%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP220-1 : TPTP v9.2.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 04:24:51 PM UTC 2026
% Result : Unsatisfiable 155.81s 121.75s
% Output : CNFRefutation 156.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 82
% Syntax : Number of clauses : 302 ( 65 unt; 223 nHn; 237 RR)
% Number of literals : 681 ( 680 equ; 162 neg)
% Maximal clause size : 17 ( 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 : 205 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_73,negated_conjecture,
( inverse(X1) != sk_c12
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,X3) != sk_c11
| inverse(X2) != X3
| multiply(X3,sk_c12) != sk_c11
| multiply(sk_c12,X4) != sk_c11
| multiply(X5,sk_c12) != X4
| inverse(X5) != sk_c12
| inverse(sk_c12) != sk_c11
| inverse(X6) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| multiply(X7,X8) != sk_c12
| inverse(X7) != X8
| multiply(X8,sk_c11) != sk_c12
| inverse(X9) != X10
| inverse(X10) != X8
| multiply(X9,X8) != X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_73) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(prove_this_63,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_63) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_60,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c10,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_60) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_58,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_58) ).
cnf(prove_this_40,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_57,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_57) ).
cnf(prove_this_39,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_54,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
cnf(prove_this_51,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_49,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_48,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c10,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c7,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(prove_this_72,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_72) ).
cnf(prove_this_69,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c10,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_69) ).
cnf(prove_this_67,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c7,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_67) ).
cnf(prove_this_66,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_66) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_33,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c10,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c7,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_62,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_62) ).
cnf(prove_this_44,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_53,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_61,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
cnf(prove_this_43,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_52,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_59,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_59) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_50,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_56,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
cnf(prove_this_38,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_47,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_55,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c10,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c7,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_71,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_71) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_70,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_70) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_68,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_68) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_65,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_65) ).
cnf(prove_this_29,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_64,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_64) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c6) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(i_0_76,negated_conjecture,
( inverse(X1) != sk_c12
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,X3) != sk_c11
| inverse(X2) != X3
| multiply(X3,sk_c12) != sk_c11
| multiply(sk_c12,X4) != sk_c11
| multiply(X5,sk_c12) != X4
| inverse(X5) != sk_c12
| inverse(sk_c12) != sk_c11
| inverse(X6) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| multiply(X7,X8) != sk_c12
| inverse(X7) != X8
| multiply(X8,sk_c11) != sk_c12
| inverse(X9) != X10
| inverse(X10) != X8
| multiply(X9,X8) != X10 ),
prove_this_73,
[final] ).
cnf(i_0_77,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity,
[final] ).
cnf(i_0_78,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_63,
[final] ).
cnf(i_0_79,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_45,
[final] ).
cnf(i_0_80,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_27,
[final] ).
cnf(i_0_81,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c10,sk_c11) = sk_c12 ),
prove_this_60,
[final] ).
cnf(i_0_82,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c12 ),
prove_this_42,
[final] ).
cnf(i_0_83,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c12 ),
prove_this_24,
[final] ).
cnf(i_0_84,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c12 ),
prove_this_58,
[final] ).
cnf(i_0_85,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c12 ),
prove_this_40,
[final] ).
cnf(i_0_86,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c12 ),
prove_this_22,
[final] ).
cnf(i_0_87,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_57,
[final] ).
cnf(i_0_88,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_39,
[final] ).
cnf(i_0_89,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_21,
[final] ).
cnf(i_0_90,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_54,
[final] ).
cnf(i_0_91,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c12 ),
prove_this_51,
[final] ).
cnf(i_0_92,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c12 ),
prove_this_49,
[final] ).
cnf(i_0_93,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_48,
[final] ).
cnf(i_0_94,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_18,
[final] ).
cnf(i_0_95,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c10,sk_c11) = sk_c12 ),
prove_this_15,
[final] ).
cnf(i_0_96,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c7,sk_c10) = sk_c12 ),
prove_this_13,
[final] ).
cnf(i_0_97,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_12,
[final] ).
cnf(i_0_98,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse,
[final] ).
cnf(i_0_99,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_72,
[final] ).
