk_c5,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_44,c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
prove_this_21 ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c3) = sk_c5
| inverse(sk_c1) = sk_c6 ),
prove_this_24 ).
cnf(c_0_56,negated_conjecture,
( multiply(X3,sk_c4) != sk_c5
| inverse(X3) != sk_c5
| multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c4
| inverse(sk_c6) != sk_c4
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c4 ),
c_0_47 ).
cnf(c_0_57,negated_conjecture,
( sk_c1 = sk_c4
| inverse(sk_c6) = sk_c2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_43]),c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c6) = sk_c2
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_50]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c6) = sk_c2
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
prove_this_8 ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c6) = sk_c4 ),
prove_this_15 ).
cnf(c_0_62,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c4,sk_c4) = sk_c5
| multiply(inverse(sk_c5),sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_52]) ).
cnf(c_0_63,negated_conjecture,
( sk_c5 = sk_c6
| inverse(sk_c5) = sk_c3
| multiply(sk_c4,sk_c4) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_53]),c_0_32]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_25,c_0_54]) ).
cnf(c_0_65,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c6,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_55]) ).
cnf(c_0_66,negated_conjecture,
( inverse(X3) != sk_c6
| inverse(X2) != sk_c6
| inverse(X1) != sk_c5
| multiply(X3,sk_c6) != sk_c4
| multiply(X2,sk_c5) != sk_c6
| multiply(X1,sk_c4) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c4
| inverse(sk_c6) = sk_c2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_43]),c_0_57]),c_0_58]),c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c5,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_46]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(inverse(sk_c2),sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_60]) ).
cnf(c_0_70,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c4,sk_c4) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_44,c_0_61]) ).
cnf(c_0_71,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c4,sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
prove_this_25 ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c6,sk_c1) = identity
| multiply(inverse(sk_c5),sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
( inverse(sk_c5) = sk_c3
| multiply(sk_c6,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_65]) ).
cnf(c_0_75,negated_conjecture,
( inverse(X3) != sk_c6
| inverse(X2) != sk_c6
| inverse(X1) != sk_c5
| multiply(X3,sk_c6) != sk_c4
| multiply(X2,sk_c5) != sk_c6
| multiply(X1,sk_c4) != sk_c5
| inverse(sk_c6) = sk_c2
| multiply(sk_c4,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_25,c_0_61]) ).
cnf(c_0_77,negated_conjecture,
( inverse(sk_c5) = sk_c3
| multiply(sk_c4,sk_c6) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_68]),c_0_32]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(inverse(inverse(sk_c2)),sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_69]) ).
cnf(c_0_79,negated_conjecture,
( sk_c5 = sk_c6
| multiply(inverse(sk_c6),multiply(sk_c4,X1)) = multiply(sk_c5,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_80,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c4,sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_25,c_0_72]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c6,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
( inverse(X2) != sk_c6
| inverse(X1) != sk_c6
| inverse(sk_c3) != sk_c5
| multiply(X2,sk_c6) != sk_c4
| multiply(X1,sk_c5) != sk_c6
| inverse(sk_c6) = sk_c2
| multiply(sk_c4,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c4,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(inverse(sk_c6),sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_78,c_0_50]) ).
cnf(c_0_86,negated_conjecture,
( sk_c5 = sk_c6
| multiply(inverse(sk_c6),sk_c5) = multiply(sk_c5,sk_c4) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_87,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c6,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c4 ),
prove_this_17 ).
cnf(c_0_89,negated_conjecture,
( inverse(X2) != sk_c6
| inverse(X1) != sk_c6
| multiply(X2,sk_c6) != sk_c4
| multiply(X1,sk_c5) != sk_c6
| inverse(sk_c6) = sk_c2
| multiply(sk_c4,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_90,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( sk_c5 = sk_c6
| inverse(sk_c6) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_87]),c_0_32]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c6) = sk_c2
| multiply(sk_c1,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_35,c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c4
| sk_c5 = sk_c6
| inverse(sk_c6) = sk_c2
| multiply(sk_c4,sk_c6) = identity ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_86]),c_0_35])]),c_0_90]) ).
cnf(c_0_94,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c1,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_91]) ).
cnf(c_0_95,negated_conjecture,
( sk_c1 = sk_c2
| sk_c5 = sk_c6
| multiply(sk_c1,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_92,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c6) = sk_c1
| inverse(sk_c3) = sk_c5 ),
inference(spm,[status(thm)],[c_0_35,c_0_55]) ).
