%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP688-1 : TPTP v9.2.1. Released v4.0.0.
% 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 : n013.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 04:26:54 PM UTC 2026
% Result : Unsatisfiable 9.38s 6.81s
% Output : CNFRefutation 9.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of clauses : 149 ( 149 unt; 0 nHn; 38 RR)
% Number of literals : 149 ( 148 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 200 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c08,axiom,
mult(i(X1),mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
cnf(c05,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(c04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(c09,axiom,
i(mult(X1,X2)) = mult(i(X1),i(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
cnf(c01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
cnf(c07,axiom,
mult(X1,mult(X2,mult(X1,X3))) = mult(mult(X1,mult(X2,X1)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
cnf(c06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(c11,axiom,
mult(op_d,mult(op_d,op_d)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c11) ).
cnf(c10,axiom,
mult(op_c,mult(op_c,mult(op_c,op_c))) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
cnf(goals,negated_conjecture,
mult(op_c,op_d) != mult(op_d,op_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_12,axiom,
mult(i(X1),mult(X1,X2)) = X2,
c08 ).
cnf(c_0_13,axiom,
mult(X1,unit) = X1,
c05 ).
cnf(c_0_14,axiom,
rd(mult(X1,X2),X2) = X1,
c04 ).
cnf(c_0_15,plain,
mult(i(X1),X1) = unit,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
i(X1) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
mult(rd(unit,X1),mult(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_18,axiom,
i(mult(X1,X2)) = mult(i(X1),i(X2)),
c09 ).
cnf(c_0_19,axiom,
mult(X1,ld(X1,X2)) = X2,
c01 ).
cnf(c_0_20,axiom,
mult(X1,mult(X2,mult(X1,X3))) = mult(mult(X1,mult(X2,X1)),X3),
c07 ).
cnf(c_0_21,axiom,
mult(unit,X1) = X1,
c06 ).
cnf(c_0_22,axiom,
ld(X1,mult(X1,X2)) = X2,
c02 ).
cnf(c_0_23,axiom,
mult(rd(X1,X2),X2) = X1,
c03 ).
cnf(c_0_24,plain,
rd(X1,mult(X2,X1)) = rd(unit,X2),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_25,plain,
mult(rd(unit,X1),rd(unit,X2)) = rd(unit,mult(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_16]),c_0_16]),c_0_16]) ).
cnf(c_0_26,plain,
mult(rd(unit,X1),X2) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_27,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_28,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
rd(unit,rd(unit,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_17]),c_0_14]) ).
cnf(c_0_30,axiom,
mult(op_d,mult(op_d,op_d)) = unit,
c11 ).
cnf(c_0_31,plain,
ld(X1,rd(unit,X2)) = rd(unit,mult(X1,X2)),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
rd(mult(X1,mult(X1,X2)),X2) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_27]) ).
cnf(c_0_33,plain,
ld(rd(unit,X1),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_34,plain,
rd(unit,rd(X1,X2)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_35,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_36,plain,
ld(X1,unit) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
mult(mult(X1,ld(X2,X1)),X3) = mult(X1,ld(X2,mult(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_26]),c_0_26]) ).
cnf(c_0_38,plain,
i(op_d) = mult(op_d,op_d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_30]),c_0_13]) ).
cnf(c_0_39,plain,
mult(X1,rd(unit,mult(X1,X2))) = rd(unit,X2),
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_40,plain,
ld(X1,ld(X1,X2)) = ld(mult(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_31]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_41,plain,
rd(mult(X1,X2),ld(X1,X2)) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_42,plain,
ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_43,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(mult(rd(X1,X2),X1),X2),
inference(spm,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_44,plain,
rd(unit,mult(X1,rd(unit,X2))) = ld(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_35]),c_0_36]) ).
cnf(c_0_45,axiom,
mult(op_c,mult(op_c,mult(op_c,op_c))) = unit,
c10 ).
cnf(c_0_46,plain,
ld(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_47,plain,
ld(X1,ld(X2,ld(X1,X3))) = ld(mult(X1,mult(X2,X1)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_31]),c_0_26]),c_0_31]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_48,plain,
rd(unit,op_d) = mult(op_d,op_d),
inference(rw,[status(thm)],[c_0_38,c_0_16]) ).
cnf(c_0_49,plain,
mult(rd(X1,X2),rd(unit,X1)) = rd(unit,X2),
inference(spm,[status(thm)],[c_0_39,c_0_23]) ).
cnf(c_0_50,plain,
ld(mult(X1,X1),mult(X1,X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_51,plain,
rd(mult(rd(X1,X2),X1),X2) = rd(X1,mult(rd(X2,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_23]),c_0_42]),c_0_43]) ).