cnf(i_0_100,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c10,sk_c11) = sk_c12 ),
prove_this_69,
[final] ).
cnf(i_0_101,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c7,sk_c10) = sk_c12 ),
prove_this_67,
[final] ).
cnf(i_0_102,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_66,
[final] ).
cnf(i_0_103,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_36,
[final] ).
cnf(i_0_104,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c10,sk_c11) = sk_c12 ),
prove_this_33,
[final] ).
cnf(i_0_105,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c7,sk_c10) = sk_c12 ),
prove_this_31,
[final] ).
cnf(i_0_106,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_30,
[final] ).
cnf(i_0_107,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c8) = sk_c10 ),
prove_this_62,
[final] ).
cnf(i_0_108,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c8) = sk_c10 ),
prove_this_44,
[final] ).
cnf(i_0_109,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c8) = sk_c10 ),
prove_this_26,
[final] ).
cnf(i_0_110,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c8) = sk_c10 ),
prove_this_53,
[final] ).
cnf(i_0_111,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c8) = sk_c10 ),
prove_this_17,
[final] ).
cnf(i_0_112,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c9) = sk_c8 ),
prove_this_61,
[final] ).
cnf(i_0_113,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c9) = sk_c8 ),
prove_this_43,
[final] ).
cnf(i_0_114,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c9) = sk_c8 ),
prove_this_25,
[final] ).
cnf(i_0_115,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c9) = sk_c8 ),
prove_this_52,
[final] ).
cnf(i_0_116,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c9) = sk_c8 ),
prove_this_16,
[final] ).
cnf(i_0_117,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c7) = sk_c10 ),
prove_this_59,
[final] ).
cnf(i_0_118,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c7) = sk_c10 ),
prove_this_41,
[final] ).
cnf(i_0_119,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c7) = sk_c10 ),
prove_this_23,
[final] ).
cnf(i_0_120,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c7) = sk_c10 ),
prove_this_50,
[final] ).
cnf(i_0_121,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c7) = sk_c10 ),
prove_this_14,
[final] ).
cnf(i_0_122,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c6) = sk_c12 ),
prove_this_56,
[final] ).
cnf(i_0_123,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c6) = sk_c12 ),
prove_this_38,
[final] ).
cnf(i_0_124,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c6) = sk_c12 ),
prove_this_20,
[final] ).
cnf(i_0_125,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c6) = sk_c12 ),
prove_this_47,
[final] ).
cnf(i_0_126,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c6) = sk_c12 ),
prove_this_11,
[final] ).
cnf(i_0_127,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c12) = sk_c11 ),
prove_this_55,
[final] ).
cnf(i_0_128,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c12) = sk_c11 ),
prove_this_37,
[final] ).
cnf(i_0_129,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c12) = sk_c11 ),
prove_this_19,
[final] ).
cnf(i_0_130,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c12) = sk_c11 ),
prove_this_46,
[final] ).
cnf(i_0_131,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c12) = sk_c11 ),
prove_this_10,
[final] ).
cnf(i_0_132,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_9,
[final] ).
cnf(i_0_133,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c10,sk_c11) = sk_c12 ),
prove_this_6,
[final] ).
cnf(i_0_134,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c7,sk_c10) = sk_c12 ),
prove_this_4,
[final] ).
cnf(i_0_135,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
prove_this_3,
[final] ).
cnf(i_0_136,axiom,
multiply(identity,X1) = X1,
left_identity,
[final] ).
cnf(i_0_137,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c8) = sk_c10 ),
prove_this_71,
[final] ).
cnf(i_0_138,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c8) = sk_c10 ),
prove_this_35,
[final] ).
cnf(i_0_139,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c9) = sk_c8 ),
prove_this_70,
[final] ).
cnf(i_0_140,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c9) = sk_c8 ),
prove_this_34,
[final] ).
cnf(i_0_141,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c7) = sk_c10 ),
prove_this_68,
[final] ).
cnf(i_0_142,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c7) = sk_c10 ),
prove_this_32,
[final] ).
cnf(i_0_143,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c6) = sk_c12 ),
prove_this_65,
[final] ).
cnf(i_0_144,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c6) = sk_c12 ),
prove_this_29,
[final] ).