cnf(c_0_97,negated_conjecture,
( identity != sk_c4
| sk_c5 = sk_c6
| inverse(sk_c6) = sk_c2
| multiply(sk_c4,sk_c6) = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_25]),c_0_35])]) ).
cnf(c_0_98,negated_conjecture,
( identity = sk_c4
| sk_c5 = sk_c6
| sk_c1 = sk_c2 ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
( inverse(sk_c6) = sk_c1
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_35,c_0_54]) ).
cnf(c_0_100,negated_conjecture,
( inverse(sk_c6) = sk_c1
| multiply(sk_c5,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c6,multiply(sk_c5,X1)) = multiply(sk_c4,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_40]) ).
cnf(c_0_102,negated_conjecture,
( sk_c5 = sk_c6
| inverse(sk_c6) = sk_c2
| multiply(sk_c4,sk_c6) = sk_c4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_49]) ).
cnf(c_0_103,negated_conjecture,
( sk_c1 = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_45,c_0_99]) ).
cnf(c_0_104,negated_conjecture,
( sk_c1 = sk_c4
| multiply(sk_c5,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_46,c_0_100]) ).
cnf(c_0_105,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c4,sk_c4) = multiply(sk_c6,sk_c6) ),
inference(spm,[status(thm)],[c_0_101,c_0_90]) ).
cnf(c_0_106,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_107,negated_conjecture,
( sk_c1 = sk_c2
| sk_c5 = sk_c6
| multiply(sk_c4,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_91,c_0_102]) ).
cnf(c_0_108,negated_conjecture,
( inverse(sk_c6) = sk_c1
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_35,c_0_72]) ).
cnf(c_0_109,negated_conjecture,
( sk_c1 = sk_c4
| multiply(inverse(sk_c5),sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( sk_c1 = sk_c4
| inverse(sk_c5) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_104]),c_0_32]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_69,c_0_50]) ).
cnf(c_0_112,negated_conjecture,
( sk_c2 != sk_c4
| inverse(sk_c6) = sk_c4 ),
inference(ef,[status(thm)],[c_0_48]) ).
cnf(c_0_113,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_80,c_0_105]) ).
cnf(c_0_114,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_106,c_0_32]) ).
cnf(c_0_115,negated_conjecture,
( identity = sk_c6
| sk_c5 = sk_c6
| sk_c1 = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_107]),c_0_25]) ).
cnf(c_0_116,negated_conjecture,
( sk_c1 = sk_c4
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_61,c_0_108]) ).
cnf(c_0_117,negated_conjecture,
( sk_c1 = sk_c4
| multiply(sk_c3,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c5,multiply(sk_c4,X1)) = multiply(sk_c6,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_111]) ).
cnf(c_0_119,negated_conjecture,
( sk_c2 != sk_c4
| multiply(sk_c4,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_112]) ).
cnf(c_0_120,negated_conjecture,
( sk_c5 = sk_c6
| multiply(inverse(sk_c6),sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_113]) ).
cnf(c_0_121,negated_conjecture,
( sk_c1 = sk_c2
| sk_c5 = sk_c6
| inverse(sk_c6) = sk_c6 ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_122,negated_conjecture,
( sk_c5 = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_91]) ).
cnf(c_0_123,negated_conjecture,
( sk_c5 = sk_c6
| sk_c1 = sk_c4 ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_124,negated_conjecture,
( sk_c2 != sk_c4
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_32])]) ).
cnf(c_0_125,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_120,c_0_91]) ).
cnf(c_0_126,negated_conjecture,
( sk_c1 = sk_c6
| sk_c5 = sk_c6
| sk_c1 = sk_c2 ),
inference(spm,[status(thm)],[c_0_91,c_0_121]) ).
cnf(c_0_127,negated_conjecture,
( sk_c5 = sk_c6
| inverse(sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_128,negated_conjecture,
( sk_c2 != sk_c4
| multiply(inverse(sk_c6),sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
( sk_c5 = sk_c6
| multiply(inverse(sk_c1),sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_125]) ).
cnf(c_0_130,negated_conjecture,
( sk_c2 = sk_c4
| sk_c5 = sk_c6
| sk_c1 = sk_c6 ),
inference(spm,[status(thm)],[c_0_123,c_0_126]) ).
cnf(c_0_131,negated_conjecture,
( sk_c5 = sk_c6
| inverse(sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_35,c_0_127]) ).
