%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP705-1 : TPTP v9.2.1. Released v4.0.0.
% 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 : n020.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 04:27:07 PM UTC 2026
% Result : Unsatisfiable 89.41s 52.28s
% Output : CNFRefutation 89.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 10
% Syntax : Number of clauses : 153 ( 153 unt; 0 nHn; 32 RR)
% Number of literals : 153 ( 152 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 218 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c05,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c07,axiom,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c08,axiom,
mult(op_a,mult(op_a,mult(op_a,op_a))) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
cnf(c02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c09,axiom,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
cnf(goals,negated_conjecture,
mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_10,axiom,
mult(X1,unit) = X1,
c05 ).
cnf(c_0_11,axiom,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
c07 ).
cnf(c_0_12,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_10]) ).
cnf(c_0_13,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
mult(rd(X1,X2),X2) = X1,
c03 ).
cnf(c_0_15,plain,
mult(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(X1,mult(X2,mult(X2,mult(X3,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_16,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_17,plain,
mult(mult(X1,mult(rd(X2,X3),X2)),X3) = mult(X1,mult(rd(X2,X3),mult(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_16]) ).
cnf(c_0_18,axiom,
mult(unit,X1) = X1,
c06 ).
cnf(c_0_19,axiom,
rd(mult(X1,X2),X2) = X1,
c04 ).
cnf(c_0_20,axiom,
mult(X1,ld(X1,X2)) = X2,
c01 ).
cnf(c_0_21,plain,
mult(mult(X1,mult(X2,mult(X2,mult(X3,X3)))),X4) = mult(X1,mult(X2,mult(X2,mult(X3,mult(X3,X4))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_13]),c_0_13]) ).
cnf(c_0_22,axiom,
mult(op_a,mult(op_a,mult(op_a,op_a))) = unit,
c08 ).
cnf(c_0_23,plain,
mult(mult(X1,rd(unit,X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_10]),c_0_18]),c_0_14]),c_0_10]) ).
cnf(c_0_24,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
mult(X1,mult(op_a,mult(op_a,mult(op_a,mult(op_a,X2))))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_10]) ).
cnf(c_0_26,plain,
mult(mult(X1,X2),ld(X2,unit)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
mult(op_a,mult(op_a,mult(op_a,mult(op_a,X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_25]),c_0_18]) ).
cnf(c_0_28,plain,
mult(X1,ld(ld(X2,unit),unit)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_26]) ).
cnf(c_0_29,plain,
ld(ld(X1,unit),unit) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_27]) ).
cnf(c_0_30,axiom,
ld(X1,mult(X1,X2)) = X2,
c02 ).
cnf(c_0_31,axiom,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit,
c09 ).
cnf(c_0_32,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_18]) ).
cnf(c_0_33,plain,
mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_34,plain,
rd(unit,X1) = ld(X1,unit),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_35,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) = ld(op_b,unit),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
mult(X1,mult(X1,ld(mult(X1,X1),X2))) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_32]) ).
cnf(c_0_37,plain,
mult(ld(X1,unit),mult(X1,mult(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_18]) ).
cnf(c_0_38,plain,
mult(mult(X1,mult(X1,X2)),X2) = mult(X1,mult(X1,mult(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_32]),c_0_32]) ).
cnf(c_0_39,plain,
mult(op_b,mult(mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(ld(op_b,unit),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(spm,[status(thm)],[c_0_12,c_0_35]) ).
cnf(c_0_40,plain,
mult(X1,mult(X2,mult(X2,mult(X1,mult(X2,mult(X2,ld(mult(X1,mult(X2,mult(X2,mult(X1,mult(X2,X2))))),X3))))))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_36]),c_0_13]),c_0_13]) ).
cnf(c_0_41,plain,
mult(X1,mult(ld(X1,unit),mult(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_37]),c_0_29]) ).
cnf(c_0_42,plain,
mult(op_b,mult(ld(op_b,unit),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_35]),c_0_20]),c_0_18]),c_0_39]) ).