cnf(i_0_145,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c12) = sk_c11 ),
prove_this_64,
[final] ).
cnf(i_0_146,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c12) = sk_c11 ),
prove_this_28,
[final] ).
cnf(i_0_147,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c8) = sk_c10 ),
prove_this_8,
[final] ).
cnf(i_0_148,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c9) = sk_c8 ),
prove_this_7,
[final] ).
cnf(i_0_149,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c7) = sk_c10 ),
prove_this_5,
[final] ).
cnf(i_0_150,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c6) = sk_c12 ),
prove_this_2,
[final] ).
cnf(i_0_151,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c12) = sk_c11 ),
prove_this_1,
[final] ).
cnf(i_0_152,axiom,
X1 = X1 ).
cnf(i_0_153,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_154,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_155,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_158,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(scs_inference,[],[i_0_77,i_0_153]) ).
cnf(i_0_159,plain,
multiply(multiply(identity,X1),X2) = multiply(X1,X2),
inference(scs_inference,[],[i_0_77,i_0_136,i_0_153,i_0_154]) ).
cnf(i_0_160,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_161,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_165,plain,
identity = multiply(inverse(X1),X1),
inference(scs_inference,[],[i_0_98,i_0_153]) ).
cnf(i_0_166,plain,
X1 = multiply(identity,X1),
inference(scs_inference,[],[i_0_136,i_0_153]) ).
cnf(i_0_168,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_172,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_175,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_178,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_180,plain,
multiply(identity,multiply(inverse(X1),X1)) = identity,
inference(scs_inference,[],[i_0_136,i_0_98,i_0_154]) ).
cnf(i_0_181,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_182,plain,
identity = multiply(identity,multiply(inverse(X1),X1)),
inference(scs_inference,[],[i_0_136,i_0_98,i_0_154,i_0_153]) ).
cnf(i_0_200,plain,
multiply(inverse(X1),X1) = identity,
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_204,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_224,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_296,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_304,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_313,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_326,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_339,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_357,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_370,plain,
inverse(multiply(inverse(X1),X1)) = inverse(identity),
inference(scs_inference,[],[i_0_98,i_0_155]) ).
cnf(i_0_371,plain,
multiply(X1,multiply(inverse(X2),X2)) = multiply(X1,identity),
inference(scs_inference,[],[i_0_98,i_0_155,i_0_157]) ).
cnf(i_0_378,plain,
inverse(multiply(identity,X1)) = inverse(X1),
inference(scs_inference,[],[i_0_136,i_0_155]) ).
cnf(i_0_379,plain,
multiply(X1,multiply(identity,X2)) = multiply(X1,X2),
inference(scs_inference,[],[i_0_136,i_0_155,i_0_157]) ).
cnf(i_0_380,plain,
multiply(inverse(multiply(identity,X1)),X2) = multiply(inverse(X1),X2),
inference(scs_inference,[],[i_0_136,i_0_155,i_0_157,i_0_156]) ).
cnf(i_0_381,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_389,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_395,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_410,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_414,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_422,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_425,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_429,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_433,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_440,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rename_variables,[],[i_0_77]) ).
cnf(c_0_187,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
i_0_158 ).
cnf(c_0_188,plain,
identity = multiply(inverse(X1),X1),
i_0_165 ).
cnf(c_0_189,plain,
X1 = multiply(identity,X1),
i_0_166 ).
cnf(c_0_190,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_189]) ).
cnf(c_0_191,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
i_0_97 ).
cnf(c_0_192,negated_conjecture,
( multiply(inverse(sk_c6),sk_c12) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_193,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c6) = sk_c12 ),
i_0_126 ).
cnf(c_0_194,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_195,plain,
( multiply(inverse(sk_c1),sk_c12) = sk_c11
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_190,c_0_194]) ).
cnf(c_0_196,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c6,sk_c11) = sk_c12 ),
i_0_135 ).
cnf(c_0_197,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_198,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c12 ),
i_0_92 ).
cnf(c_0_199,plain,
( multiply(inverse(sk_c6),sk_c12) = sk_c11
| multiply(sk_c12,sk_c12) = sk_c11 ),
inference(spm,[status(thm)],[c_0_190,c_0_197]) ).