cnf(c_0_132,negated_conjecture,
( sk_c2 != sk_c4
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_128,c_0_112]) ).
cnf(c_0_133,negated_conjecture,
( identity = sk_c5
| sk_c5 = sk_c6
| sk_c2 = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_25]) ).
cnf(c_0_134,negated_conjecture,
( sk_c1 != sk_c2
| sk_c2 = sk_c4
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_49,c_0_131]) ).
cnf(c_0_135,negated_conjecture,
( sk_c2 != sk_c4
| sk_c5 = sk_c6
| multiply(sk_c5,sk_c5) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_132]),c_0_25]) ).
cnf(c_0_136,negated_conjecture,
( sk_c5 = sk_c6
| sk_c2 = sk_c4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_133]),c_0_134]) ).
cnf(c_0_137,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c4 ),
prove_this_19 ).
cnf(c_0_138,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c5,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c4 ),
prove_this_20 ).
cnf(c_0_140,negated_conjecture,
( inverse(sk_c5) = sk_c3
| multiply(sk_c1,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_35,c_0_137]) ).
cnf(c_0_141,negated_conjecture,
( sk_c5 = sk_c6
| inverse(sk_c5) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_138]),c_0_32]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(inverse(sk_c1),sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_139]) ).
cnf(c_0_143,negated_conjecture,
( sk_c3 = sk_c5
| sk_c5 = sk_c6
| multiply(sk_c1,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(inverse(inverse(sk_c1)),sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_27,c_0_142]) ).
cnf(c_0_145,negated_conjecture,
( identity = sk_c4
| sk_c5 = sk_c6
| sk_c3 = sk_c5 ),
inference(spm,[status(thm)],[c_0_94,c_0_143]) ).
cnf(c_0_146,negated_conjecture,
( identity = sk_c4
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_72]),c_0_25]) ).
cnf(c_0_147,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_120,c_0_131]) ).
cnf(c_0_148,negated_conjecture,
( sk_c3 = sk_c5
| sk_c5 = sk_c6
| multiply(sk_c4,X1) = X1 ),
inference(spm,[status(thm)],[c_0_26,c_0_145]) ).
cnf(c_0_149,negated_conjecture,
( identity = sk_c4
| multiply(inverse(sk_c3),sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_27,c_0_146]) ).
cnf(c_0_150,negated_conjecture,
( sk_c5 = sk_c6
| sk_c3 = sk_c5 ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_151,negated_conjecture,
( identity = sk_c4
| sk_c5 = sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_25])]) ).
cnf(c_0_152,negated_conjecture,
( sk_c5 = sk_c6
| multiply(sk_c4,X1) = X1 ),
inference(spm,[status(thm)],[c_0_26,c_0_151]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
prove_this_3 ).
cnf(c_0_154,negated_conjecture,
sk_c5 = sk_c6,
inference(spm,[status(thm)],[c_0_147,c_0_152]) ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c2,multiply(sk_c5,X1)) = multiply(sk_c6,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_153]) ).
cnf(c_0_156,negated_conjecture,
( identity = sk_c6
| multiply(sk_c6,sk_c4) = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_154]),c_0_25]),c_0_154]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c2,sk_c4) = multiply(sk_c6,sk_c5) ),
inference(spm,[status(thm)],[c_0_155,c_0_34]) ).
cnf(c_0_158,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c2,sk_c4) = multiply(sk_c6,sk_c6) ),
inference(spm,[status(thm)],[c_0_155,c_0_33]) ).
cnf(c_0_159,negated_conjecture,
( identity = sk_c4
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_156]),c_0_25]) ).
cnf(c_0_160,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
prove_this_9 ).
cnf(c_0_161,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c6,sk_c5) = multiply(sk_c6,sk_c6) ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_162,negated_conjecture,
( sk_c4 != sk_c6
| identity = sk_c6 ),
inference(ef,[status(thm)],[c_0_159]) ).
cnf(c_0_163,negated_conjecture,
( inverse(sk_c5) = sk_c3
| inverse(sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_164,negated_conjecture,
( inverse(sk_c5) = sk_c3
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_160]) ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c6,sk_c6) != sk_c4
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(ef,[status(thm)],[c_0_161]) ).
cnf(c_0_166,negated_conjecture,
( sk_c4 != sk_c6
| inverse(sk_c6) = sk_c6 ),
inference(spm,[status(thm)],[c_0_114,c_0_162]) ).