cnf(c_0_43,plain,
mult(X1,mult(ld(X1,X2),ld(X1,X2))) = mult(X2,ld(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_44,plain,
mult(X1,mult(ld(X1,unit),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_37]),c_0_36]),c_0_37]) ).
cnf(c_0_45,plain,
rd(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_46,plain,
mult(ld(op_b,unit),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_42]),c_0_30]) ).
cnf(c_0_47,plain,
ld(X1,mult(X2,ld(X1,X2))) = mult(ld(X1,X2),ld(X1,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_43]) ).
cnf(c_0_48,plain,
ld(ld(X1,unit),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_44,c_0_20]) ).
cnf(c_0_49,plain,
rd(mult(X1,mult(X2,X2)),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_50,plain,
mult(ld(op_b,unit),mult(op_b,op_b)) = op_b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_19]) ).
cnf(c_0_51,plain,
rd(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_52,plain,
mult(mult(X1,X2),mult(X1,X2)) = mult(X1,mult(X2,mult(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_48]),c_0_48]),c_0_48]) ).
cnf(c_0_53,plain,
mult(rd(X1,X2),mult(X2,X3)) = mult(mult(X1,X2),ld(X2,X3)),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_54,plain,
mult(ld(op_b,unit),op_b) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_55,plain,
mult(mult(X1,X2),ld(X2,X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_14]),c_0_53]) ).
cnf(c_0_56,plain,
mult(mult(X1,ld(op_b,unit)),op_b) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_54]),c_0_10]),c_0_50]),c_0_54]),c_0_10]) ).
cnf(c_0_57,plain,
mult(X1,mult(X2,mult(X2,ld(mult(X1,mult(X2,X2)),X3)))) = X3,
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_58,plain,
mult(X1,mult(X1,ld(ld(X2,X1),unit))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_55]),c_0_32]) ).
cnf(c_0_59,plain,
mult(X1,ld(op_b,unit)) = rd(X1,op_b),
inference(spm,[status(thm)],[c_0_19,c_0_56]) ).
cnf(c_0_60,plain,
mult(ld(op_b,unit),mult(op_b,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_50]),c_0_20]) ).
cnf(c_0_61,plain,
mult(X1,ld(mult(op_a,mult(op_a,mult(op_a,X1))),unit)) = op_a,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_62,plain,
mult(X1,ld(ld(X2,X1),unit)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_58]),c_0_30]) ).
cnf(c_0_63,plain,
mult(op_a,mult(op_a,mult(op_a,rd(op_a,op_b)))) = ld(op_b,unit),
inference(spm,[status(thm)],[c_0_27,c_0_59]) ).
cnf(c_0_64,plain,
mult(ld(op_b,unit),X1) = ld(op_b,X1),
inference(spm,[status(thm)],[c_0_60,c_0_20]) ).
cnf(c_0_65,plain,
mult(ld(X1,unit),mult(X1,op_a)) = op_a,
inference(spm,[status(thm)],[c_0_37,c_0_61]) ).
cnf(c_0_66,plain,
ld(ld(X1,ld(X2,unit)),unit) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_62]) ).
cnf(c_0_67,plain,
ld(op_b,ld(mult(op_a,mult(op_a,rd(op_a,op_b))),unit)) = op_a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_63]),c_0_64]) ).
cnf(c_0_68,plain,
mult(mult(X1,X2),mult(ld(X2,ld(X1,unit)),op_a)) = op_a,
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,plain,
mult(X1,ld(X2,unit)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_70,plain,
mult(mult(X1,op_a),mult(op_a,mult(op_a,op_a))) = 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(spm,[status(thm)],[c_0_15,c_0_22]),c_0_10]),c_0_13]),c_0_22]),c_0_10]),c_0_22]),c_0_10]) ).