cnf(c_0_200,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c6) = sk_c12 ),
i_0_150 ).
cnf(c_0_201,negated_conjecture,
( multiply(inverse(sk_c7),sk_c12) = sk_c10
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_190,c_0_198]) ).
cnf(c_0_202,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c7) = sk_c10 ),
i_0_120 ).
cnf(c_0_203,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_204,plain,
( multiply(sk_c7,multiply(sk_c10,X1)) = multiply(sk_c12,X1)
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_187,c_0_198]) ).
cnf(c_0_205,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c10,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_206,plain,
multiply(sk_c12,sk_c12) = sk_c11,
inference(spm,[status(thm)],[c_0_195,c_0_203]) ).
cnf(c_0_207,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_206]) ).
cnf(c_0_208,negated_conjecture,
( inverse(X1) != sk_c12
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,X3) != sk_c11
| inverse(X2) != X3
| multiply(X3,sk_c12) != sk_c11
| multiply(sk_c12,X4) != sk_c11
| multiply(X5,sk_c12) != X4
| inverse(X5) != sk_c12
| inverse(sk_c12) != sk_c11
| inverse(X6) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| multiply(X7,X8) != sk_c12
| inverse(X7) != X8
| multiply(X8,sk_c11) != sk_c12
| inverse(X9) != X10
| inverse(X10) != X8
| multiply(X9,X8) != X10 ),
i_0_76 ).
cnf(c_0_209,plain,
( multiply(inverse(sk_c7),sk_c11) = sk_c10
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_190,c_0_207]) ).
cnf(c_0_210,negated_conjecture,
( multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(inverse(X4),sk_c12) != sk_c11
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X4,inverse(X4)) != sk_c11
| multiply(X5,sk_c11) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(sk_c12) != sk_c11
| inverse(X5) != sk_c12
| inverse(X1) != sk_c12
| inverse(X6) != sk_c12 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_208])])])]) ).
cnf(c_0_211,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c12) = sk_c11 ),
i_0_130 ).
cnf(c_0_212,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c12 ),
i_0_91 ).
cnf(c_0_213,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_209,c_0_202]) ).
cnf(c_0_214,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(inverse(X3),sk_c11) != sk_c12
| multiply(inverse(X4),sk_c12) != sk_c11
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X4,inverse(X4)) != sk_c11
| multiply(X5,sk_c11) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != sk_c12
| inverse(X1) != sk_c12
| inverse(X6) != sk_c12 ),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_215,negated_conjecture,
( multiply(sk_c7,sk_c12) = multiply(sk_c12,sk_c11)
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_204,c_0_212]) ).
cnf(c_0_216,plain,
( multiply(sk_c7,sk_c10) = multiply(sk_c12,sk_c11)
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_204,c_0_213]) ).
cnf(c_0_217,plain,
multiply(inverse(sk_c12),sk_c11) = sk_c12,
inference(spm,[status(thm)],[c_0_190,c_0_206]) ).
cnf(c_0_218,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c12,multiply(sk_c12,sk_c11)) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c12) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c12
| inverse(sk_c7) != sk_c12
| inverse(X4) != sk_c12
| inverse(X5) != sk_c12 ),
inference(spm,[status(thm)],[c_0_214,c_0_215]) ).
cnf(c_0_219,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| sk_c10 = sk_c12 ),
inference(spm,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_220,negated_conjecture,
( multiply(sk_c12,sk_c11) = sk_c12
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_198,c_0_216]) ).
cnf(c_0_221,plain,
( multiply(sk_c10,multiply(sk_c11,X1)) = multiply(sk_c12,X1)
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_187,c_0_212]) ).
cnf(c_0_222,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c12 ),
inference(spm,[status(thm)],[c_0_217,c_0_211]) ).
cnf(c_0_223,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c12,multiply(sk_c12,sk_c11)) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c12) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c12
| inverse(X4) != sk_c12
| inverse(X5) != sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_202]),c_0_219]) ).
cnf(c_0_224,plain,
( multiply(sk_c12,sk_c11) = sk_c12
| sk_c5 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_220]),c_0_217]) ).