cnf(c_0_167,negated_conjecture,
multiply(sk_c6,sk_c6) = sk_c4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_154]),c_0_154]),c_0_154])]) ).
cnf(c_0_168,negated_conjecture,
( inverse(sk_c6) = sk_c4
| inverse(sk_c6) = sk_c3 ),
inference(rw,[status(thm)],[c_0_163,c_0_154]) ).
cnf(c_0_169,negated_conjecture,
( inverse(sk_c6) = sk_c2
| multiply(sk_c6,sk_c4) = sk_c6 ),
inference(rw,[status(thm)],[c_0_58,c_0_154]) ).
cnf(c_0_170,negated_conjecture,
( inverse(sk_c6) = sk_c3
| multiply(sk_c6,sk_c4) = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_154]),c_0_154]) ).
cnf(c_0_171,negated_conjecture,
( multiply(sk_c6,sk_c6) != sk_c4
| multiply(inverse(sk_c6),sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_165]) ).
cnf(c_0_172,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(inverse(sk_c5),sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_27,c_0_111]) ).
cnf(c_0_173,negated_conjecture,
( sk_c4 != sk_c6
| identity = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_166]),c_0_167]) ).
cnf(c_0_174,negated_conjecture,
( sk_c3 != sk_c4
| inverse(sk_c6) = sk_c4 ),
inference(ef,[status(thm)],[c_0_168]) ).
cnf(c_0_175,negated_conjecture,
( sk_c3 = sk_c2
| multiply(sk_c6,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_176,negated_conjecture,
( multiply(sk_c6,sk_c6) != sk_c4
| multiply(inverse(inverse(sk_c6)),sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_27,c_0_171]) ).
cnf(c_0_177,negated_conjecture,
identity = sk_c4,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_154]),c_0_25]),c_0_154]),c_0_167]),c_0_173]) ).
cnf(c_0_178,negated_conjecture,
( sk_c3 = sk_c2
| inverse(sk_c6) = sk_c4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_168]),c_0_174]) ).
cnf(c_0_179,negated_conjecture,
( identity = sk_c4
| sk_c3 = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_175]),c_0_25]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c6,sk_c6) != sk_c4
| multiply(sk_c3,sk_c4) = sk_c5
| multiply(inverse(sk_c4),sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_176,c_0_61]) ).
cnf(c_0_181,plain,
inverse(sk_c4) = sk_c4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_177]),c_0_177]) ).
cnf(c_0_182,plain,
multiply(X1,sk_c4) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_177]) ).
cnf(c_0_183,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c6) = sk_c4 ),
prove_this_13 ).
cnf(c_0_184,negated_conjecture,
( sk_c3 = sk_c2
| inverse(sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_178]) ).
cnf(c_0_185,negated_conjecture,
( sk_c3 = sk_c2
| inverse(sk_c4) = sk_c4 ),
inference(spm,[status(thm)],[c_0_114,c_0_179]) ).
cnf(c_0_186,negated_conjecture,
( sk_c3 = sk_c6
| multiply(sk_c4,sk_c6) = sk_c4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_154]),c_0_154]),c_0_181]),c_0_182]),c_0_167])]) ).
cnf(c_0_187,negated_conjecture,
( sk_c2 != sk_c4
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_154]),c_0_25]) ).
cnf(c_0_188,negated_conjecture,
( multiply(sk_c6,sk_c6) != sk_c4
| multiply(sk_c4,sk_c4) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_171,c_0_183]) ).
cnf(c_0_189,negated_conjecture,
( sk_c4 = sk_c6
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_190,negated_conjecture,
( sk_c4 = sk_c6
| sk_c3 = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_186]),c_0_25]),c_0_177]) ).
cnf(c_0_191,negated_conjecture,
( sk_c2 != sk_c4
| inverse(sk_c6) = sk_c6 ),
inference(spm,[status(thm)],[c_0_114,c_0_187]) ).
cnf(c_0_192,negated_conjecture,
( sk_c4 = sk_c6
| multiply(sk_c2,sk_c6) = sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_154]),c_0_154]),c_0_182]),c_0_167])]) ).
cnf(c_0_193,negated_conjecture,
( sk_c2 = sk_c6
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
cnf(c_0_194,negated_conjecture,
( sk_c2 != sk_c4
| identity = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_191]),c_0_167]) ).