cnf(c_0_52,plain,
mult(rd(rd(unit,X1),X2),X1) = rd(unit,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_23]),c_0_42]) ).
cnf(c_0_53,plain,
rd(unit,mult(op_c,op_c)) = mult(op_c,op_c),
inference(spm,[status(thm)],[c_0_32,c_0_45]) ).
cnf(c_0_54,plain,
ld(mult(X1,X1),X1) = rd(unit,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_46]),c_0_36]) ).
cnf(c_0_55,plain,
ld(mult(X1,mult(X2,X1)),X1) = rd(unit,mult(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_46]),c_0_36]),c_0_31]) ).
cnf(c_0_56,plain,
ld(mult(op_d,op_d),X1) = mult(op_d,X1),
inference(spm,[status(thm)],[c_0_33,c_0_48]) ).
cnf(c_0_57,plain,
rd(rd(unit,X1),rd(unit,X2)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_14,c_0_49]) ).
cnf(c_0_58,plain,
rd(unit,mult(op_d,op_d)) = op_d,
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_59,plain,
mult(rd(X1,mult(rd(X2,X1),X2)),X2) = mult(rd(X1,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_23]),c_0_42]),c_0_43]),c_0_51]),c_0_42]),c_0_51]) ).
cnf(c_0_60,plain,
mult(rd(mult(op_c,op_c),X1),mult(op_c,op_c)) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_61,plain,
rd(X1,rd(unit,X1)) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_35,c_0_54]) ).
cnf(c_0_62,plain,
rd(mult(X1,mult(X2,mult(X1,X3))),X3) = mult(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_63,plain,
rd(X1,rd(unit,mult(X1,X2))) = mult(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_55]) ).
cnf(c_0_64,plain,
mult(op_d,mult(op_d,mult(op_d,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_56]),c_0_27]) ).
cnf(c_0_65,plain,
rd(op_d,rd(unit,X1)) = rd(X1,mult(op_d,op_d)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,plain,
mult(rd(X1,mult(op_c,op_c)),X1) = mult(X1,mult(X1,mult(op_c,op_c))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_27]) ).
cnf(c_0_67,plain,
mult(X1,mult(rd(X2,mult(X1,X3)),X1)) = rd(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_62,c_0_23]) ).
cnf(c_0_68,plain,
mult(X1,mult(rd(X2,X1),mult(X1,X3))) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_69,plain,
rd(unit,mult(X1,rd(X2,X3))) = ld(X1,rd(X3,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_70,plain,
rd(unit,mult(X1,mult(op_d,op_d))) = ld(X1,op_d),
inference(spm,[status(thm)],[c_0_31,c_0_58]) ).
cnf(c_0_71,plain,
rd(X1,mult(op_d,op_d)) = mult(op_d,mult(mult(op_d,mult(op_d,X1)),op_d)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_72,plain,
rd(mult(X1,mult(X1,mult(op_c,op_c))),X1) = rd(X1,mult(op_c,op_c)),
inference(spm,[status(thm)],[c_0_14,c_0_66]) ).
cnf(c_0_73,plain,
rd(unit,op_c) = mult(op_c,mult(op_c,op_c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_45]),c_0_36]) ).
cnf(c_0_74,plain,
ld(X1,rd(mult(X1,X2),X3)) = mult(rd(X2,mult(X1,X3)),X1),
inference(spm,[status(thm)],[c_0_22,c_0_67]) ).
cnf(c_0_75,plain,
ld(X1,mult(mult(X1,X2),X3)) = mult(rd(X2,X1),mult(X1,X3)),
inference(spm,[status(thm)],[c_0_22,c_0_68]) ).
cnf(c_0_76,plain,
rd(unit,mult(op_c,mult(op_c,op_c))) = op_c,
inference(spm,[status(thm)],[c_0_14,c_0_45]) ).
cnf(c_0_77,plain,
ld(X1,rd(X1,X2)) = ld(mult(X1,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_23]),c_0_69]) ).
cnf(c_0_78,plain,
mult(rd(mult(op_d,op_d),X1),op_d) = rd(unit,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_23]),c_0_42]) ).
cnf(c_0_79,plain,
rd(mult(op_d,op_d),mult(op_c,op_c)) = mult(op_d,mult(op_c,mult(op_c,op_d))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_27]),c_0_27]),c_0_64]),c_0_64]),c_0_27]) ).
cnf(c_0_80,plain,
mult(mult(X1,mult(X2,mult(X2,X1))),X3) = mult(X1,mult(X2,mult(X2,mult(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_27]),c_0_27]) ).