cnf(c_0_225,negated_conjecture,
( multiply(sk_c10,sk_c12) = multiply(sk_c12,sk_c11)
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_226,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| sk_c5 = sk_c12
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c11) != sk_c12
| multiply(inverse(X3),sk_c12) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c12
| inverse(X4) != sk_c12
| inverse(X5) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_206])]) ).
cnf(c_0_227,negated_conjecture,
( multiply(sk_c12,sk_c11) = sk_c10
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_205,c_0_225]) ).
cnf(c_0_228,negated_conjecture,
( multiply(sk_c12,sk_c11) = sk_c11
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_207,c_0_216]) ).
cnf(c_0_229,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| sk_c5 = sk_c12
| inverse(multiply(X1,sk_c10)) != sk_c10
| multiply(inverse(X2),sk_c12) != sk_c11
| inverse(X1) != multiply(X1,sk_c10)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c11) != sk_c12
| multiply(X4,sk_c11) != sk_c12
| inverse(X3) != sk_c12
| inverse(X4) != sk_c12 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_202]),c_0_198]),c_0_212]) ).
cnf(c_0_230,plain,
( multiply(sk_c12,sk_c11) = sk_c10
| sk_c5 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_227]),c_0_217]) ).
cnf(c_0_231,plain,
( multiply(sk_c12,sk_c11) = sk_c11
| sk_c5 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_228]),c_0_217]) ).
cnf(c_0_232,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| sk_c5 = sk_c12
| multiply(inverse(X1),sk_c12) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| multiply(X3,sk_c11) != sk_c12
| inverse(sk_c12) != sk_c10
| inverse(sk_c7) != sk_c12
| inverse(X2) != sk_c12
| inverse(X3) != sk_c12 ),
inference(spm,[status(thm)],[c_0_229,c_0_198]) ).
cnf(c_0_233,plain,
( sk_c5 = sk_c12
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_234,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| sk_c5 = sk_c12
| multiply(inverse(X1),sk_c12) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| multiply(X3,sk_c11) != sk_c12
| inverse(sk_c7) != sk_c12
| inverse(X2) != sk_c12
| inverse(X3) != sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_211]),c_0_233]) ).
cnf(c_0_235,plain,
( sk_c10 = sk_c12
| sk_c5 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_219]),c_0_217]) ).
cnf(c_0_236,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| multiply(sk_c6,sk_c11) = sk_c12 ),
i_0_93 ).
cnf(c_0_237,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| sk_c5 = sk_c12
| multiply(inverse(X1),sk_c12) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| multiply(X3,sk_c11) != sk_c12
| inverse(X2) != sk_c12
| inverse(X3) != sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_202]),c_0_235]) ).
cnf(c_0_238,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| inverse(sk_c6) = sk_c12 ),
i_0_125 ).
cnf(c_0_239,plain,
( multiply(sk_c6,multiply(sk_c11,X1)) = multiply(sk_c12,X1)
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_187,c_0_236]) ).
cnf(c_0_240,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| sk_c5 = sk_c12
| multiply(sk_c6,sk_c12) != sk_c11
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,sk_c11) != sk_c12
| inverse(X1) != sk_c12
| inverse(X2) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_206])]) ).
cnf(c_0_241,negated_conjecture,
( multiply(sk_c6,sk_c12) = multiply(sk_c12,sk_c11)
| multiply(sk_c12,sk_c5) = sk_c11 ),
inference(spm,[status(thm)],[c_0_239,c_0_222]) ).
cnf(c_0_242,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| sk_c5 = sk_c12
| multiply(X1,sk_c11) != sk_c12
| multiply(X2,sk_c11) != sk_c12
| inverse(X1) != sk_c12
| inverse(X2) != sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_241]),c_0_231]) ).
cnf(c_0_243,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| sk_c5 = sk_c12
| multiply(X1,sk_c11) != sk_c12
| inverse(X1) != sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_236]),c_0_238]) ).
cnf(c_0_244,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c6) = sk_c12 ),
i_0_122 ).
cnf(c_0_245,negated_conjecture,
( multiply(sk_c12,sk_c5) = sk_c11
| sk_c5 = sk_c12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_236]),c_0_238]) ).