cnf(c_0_195,negated_conjecture,
( inverse(sk_c6) = sk_c4
| multiply(sk_c6,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_42]) ).
cnf(c_0_196,plain,
multiply(sk_c4,X1) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_177]) ).
cnf(c_0_197,negated_conjecture,
sk_c4 = sk_c6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_167])]) ).
cnf(c_0_198,negated_conjecture,
multiply(inverse(sk_c6),sk_c4) = sk_c6,
inference(spm,[status(thm)],[c_0_27,c_0_167]) ).
cnf(c_0_199,negated_conjecture,
( sk_c2 != sk_c4
| inverse(X3) != sk_c6
| inverse(X2) != sk_c6
| inverse(X1) != sk_c5
| multiply(X3,sk_c6) != sk_c4
| multiply(X2,sk_c5) != sk_c6
| multiply(X1,sk_c4) != sk_c5
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c5) != sk_c4 ),
inference(spm,[status(thm)],[c_0_56,c_0_112]) ).
cnf(c_0_200,negated_conjecture,
( sk_c2 != sk_c4
| multiply(X1,sk_c4) = X1 ),
inference(spm,[status(thm)],[c_0_32,c_0_194]) ).
cnf(c_0_201,negated_conjecture,
( inverse(X3) != sk_c6
| inverse(X2) != sk_c6
| inverse(X1) != sk_c5
| multiply(X3,sk_c6) != sk_c4
| multiply(X2,sk_c5) != sk_c6
| multiply(X1,sk_c4) != sk_c5
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c5) != sk_c4
| multiply(sk_c6,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_195]) ).
cnf(c_0_202,plain,
multiply(sk_c6,X1) = X1,
inference(rw,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_203,plain,
multiply(X1,sk_c6) = X1,
inference(rw,[status(thm)],[c_0_182,c_0_197]) ).
cnf(c_0_204,negated_conjecture,
inverse(sk_c6) = sk_c6,
inference(rw,[status(thm)],[c_0_198,c_0_182]) ).
cnf(c_0_205,negated_conjecture,
( sk_c2 != sk_c4
| inverse(X3) != sk_c6
| inverse(X2) != sk_c6
| inverse(X1) != sk_c6
| multiply(X3,sk_c6) != sk_c4
| multiply(X2,sk_c6) != sk_c6
| multiply(X1,sk_c4) != sk_c6 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_154]),c_0_154]),c_0_154]),c_0_154]),c_0_154]),c_0_154])]),c_0_167])]),c_0_200]) ).
cnf(c_0_206,negated_conjecture,
sk_c2 = sk_c6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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)],[c_0_201,c_0_154]),c_0_154]),c_0_154]),c_0_154]),c_0_154]),c_0_154])]),c_0_202]),c_0_177]),c_0_197]),c_0_202]),c_0_197]),c_0_182]),c_0_197]),c_0_203]),c_0_203]),c_0_203]),c_0_197])])])])]),c_0_204])]) ).
cnf(c_0_207,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_182])]),c_0_203]),c_0_203]),c_0_197]),c_0_204]),c_0_206]),c_0_197])])])]),c_0_204])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP305-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:09:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.95/0.69 % Version: 3.5.1
% 1.95/0.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.95/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.95/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.95/0.69 % Starting new_bool_3 with 300s (1) cores
% 1.95/0.69 % Starting new_bool_1 with 300s (1) cores
% 1.95/0.69 % Starting sh5l with 300s (1) cores
% 1.95/0.69 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1116935 completed with status 0
% 1.95/0.69 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.95/0.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.95/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.95/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.95/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.95/0.69 % No SInE strategy applied
% 1.95/0.69 % Search class: FGHPS-FFMM21-SFFFFFNN
% 1.95/0.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.95/0.69 % Starting SubtermCWHack with 136s (1) cores
% 1.95/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.95/0.69 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.95/0.69 % Starting new_bool_3 with 136s (1) cores
% 1.95/0.69 % Starting new_bool_1 with 136s (1) cores
% 1.95/0.69 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1116941 completed with status 0
% 1.95/0.69 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 1.95/0.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.95/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.95/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.95/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.95/0.69 % No SInE strategy applied
% 1.95/0.69 % Search class: FGHPS-FFMM21-SFFFFFNN
% 1.95/0.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.95/0.69 % Starting SubtermCWHack with 136s (1) cores
% 1.95/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.95/0.69 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.95/0.69 % Preprocessing time : 0.001 s
% 1.95/0.69 % Presaturation interreduction done
% 1.95/0.69
% 1.95/0.69 % Proof found!