cnf(c_0_81,plain,
ld(op_c,X1) = mult(mult(op_c,mult(op_c,op_c)),X1),
inference(spm,[status(thm)],[c_0_26,c_0_73]) ).
cnf(c_0_82,plain,
rd(unit,ld(X1,X2)) = mult(X1,rd(unit,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_19]) ).
cnf(c_0_83,plain,
mult(rd(X1,X2),mult(X2,mult(X2,X1))) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_61]),c_0_75]),c_0_39]),c_0_61]),c_0_27]) ).
cnf(c_0_84,plain,
rd(op_c,rd(unit,X1)) = rd(X1,mult(op_c,mult(op_c,op_c))),
inference(spm,[status(thm)],[c_0_57,c_0_76]) ).
cnf(c_0_85,plain,
rd(X1,unit) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_86,plain,
mult(X1,ld(mult(X1,X2),X1)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_77]) ).
cnf(c_0_87,plain,
rd(ld(X1,X2),X2) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_88,plain,
mult(op_d,mult(op_c,mult(op_c,mult(op_d,op_d)))) = mult(op_c,op_c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_53]) ).
cnf(c_0_89,plain,
ld(op_c,X1) = mult(op_c,mult(op_c,mult(op_c,X1))),
inference(rw,[status(thm)],[c_0_81,c_0_20]) ).
cnf(c_0_90,plain,
mult(mult(X1,X2),rd(unit,X1)) = mult(X1,rd(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_77]),c_0_82]),c_0_34]) ).
cnf(c_0_91,plain,
mult(mult(X1,X2),mult(X1,X2)) = mult(X1,mult(X2,mult(X2,X1))),
inference(spm,[status(thm)],[c_0_68,c_0_83]) ).
cnf(c_0_92,plain,
rd(X1,mult(X2,mult(X3,mult(X2,X1)))) = rd(unit,mult(X2,mult(X3,X2))),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_93,plain,
rd(mult(op_c,X1),mult(op_c,mult(op_c,op_c))) = mult(op_c,mult(X1,op_c)),
inference(spm,[status(thm)],[c_0_84,c_0_63]) ).
cnf(c_0_94,plain,
rd(mult(op_c,op_c),mult(op_d,op_d)) = rd(op_d,mult(op_c,op_c)),
inference(spm,[status(thm)],[c_0_65,c_0_53]) ).
cnf(c_0_95,plain,
rd(unit,mult(X1,mult(X1,mult(op_d,op_d)))) = ld(mult(X1,X1),op_d),
inference(spm,[status(thm)],[c_0_70,c_0_27]) ).
cnf(c_0_96,plain,
ld(mult(op_c,op_c),X1) = mult(op_c,mult(op_c,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_53]),c_0_85]),c_0_27]) ).
cnf(c_0_97,plain,
ld(X1,mult(rd(X1,X2),X3)) = ld(mult(X1,X2),mult(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_86]),c_0_87]),c_0_26]) ).
cnf(c_0_98,plain,
rd(mult(op_c,op_c),mult(op_c,mult(op_c,mult(op_d,op_d)))) = op_d,
inference(spm,[status(thm)],[c_0_14,c_0_88]) ).
cnf(c_0_99,plain,
mult(op_c,mult(op_c,mult(op_c,mult(op_c,X1)))) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_89]) ).
cnf(c_0_100,plain,
ld(op_d,X1) = mult(mult(op_d,op_d),X1),
inference(spm,[status(thm)],[c_0_33,c_0_58]) ).
cnf(c_0_101,plain,
ld(mult(X1,X2),mult(X1,rd(X2,X1))) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_22,c_0_90]) ).
cnf(c_0_102,plain,
mult(rd(X1,X2),mult(X2,mult(X2,rd(X1,X2)))) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_91,c_0_23]) ).
cnf(c_0_103,plain,
rd(rd(X1,X2),mult(op_c,mult(op_c,op_c))) = rd(op_c,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_84,c_0_34]) ).
cnf(c_0_104,plain,
rd(unit,mult(op_c,mult(op_d,op_c))) = mult(op_c,mult(op_d,mult(op_d,op_c))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_88]),c_0_93]),c_0_27]) ).
cnf(c_0_105,plain,
rd(op_d,mult(op_c,op_c)) = mult(op_d,mult(mult(op_d,mult(op_d,mult(op_c,op_c))),op_d)),
inference(rw,[status(thm)],[c_0_94,c_0_71]) ).
cnf(c_0_106,plain,
mult(op_d,mult(op_c,op_c)) = mult(op_c,mult(op_c,op_d)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_88]),c_0_53]),c_0_95]),c_0_96]) ).