cnf(c_0_246,plain,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c12,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_188,c_0_244]) ).
cnf(c_0_247,plain,
sk_c5 = sk_c12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_245]),c_0_217])]) ).
cnf(c_0_248,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| inverse(sk_c7) = sk_c10 ),
i_0_117 ).
cnf(c_0_249,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c12 ),
i_0_84 ).
cnf(c_0_250,plain,
( multiply(sk_c12,sk_c6) = identity
| multiply(sk_c4,sk_c12) = sk_c12 ),
inference(rw,[status(thm)],[c_0_246,c_0_247]) ).
cnf(c_0_251,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c6) = sk_c12 ),
i_0_143 ).
cnf(c_0_252,plain,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c10,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_188,c_0_248]) ).
cnf(c_0_253,negated_conjecture,
( multiply(inverse(sk_c7),sk_c12) = sk_c10
| multiply(sk_c4,sk_c12) = sk_c5 ),
inference(spm,[status(thm)],[c_0_190,c_0_249]) ).
cnf(c_0_254,plain,
( multiply(inverse(sk_c4),sk_c12) = sk_c12
| multiply(sk_c12,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_190,c_0_250]) ).
cnf(c_0_255,plain,
( multiply(sk_c12,sk_c6) = identity
| inverse(sk_c4) = sk_c12 ),
inference(spm,[status(thm)],[c_0_188,c_0_251]) ).
cnf(c_0_256,plain,
( multiply(sk_c10,sk_c7) = identity
| multiply(sk_c4,sk_c12) = sk_c12 ),
inference(rw,[status(thm)],[c_0_252,c_0_247]) ).
cnf(c_0_257,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c7) = sk_c10 ),
i_0_141 ).
cnf(c_0_258,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c10,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_253,c_0_248]) ).
cnf(c_0_259,plain,
( multiply(sk_c12,sk_c6) = identity
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_255]),c_0_206]) ).
cnf(c_0_260,plain,
( multiply(inverse(sk_c4),sk_c12) = sk_c12
| multiply(sk_c10,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_190,c_0_256]) ).
cnf(c_0_261,plain,
( multiply(sk_c10,sk_c7) = identity
| inverse(sk_c4) = sk_c12 ),
inference(spm,[status(thm)],[c_0_188,c_0_257]) ).
cnf(c_0_262,plain,
( multiply(inverse(sk_c4),sk_c5) = sk_c12
| multiply(sk_c10,sk_c12) = sk_c10 ),
inference(spm,[status(thm)],[c_0_190,c_0_258]) ).
cnf(c_0_263,plain,
( multiply(inverse(sk_c12),identity) = sk_c6
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_190,c_0_259]) ).
cnf(c_0_264,plain,
( multiply(sk_c10,sk_c7) = identity
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_206]) ).
cnf(c_0_265,plain,
( multiply(inverse(sk_c4),sk_c12) = sk_c12
| multiply(sk_c10,sk_c12) = sk_c10 ),
inference(rw,[status(thm)],[c_0_262,c_0_247]) ).
cnf(c_0_266,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c7,sk_c10) = sk_c12 ),
i_0_101 ).
cnf(c_0_267,plain,
( multiply(inverse(sk_c12),X1) = multiply(sk_c6,X1)
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_263]),c_0_189]) ).
cnf(c_0_268,plain,
( multiply(sk_c10,multiply(sk_c7,X1)) = X1
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_264]),c_0_189]) ).
cnf(c_0_269,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| multiply(sk_c10,sk_c12) = sk_c10
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_266]),c_0_206]) ).
cnf(c_0_270,plain,
( multiply(sk_c12,sk_c5) = sk_c11
| identity = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_205]),c_0_188]) ).
cnf(c_0_271,plain,
( multiply(sk_c12,multiply(sk_c6,X1)) = X1
| sk_c11 = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_259]),c_0_189]) ).
cnf(c_0_272,plain,
( multiply(sk_c6,sk_c12) = identity
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_188,c_0_267]) ).
cnf(c_0_273,negated_conjecture,
( multiply(sk_c10,sk_c12) = sk_c10
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_268,c_0_269]) ).