cnf(c_0_71,plain,
ld(mult(op_a,mult(op_a,rd(op_a,op_b))),unit) = mult(op_b,op_a),
inference(spm,[status(thm)],[c_0_20,c_0_67]) ).
cnf(c_0_72,plain,
rd(mult(X1,mult(X1,X2)),X2) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_19,c_0_32]) ).
cnf(c_0_73,plain,
rd(X1,ld(X2,unit)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_74,plain,
mult(rd(X1,X2),mult(rd(X2,X1),op_a)) = op_a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_48]),c_0_69]) ).
cnf(c_0_75,plain,
rd(op_a,mult(X1,op_a)) = ld(X1,unit),
inference(spm,[status(thm)],[c_0_19,c_0_65]) ).
cnf(c_0_76,plain,
ld(mult(X1,op_a),X1) = mult(op_a,mult(op_a,op_a)),
inference(spm,[status(thm)],[c_0_30,c_0_70]) ).
cnf(c_0_77,plain,
mult(op_a,mult(op_a,rd(op_a,op_b))) = rd(unit,mult(op_b,op_a)),
inference(spm,[status(thm)],[c_0_24,c_0_71]) ).
cnf(c_0_78,plain,
ld(ld(op_b,unit),X1) = mult(op_b,X1),
inference(spm,[status(thm)],[c_0_30,c_0_60]) ).
cnf(c_0_79,plain,
mult(mult(X1,op_a),mult(op_a,mult(op_a,mult(op_a,X1)))) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_61]),c_0_73]) ).
cnf(c_0_80,plain,
mult(rd(X1,mult(X2,X2)),mult(X2,mult(X2,X3))) = mult(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_81,plain,
ld(rd(X1,X2),unit) = rd(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_74]),c_0_75]) ).
cnf(c_0_82,plain,
rd(X1,mult(op_a,mult(op_a,op_a))) = mult(X1,op_a),
inference(spm,[status(thm)],[c_0_24,c_0_76]) ).
cnf(c_0_83,plain,
mult(op_a,rd(unit,mult(op_b,op_a))) = ld(op_b,unit),
inference(rw,[status(thm)],[c_0_63,c_0_77]) ).
cnf(c_0_84,plain,
ld(rd(X1,X2),mult(mult(X1,X2),X3)) = mult(X2,mult(X2,X3)),
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_85,plain,
rd(X1,mult(op_b,X1)) = ld(op_b,unit),
inference(spm,[status(thm)],[c_0_24,c_0_78]) ).
cnf(c_0_86,plain,
mult(mult(X1,X2),mult(X2,X2)) = mult(X1,mult(X2,mult(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_12]),c_0_13]) ).
cnf(c_0_87,plain,
mult(mult(X1,op_a),mult(X1,op_a)) = mult(X1,mult(op_a,mult(X1,op_a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_12]),c_0_13]),c_0_27]) ).
cnf(c_0_88,plain,
ld(rd(X1,mult(X2,X2)),mult(X1,X3)) = mult(X2,mult(X2,X3)),
inference(spm,[status(thm)],[c_0_30,c_0_80]) ).
cnf(c_0_89,plain,
rd(mult(op_a,mult(op_a,op_a)),X1) = ld(mult(X1,op_a),unit),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,plain,
mult(op_a,ld(mult(op_b,op_a),unit)) = ld(op_b,unit),
inference(rw,[status(thm)],[c_0_83,c_0_34]) ).
cnf(c_0_91,plain,
mult(mult(X1,mult(X2,X3)),ld(X2,X3)) = mult(X1,mult(X2,mult(X3,ld(X2,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_43]) ).
cnf(c_0_92,plain,
mult(mult(op_b,X1),mult(mult(op_b,X1),X2)) = mult(op_b,mult(mult(X1,mult(op_b,X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_78]) ).
cnf(c_0_93,plain,
mult(mult(X1,mult(X2,mult(X2,X3))),mult(X3,X3)) = mult(X1,mult(X2,mult(X2,mult(X3,mult(X3,X3))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_13]),c_0_13]) ).