cnf(c_0_107,plain,
rd(unit,mult(X1,mult(op_c,mult(op_c,op_c)))) = ld(X1,op_c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_73]),c_0_85]) ).
cnf(c_0_108,plain,
mult(op_d,mult(op_c,mult(op_c,X1))) = mult(op_c,mult(op_c,mult(op_d,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_96]),c_0_27]),c_0_99]),c_0_27]),c_0_56]) ).
cnf(c_0_109,plain,
ld(op_d,X1) = mult(op_d,mult(op_d,X1)),
inference(rw,[status(thm)],[c_0_100,c_0_27]) ).
cnf(c_0_110,plain,
ld(mult(X1,X1),mult(rd(X1,X2),mult(X2,X2))) = rd(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_32]),c_0_34]) ).
cnf(c_0_111,plain,
rd(op_c,mult(op_c,mult(op_d,op_c))) = mult(op_c,mult(mult(op_d,mult(op_d,op_c)),op_c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_93]),c_0_85]) ).
cnf(c_0_112,plain,
mult(mult(X1,X2),mult(mult(X1,X2),X3)) = mult(X1,mult(X2,mult(X2,mult(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_91]),c_0_80]) ).
cnf(c_0_113,plain,
mult(X1,ld(mult(X1,X1),X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_40]) ).
cnf(c_0_114,plain,
rd(mult(X1,mult(X2,mult(X2,X1))),mult(X1,X2)) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_83]),c_0_23]) ).
cnf(c_0_115,plain,
mult(rd(op_d,X1),mult(op_d,op_d)) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_52,c_0_58]) ).
cnf(c_0_116,plain,
rd(op_d,mult(op_c,op_c)) = mult(op_c,mult(op_c,op_d)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106]),c_0_80]),c_0_88]),c_0_106]) ).
cnf(c_0_117,plain,
rd(unit,mult(rd(X1,mult(X2,X3)),X2)) = mult(X2,rd(X3,mult(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_67]),c_0_34]) ).
cnf(c_0_118,plain,
rd(unit,mult(op_c,mult(op_c,mult(op_d,op_c)))) = mult(op_d,mult(op_d,op_c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_119,plain,
rd(mult(op_c,mult(op_d,op_c)),op_c) = mult(op_c,op_d),
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(spm,[status(thm)],[c_0_110,c_0_111]),c_0_20]),c_0_108]),c_0_20]),c_0_99]),c_0_91]),c_0_112]),c_0_108]),c_0_30]),c_0_13]),c_0_106]),c_0_96]),c_0_99]) ).
cnf(c_0_120,plain,
mult(X1,mult(rd(X2,X1),ld(X1,X3))) = mult(mult(X1,X2),ld(mult(X1,X1),X3)),
inference(spm,[status(thm)],[c_0_68,c_0_113]) ).
cnf(c_0_121,plain,
rd(mult(op_d,op_d),mult(op_c,mult(op_c,op_d))) = mult(op_c,mult(op_c,op_d)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_106]),c_0_27]),c_0_27]),c_0_99]) ).
cnf(c_0_122,plain,
mult(mult(op_c,mult(op_c,op_d)),mult(op_d,op_d)) = mult(op_c,op_c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_53]) ).
cnf(c_0_123,plain,
rd(op_d,mult(op_c,mult(op_c,op_c))) = rd(op_c,mult(op_d,op_d)),
inference(spm,[status(thm)],[c_0_65,c_0_73]) ).
cnf(c_0_124,plain,
rd(unit,mult(mult(op_d,mult(op_d,op_c)),op_c)) = mult(op_c,mult(op_c,op_d)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_13]),c_0_119]) ).
cnf(c_0_125,plain,
mult(mult(op_c,mult(op_c,op_d)),X1) = mult(op_c,mult(op_c,mult(op_d,X1))),
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(spm,[status(thm)],[c_0_120,c_0_121]),c_0_19]),c_0_122]),c_0_91]),c_0_112]),c_0_106]),c_0_108]),c_0_99]),c_0_56]),c_0_27]) ).
cnf(c_0_126,plain,
rd(unit,mult(X1,mult(op_c,op_c))) = ld(X1,mult(op_c,op_c)),
inference(spm,[status(thm)],[c_0_31,c_0_53]) ).
cnf(c_0_127,plain,
rd(X1,mult(X2,mult(X2,X1))) = rd(unit,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_128,plain,
rd(op_d,mult(op_c,mult(op_c,op_c))) = mult(op_d,mult(mult(op_d,mult(op_d,op_c)),op_d)),
inference(rw,[status(thm)],[c_0_123,c_0_71]) ).