cnf(c_0_274,plain,
( multiply(inverse(sk_c12),sk_c11) = sk_c5
| identity = sk_c12 ),
inference(spm,[status(thm)],[c_0_190,c_0_270]) ).
cnf(c_0_275,plain,
( multiply(sk_c12,identity) = sk_c12
| sk_c11 = sk_c12 ),
inference(spm,[status(thm)],[c_0_271,c_0_272]) ).
cnf(c_0_276,plain,
( sk_c11 = sk_c12
| identity = sk_c12 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_273]),c_0_188]) ).
cnf(c_0_277,plain,
( multiply(inverse(sk_c12),sk_c11) = sk_c12
| identity = sk_c12 ),
inference(rw,[status(thm)],[c_0_274,c_0_247]) ).
cnf(c_0_278,plain,
sk_c11 = sk_c12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_276]),c_0_206])]) ).
cnf(c_0_279,plain,
identity = sk_c12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_277,c_0_278]),c_0_188])]) ).
cnf(c_0_280,plain,
multiply(inverse(X1),X1) = sk_c12,
inference(rw,[status(thm)],[c_0_188,c_0_279]) ).
cnf(c_0_281,plain,
multiply(inverse(inverse(X1)),sk_c12) = X1,
inference(spm,[status(thm)],[c_0_190,c_0_280]) ).
cnf(c_0_282,plain,
multiply(sk_c12,X1) = X1,
inference(rw,[status(thm)],[c_0_189,c_0_279]) ).
cnf(c_0_283,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_281]),c_0_282]) ).
cnf(c_0_284,plain,
multiply(X1,sk_c12) = X1,
inference(rw,[status(thm)],[c_0_281,c_0_283]) ).
cnf(c_0_285,plain,
multiply(inverse(sk_c12),X1) = X1,
inference(spm,[status(thm)],[c_0_190,c_0_282]) ).
cnf(c_0_286,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_284]),c_0_284]) ).
cnf(c_0_287,plain,
multiply(inverse(inverse(sk_c12)),X1) = X1,
inference(spm,[status(thm)],[c_0_190,c_0_285]) ).
cnf(c_0_288,plain,
multiply(X1,inverse(X1)) = sk_c12,
inference(spm,[status(thm)],[c_0_280,c_0_286]) ).
cnf(c_0_289,plain,
inverse(sk_c12) = sk_c12,
inference(spm,[status(thm)],[c_0_280,c_0_287]) ).
cnf(c_0_290,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(X2) != sk_c12
| inverse(X3) != sk_c12 ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_210,c_0_278]),c_0_278]),c_0_278]),c_0_278]),c_0_278]),c_0_278]),c_0_278]),c_0_282]),c_0_284]),c_0_284]),c_0_284]),c_0_288]),c_0_288]),c_0_284]),c_0_284]),c_0_289])])])])]),c_0_289])]) ).
cnf(c_0_291,plain,
( inverse(X1) != sk_c12
| inverse(X2) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_290,c_0_280]),c_0_289]),c_0_286])]) ).
cnf(c_0_292,plain,
inverse(X1) != sk_c12,
inference(spm,[status(thm)],[c_0_291,c_0_289]) ).
cnf(c_0_293,plain,
$false,
inference(sr,[status(thm)],[c_0_289,c_0_292]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP220-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.08/0.24 % Computer : n012.cluster.edu
% 0.08/0.24 % Model : x86_64 x86_64
% 0.08/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.24 % Memory : 8042.1875MB
% 0.08/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.24 % CPULimit : 300
% 0.08/0.24 % WCLimit : 300
% 0.08/0.24 % DateTime : Mon May 4 18:28:31 EDT 2026
% 0.08/0.24 % CPUTime :
% 0.08/0.25 % start to proof: theBenchmark
% 155.81/121.75 % Version : CSE_E---1.7
% 155.81/121.75 % Problem : theBenchmark.p
% 155.81/121.75 % SZS status Unsatisfiable for theBenchmark.p
% 155.81/121.75 % SZS output start CNFRefutation
% See solution above
% 156.00/122.00 % Total time : 121.356s
%------------------------------------------------------------------------------