cnf(c_0_94,plain,
mult(mult(X1,mult(X1,X2)),mult(X2,X2)) = mult(X1,mult(X1,mult(X2,mult(X2,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_32]),c_0_32]) ).
cnf(c_0_95,plain,
ld(mult(X1,X1),mult(X1,mult(X1,X2))) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_96,plain,
rd(mult(X1,mult(X2,mult(mult(X2,X3),mult(X2,mult(X2,X3))))),X3) = mult(mult(X1,mult(X2,mult(X2,X3))),mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_12]),c_0_52]) ).
cnf(c_0_97,plain,
mult(mult(X1,mult(X2,mult(op_a,mult(X2,op_a)))),X3) = mult(X1,mult(mult(X2,op_a),mult(mult(X2,op_a),X3))),
inference(spm,[status(thm)],[c_0_13,c_0_87]) ).
cnf(c_0_98,plain,
mult(mult(X1,mult(X1,op_a)),mult(op_a,mult(op_a,mult(op_a,X2)))) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_32]),c_0_13]),c_0_48]) ).
cnf(c_0_99,plain,
ld(mult(op_a,op_a),X1) = mult(op_a,mult(op_a,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_36]) ).
cnf(c_0_100,plain,
mult(X1,mult(ld(X1,unit),op_a)) = op_a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_65]),c_0_29]) ).
cnf(c_0_101,plain,
mult(ld(mult(op_b,op_a),unit),ld(mult(op_a,rd(op_a,op_b)),unit)) = op_a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_90]),c_0_59]) ).
cnf(c_0_102,plain,
mult(mult(X1,mult(op_b,mult(mult(X2,mult(op_b,X2)),X3))),X3) = mult(X1,mult(op_b,mult(mult(X2,mult(op_b,X2)),mult(X3,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_30]),c_0_30]),c_0_12]),c_0_92]) ).
cnf(c_0_103,plain,
mult(mult(X1,mult(X2,mult(X2,X3))),mult(X2,mult(X2,mult(X3,mult(X3,X3))))) = mult(X1,mult(mult(X2,mult(X2,X3)),mult(X2,mult(X2,mult(X3,mult(X3,X3)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_12]),c_0_13]),c_0_94]) ).
cnf(c_0_104,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = ld(mult(op_b,op_b),unit),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_35]),c_0_20]) ).
cnf(c_0_105,plain,
mult(X1,ld(mult(X1,X1),X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_106,plain,
mult(mult(X1,mult(X2,op_a)),mult(X2,X2)) = mult(X1,mult(mult(X2,op_a),mult(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_61]),c_0_73]),c_0_97]),c_0_79]) ).
cnf(c_0_107,plain,
mult(mult(X1,mult(X1,op_a)),X2) = mult(X1,mult(X1,mult(op_a,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_40]),c_0_22]),c_0_10]),c_0_99]),c_0_27]) ).
cnf(c_0_108,plain,
mult(ld(X1,unit),op_a) = ld(X1,op_a),
inference(spm,[status(thm)],[c_0_30,c_0_100]) ).
cnf(c_0_109,plain,
ld(mult(op_a,rd(op_a,op_b)),unit) = mult(op_b,mult(op_a,op_a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_101]),c_0_48]),c_0_12]) ).
cnf(c_0_110,plain,
rd(rd(op_a,op_b),mult(op_a,mult(op_a,rd(op_a,op_b)))) = mult(op_a,op_a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_63]),c_0_59]) ).
cnf(c_0_111,plain,
rd(X1,rd(unit,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_112,plain,
mult(mult(X1,mult(op_b,X2)),X2) = mult(X1,mult(op_b,mult(X2,X2))),
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_102,c_0_103]),c_0_13]),c_0_104]),c_0_105]),c_0_20]),c_0_18]),c_0_13]),c_0_104]),c_0_105]),c_0_20]),c_0_18]) ).