% 1.95/0.69 % SZS status Unsatisfiable
% 1.95/0.69 % SZS output start CNFRefutation
% See solution above
% 1.95/0.69 % Parsed axioms : 29
% 1.95/0.69 % Removed by relevancy pruning/SinE : 0
% 1.95/0.69 % Initial clauses : 29
% 1.95/0.69 % Removed in clause preprocessing : 0
% 1.95/0.69 % Initial clauses in saturation : 29
% 1.95/0.69 % Processed clauses : 5653
% 1.95/0.69 % ...of these trivial : 342
% 1.95/0.69 % ...subsumed : 3853
% 1.95/0.69 % ...remaining for further processing : 1458
% 1.95/0.69 % Other redundant clauses eliminated : 99
% 1.95/0.69 % Clauses deleted for lack of memory : 0
% 1.95/0.69 % Backward-subsumed : 492
% 1.95/0.69 % Backward-rewritten : 908
% 1.95/0.69 % Generated clauses : 19659
% 1.95/0.69 % ...of the previous two non-redundant : 18915
% 1.95/0.69 % ...aggressively subsumed : 0
% 1.95/0.69 % Contextual simplify-reflections : 63
% 1.95/0.69 % Paramodulations : 19556
% 1.95/0.69 % Factorizations : 9
% 1.95/0.69 % NegExts : 0
% 1.95/0.69 % Equation resolutions : 99
% 1.95/0.69 % Disequality decompositions : 0
% 1.95/0.69 % Total rewrite steps : 5786
% 1.95/0.69 % ...of those cached : 5574
% 1.95/0.69 % Propositional unsat checks : 0
% 1.95/0.69 % Propositional check models : 0
% 1.95/0.69 % Propositional check unsatisfiable : 0
% 1.95/0.69 % Propositional clauses : 0
% 1.95/0.69 % Propositional clauses after purity: 0
% 1.95/0.69 % Propositional unsat core size : 0
% 1.95/0.69 % Propositional preprocessing time : 0.000
% 1.95/0.69 % Propositional encoding time : 0.000
% 1.95/0.69 % Propositional solver time : 0.000
% 1.95/0.69 % Success case prop preproc time : 0.000
% 1.95/0.69 % Success case prop encoding time : 0.000
% 1.95/0.69 % Success case prop solver time : 0.000
% 1.95/0.69 % Current number of processed clauses : 26
% 1.95/0.69 % Positive orientable unit clauses : 20
% 1.95/0.69 % Positive unorientable unit clauses: 0
% 1.95/0.69 % Negative unit clauses : 0
% 1.95/0.69 % Non-unit-clauses : 6
% 1.95/0.69 % Current number of unprocessed clauses: 5648
% 1.95/0.69 % ...number of literals in the above : 30591
% 1.95/0.69 % Current number of archived formulas : 0
% 1.95/0.69 % Current number of archived clauses : 1429
% 1.95/0.69 % Clause-clause subsumption calls (NU) : 86556
% 1.95/0.69 % Rec. Clause-clause subsumption calls : 20901
% 1.95/0.69 % Non-unit clause-clause subsumptions : 4358
% 1.95/0.69 % Unit Clause-clause subsumption calls : 335
% 1.95/0.69 % Rewrite failures with RHS unbound : 0
% 1.95/0.69 % BW rewrite match attempts : 47
% 1.95/0.69 % BW rewrite match successes : 45
% 1.95/0.69 % Condensation attempts : 0
% 1.95/0.69 % Condensation successes : 0
% 1.95/0.69 % Termbank termtop insertions : 240093
% 1.95/0.69 % Search garbage collected termcells : 25
% 1.95/0.69
% 1.95/0.69 % -------------------------------------------------
% 1.95/0.69 % User time : 0.251 s
% 1.95/0.69 % System time : 0.011 s
% 1.95/0.69 % Total time : 0.262 s
% 1.95/0.69 % Maximum resident set size: 3644 pages
% 1.95/0.69
% 1.95/0.69 % -------------------------------------------------
% 1.95/0.69 % User time : 1.110 s
% 1.95/0.69 % System time : 0.073 s
% 1.95/0.69 % Total time : 1.182 s
% 1.95/0.69 % Maximum resident set size: 4864 pages
% 1.95/0.69 % E exiting
%------------------------------------------------------------------------------