cnf(c_0_129,plain,
mult(mult(op_d,mult(op_d,op_c)),op_d) = op_c,
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(spm,[status(thm)],[c_0_117,c_0_124]),c_0_125]),c_0_64]),c_0_126]),c_0_89]),c_0_45]),c_0_13]),c_0_13]),c_0_127]),c_0_71]),c_0_13]),c_0_27]),c_0_30]),c_0_13]) ).
cnf(c_0_130,plain,
rd(op_d,mult(op_c,mult(op_c,op_c))) = mult(op_d,op_c),
inference(rw,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_131,plain,
mult(rd(X1,X2),ld(mult(X1,X2),X1)) = rd(rd(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_23]),c_0_77]) ).
cnf(c_0_132,plain,
mult(mult(op_d,op_c),mult(op_d,op_d)) = op_c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_130]),c_0_126]),c_0_89]),c_0_45]),c_0_13]) ).
cnf(c_0_133,plain,
ld(X1,rd(rd(X1,X2),X2)) = ld(mult(X1,X2),rd(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_131]),c_0_86]) ).
cnf(c_0_134,plain,
rd(rd(X1,X2),ld(mult(X1,X2),X1)) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_77]) ).
cnf(c_0_135,plain,
mult(op_d,mult(op_d,rd(unit,X1))) = rd(unit,mult(op_d,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_109]) ).
cnf(c_0_136,plain,
rd(unit,mult(op_d,mult(op_d,X1))) = mult(op_d,rd(unit,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_31]),c_0_27]) ).
cnf(c_0_137,plain,
mult(mult(op_d,op_c),op_c) = mult(op_c,mult(op_c,op_d)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_132]),c_0_30]),c_0_13]),c_0_106]) ).
cnf(c_0_138,plain,
mult(rd(X1,rd(X2,X1)),X2) = mult(rd(X1,X2),mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_35]),c_0_42]),c_0_131]),c_0_42]) ).
cnf(c_0_139,plain,
mult(op_d,rd(X1,op_d)) = mult(mult(op_d,X1),mult(op_d,op_d)),
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(spm,[status(thm)],[c_0_55,c_0_115]),c_0_27]),c_0_135]),c_0_42]),c_0_85]),c_0_27]),c_0_136]),c_0_34]) ).
cnf(c_0_140,plain,
rd(mult(op_c,mult(op_c,op_d)),op_c) = mult(op_d,op_c),
inference(spm,[status(thm)],[c_0_14,c_0_137]) ).
cnf(c_0_141,plain,
rd(mult(rd(X1,X2),mult(X2,X1)),X2) = rd(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_138]) ).
cnf(c_0_142,plain,
mult(mult(op_d,op_c),mult(op_d,mult(op_d,op_c))) = mult(op_c,op_c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_132]),c_0_27]),c_0_64]),c_0_27]) ).
cnf(c_0_143,plain,
rd(X1,op_d) = mult(op_d,mult(op_d,mult(mult(op_d,X1),mult(op_d,op_d)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_139]),c_0_109]) ).
cnf(c_0_144,plain,
mult(mult(op_d,op_c),op_d) = mult(op_d,mult(op_d,op_c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_140]),c_0_99]),c_0_125]),c_0_125]),c_0_108]),c_0_99]) ).
cnf(c_0_145,plain,
rd(mult(op_c,mult(op_c,op_d)),mult(op_d,op_c)) = op_c,
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(spm,[status(thm)],[c_0_141,c_0_142]),c_0_14]),c_0_106]),c_0_24]),c_0_143]),c_0_13]),c_0_30]),c_0_13]),c_0_71]),c_0_64]),c_0_144]),c_0_64]) ).
cnf(c_0_146,plain,
mult(op_c,mult(op_d,op_c)) = mult(op_c,mult(op_c,op_d)),
inference(spm,[status(thm)],[c_0_23,c_0_145]) ).
cnf(c_0_147,negated_conjecture,
mult(op_c,op_d) != mult(op_d,op_c),
goals ).
cnf(c_0_148,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_146]),c_0_140]),c_0_147]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP688-1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n013.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 19:01:41 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 9.38/6.81 % Version : CSE_E---1.7
% 9.38/6.81 % Problem : theBenchmark.p
% 9.38/6.81 % SZS status Unsatisfiable for theBenchmark.p
% 9.38/6.81 % SZS output start CNFRefutation
% See solution above
% 9.38/6.83 % Total time : 5.371s
%------------------------------------------------------------------------------