cnf(c_0_113,plain,
mult(X1,mult(mult(X1,op_a),mult(X1,X1))) = mult(X1,mult(X1,mult(op_a,mult(X1,X1)))),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_114,plain,
ld(ld(X1,op_a),unit) = mult(op_a,mult(op_a,mult(op_a,X1))),
inference(spm,[status(thm)],[c_0_27,c_0_58]) ).
cnf(c_0_115,plain,
ld(mult(op_a,rd(op_a,op_b)),op_a) = mult(op_b,mult(op_a,mult(op_a,op_a))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_13]) ).
cnf(c_0_116,plain,
mult(rd(op_a,op_b),mult(op_b,op_a)) = mult(op_a,op_a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_77]),c_0_111]) ).
cnf(c_0_117,plain,
mult(mult(X1,mult(op_b,mult(X2,X2))),X2) = mult(mult(X1,mult(op_b,X2)),mult(X2,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_112]) ).
cnf(c_0_118,plain,
mult(mult(X1,op_a),mult(X1,X1)) = mult(X1,mult(op_a,mult(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_113]),c_0_30]) ).
cnf(c_0_119,plain,
ld(mult(op_b,mult(op_a,mult(op_a,op_a))),unit) = rd(op_a,op_b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_77]),c_0_34]),c_0_90]),c_0_59]) ).
cnf(c_0_120,plain,
mult(mult(op_a,op_b),ld(op_b,op_a)) = mult(op_a,op_a),
inference(rw,[status(thm)],[c_0_116,c_0_53]) ).
cnf(c_0_121,plain,
mult(mult(X1,op_b),mult(op_a,op_a)) = mult(X1,mult(op_b,mult(op_a,op_a))),
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_118]),c_0_22]),c_0_10]),c_0_22]),c_0_10]) ).
cnf(c_0_122,plain,
mult(rd(X1,mult(X2,mult(X2,X3))),mult(X2,X2)) = rd(X1,X3),
inference(spm,[status(thm)],[c_0_45,c_0_14]) ).
cnf(c_0_123,plain,
mult(op_a,mult(op_a,rd(op_a,op_b))) = ld(mult(op_b,op_a),unit),
inference(rw,[status(thm)],[c_0_77,c_0_34]) ).
cnf(c_0_124,plain,
rd(X1,rd(op_a,op_b)) = mult(X1,mult(op_b,mult(op_a,mult(op_a,op_a)))),
inference(spm,[status(thm)],[c_0_73,c_0_119]) ).
cnf(c_0_125,plain,
mult(op_a,mult(op_a,ld(ld(op_b,op_a),unit))) = mult(op_a,op_b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_120]),c_0_32]) ).
cnf(c_0_126,plain,
ld(op_a,X1) = mult(op_a,mult(op_a,mult(op_a,X1))),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_127,plain,
mult(mult(X1,mult(op_b,mult(op_a,op_a))),X2) = mult(mult(X1,op_b),mult(op_a,mult(op_a,X2))),
inference(spm,[status(thm)],[c_0_13,c_0_121]) ).
cnf(c_0_128,plain,
mult(mult(X1,mult(op_b,op_a)),mult(op_a,op_a)) = mult(X1,mult(op_b,mult(op_a,mult(op_a,op_a)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_73]),c_0_124]) ).
cnf(c_0_129,plain,
mult(op_a,ld(ld(op_b,op_a),unit)) = op_b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_125]),c_0_126]),c_0_27]) ).
cnf(c_0_130,plain,
mult(mult(X1,op_b),mult(op_a,mult(op_a,op_a))) = mult(X1,mult(op_b,mult(op_a,mult(op_a,op_a)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_127]),c_0_128]) ).
cnf(c_0_131,plain,
mult(mult(X1,mult(op_b,mult(op_a,mult(op_a,op_a)))),X2) = mult(mult(X1,mult(op_b,op_a)),mult(op_a,mult(op_a,X2))),
inference(spm,[status(thm)],[c_0_13,c_0_128]) ).
cnf(c_0_132,plain,
ld(ld(op_b,op_a),unit) = mult(op_a,mult(op_a,mult(op_a,op_b))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_129]),c_0_126]) ).
cnf(c_0_133,plain,
mult(mult(X1,op_b),op_a) = mult(X1,mult(op_b,op_a)),
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_86,c_0_130]),c_0_13]),c_0_22]),c_0_10]),c_0_131]),c_0_22]),c_0_10]),c_0_13]),c_0_22]),c_0_10]),c_0_13]),c_0_22]),c_0_10]) ).
cnf(c_0_134,plain,
mult(ld(op_b,op_a),mult(op_a,mult(op_a,mult(op_a,op_b)))) = unit,
inference(spm,[status(thm)],[c_0_20,c_0_132]) ).
cnf(c_0_135,plain,
mult(rd(X1,mult(X2,X2)),X2) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_49,c_0_14]) ).
cnf(c_0_136,plain,
mult(mult(X1,op_b),ld(op_b,op_a)) = mult(X1,op_a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_14]),c_0_53]) ).
cnf(c_0_137,plain,
rd(X1,ld(op_b,op_a)) = mult(X1,mult(op_a,mult(op_a,mult(op_a,op_b)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_134]),c_0_10]),c_0_135]) ).
cnf(c_0_138,plain,
rd(mult(X1,mult(X2,mult(X2,X2))),mult(X2,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_86]) ).
cnf(c_0_139,plain,
mult(mult(X1,op_a),mult(op_a,mult(op_a,mult(op_a,op_b)))) = mult(X1,op_b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_136]),c_0_137]) ).
cnf(c_0_140,plain,
mult(rd(X1,mult(X2,mult(X2,X2))),X2) = rd(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_138,c_0_14]) ).
cnf(c_0_141,plain,
rd(X1,mult(op_a,op_a)) = mult(X1,mult(op_a,op_a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_22]),c_0_10]) ).
cnf(c_0_142,plain,
mult(mult(X1,op_a),op_b) = mult(X1,mult(op_a,op_b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]),c_0_13]),c_0_27]),c_0_82]) ).
cnf(c_0_143,plain,
mult(ld(X1,unit),X2) = ld(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_105]),c_0_20]) ).
cnf(c_0_144,plain,
ld(X1,mult(op_a,op_b)) = mult(ld(X1,op_a),op_b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_143]) ).
cnf(c_0_145,plain,
mult(X1,mult(ld(X1,op_a),op_b)) = mult(op_a,op_b),
inference(spm,[status(thm)],[c_0_20,c_0_144]) ).
cnf(c_0_146,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_14]) ).
cnf(c_0_147,plain,
mult(mult(op_a,X1),ld(X1,op_b)) = mult(op_a,op_b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_53]) ).
cnf(c_0_148,plain,
mult(mult(op_a,rd(op_b,X1)),X1) = mult(op_a,op_b),
inference(spm,[status(thm)],[c_0_147,c_0_146]) ).
cnf(c_0_149,plain,
rd(mult(op_a,op_b),X1) = mult(op_a,rd(op_b,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_148]) ).
cnf(c_0_150,negated_conjecture,
mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a),
goals ).
cnf(c_0_151,plain,
mult(mult(op_a,op_b),X1) = mult(op_a,mult(op_b,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_149]),c_0_73]) ).
cnf(c_0_152,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP705-1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.14/0.32 % Computer : n020.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 19:03:04 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 89.41/52.28 % Version : CSE_E---1.7
% 89.41/52.28 % Problem : theBenchmark.p
% 89.41/52.28 % SZS status Unsatisfiable for theBenchmark.p
% 89.41/52.28 % SZS output start CNFRefutation
% See solution above
% 89.71/52.58 % Total time : 40.832s
%------------------------------------------------------------------------------