%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP667-2 : 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 : n026.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 04:26:50 PM UTC 2026
% Result : Unsatisfiable 139.87s 58.12s
% Output : CNFRefutation 140.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 10
% Syntax : Number of clauses : 133 ( 133 unt; 0 nHn; 4 RR)
% Number of literals : 133 ( 132 equ; 3 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 259 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c07,axiom,
mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
cnf(c08,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
cnf(c05,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(c06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(c03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(c09,axiom,
mult(f(X1),f(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
cnf(c02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
cnf(goals,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_10,axiom,
mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
c07 ).
cnf(c_0_11,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
c08 ).
cnf(c_0_12,axiom,
mult(X1,unit) = X1,
c05 ).
cnf(c_0_13,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(mult(X1,X2),mult(X3,mult(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_14,axiom,
mult(unit,X1) = X1,
c06 ).
cnf(c_0_15,axiom,
rd(mult(X1,X2),X2) = X1,
c04 ).
cnf(c_0_16,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_12]),c_0_14]),c_0_14]) ).
cnf(c_0_17,plain,
rd(mult(X1,mult(X2,X2)),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
mult(rd(X1,X2),X2) = X1,
c03 ).
cnf(c_0_19,plain,
mult(rd(X1,mult(X2,X2)),X2) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
rd(rd(X1,X2),X2) = rd(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_21,plain,
rd(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_22,axiom,
mult(f(X1),f(X1)) = X1,
c09 ).
cnf(c_0_23,plain,
rd(mult(X1,mult(X2,X1)),X1) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_24,plain,
rd(X1,mult(X1,X1)) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
mult(f(X1),X1) = mult(X1,f(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_22]),c_0_22]) ).
cnf(c_0_26,axiom,
ld(X1,mult(X1,X2)) = X2,
c02 ).
cnf(c_0_27,plain,
mult(X1,rd(X2,X1)) = rd(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_28,plain,
rd(f(X1),X1) = rd(unit,f(X1)),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_29,plain,
rd(mult(X1,f(X1)),X1) = f(X1),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_30,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_31,plain,
mult(mult(X1,mult(X2,f(X2))),f(X2)) = mult(mult(X1,f(X2)),mult(X2,f(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_22]),c_0_22]),c_0_25]),c_0_25]) ).
cnf(c_0_32,axiom,
mult(X1,ld(X1,X2)) = X2,
c01 ).
cnf(c_0_33,plain,
ld(mult(X1,mult(X2,mult(X3,X2))),mult(mult(X1,X2),mult(X3,mult(X2,X3)))) = X3,
inference(spm,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_34,plain,
mult(X1,rd(unit,f(X1))) = f(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_35,plain,
mult(rd(X1,f(X2)),X2) = mult(X1,f(X2)),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_36,plain,
mult(mult(X1,mult(X2,f(X2))),X2) = mult(mult(X1,X2),mult(X2,f(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_31]),c_0_31]),c_0_16]),c_0_22]),c_0_22]) ).
cnf(c_0_37,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_11,c_0_32]) ).
cnf(c_0_38,plain,
ld(mult(X1,mult(X2,f(X2))),mult(X1,X2)) = rd(unit,f(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_14]),c_0_18]),c_0_12]) ).
cnf(c_0_39,plain,
rd(mult(mult(X1,X2),mult(X2,f(X2))),X2) = mult(X1,mult(X2,f(X2))),
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_40,plain,
mult(ld(X1,X2),X1) = ld(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_41,plain,
ld(f(X1),mult(X1,f(X1))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_42,plain,
ld(X1,rd(mult(X1,X2),X1)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_43,plain,
ld(mult(rd(X1,X2),mult(X2,f(X2))),X1) = rd(unit,f(X2)),
inference(spm,[status(thm)],[c_0_38,c_0_18]) ).
cnf(c_0_44,plain,
mult(rd(X1,X2),mult(X2,f(X2))) = rd(mult(X1,mult(X2,f(X2))),X2),
inference(spm,[status(thm)],[c_0_39,c_0_18]) ).
cnf(c_0_45,plain,
ld(f(X1),mult(X1,X1)) = mult(X1,f(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_16]),c_0_22]) ).
cnf(c_0_46,plain,
rd(ld(X1,X2),X1) = ld(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_47,plain,
ld(X1,unit) = rd(unit,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_12]),c_0_21]) ).
cnf(c_0_48,plain,
ld(rd(mult(X1,mult(X2,f(X2))),X2),X1) = rd(unit,f(X2)),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
mult(mult(X1,mult(X2,X1)),X2) = mult(X1,mult(X2,mult(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_50,plain,
mult(f(X1),mult(X1,f(X1))) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_32,c_0_45]) ).
cnf(c_0_51,plain,
rd(mult(X1,X2),f(X2)) = mult(X1,f(X2)),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_52,plain,
ld(X1,rd(unit,X1)) = rd(rd(unit,X1),X1),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_32]) ).
cnf(c_0_54,plain,
ld(rd(X1,X2),rd(X1,mult(X2,f(X2)))) = rd(unit,f(X2)),
inference(spm,[status(thm)],[c_0_48,c_0_18]) ).
cnf(c_0_55,plain,
mult(mult(X1,X2),mult(X1,mult(X2,X1))) = mult(X1,mult(X2,mult(X1,mult(X2,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_13]),c_0_49]) ).
cnf(c_0_56,plain,
mult(mult(X1,mult(X2,mult(X2,f(X2)))),f(X2)) = mult(mult(X1,X2),mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_25]),c_0_50]) ).
cnf(c_0_57,plain,
rd(mult(X1,mult(X2,X2)),f(X2)) = mult(mult(X1,X2),f(X2)),
inference(spm,[status(thm)],[c_0_51,c_0_16]) ).
cnf(c_0_58,plain,
mult(mult(X1,f(X2)),X2) = mult(mult(X1,X2),f(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_51]),c_0_22]) ).
cnf(c_0_59,plain,
mult(rd(unit,f(X1)),mult(X1,f(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_34]),c_0_18]),c_0_14]),c_0_35]),c_0_14]) ).
cnf(c_0_60,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_61,plain,
ld(rd(unit,X1),X1) = rd(X1,rd(unit,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_47]),c_0_47]) ).
cnf(c_0_62,plain,
mult(mult(rd(X1,mult(X2,mult(X3,X2))),X2),mult(X3,mult(X2,X3))) = mult(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_63,plain,
mult(rd(X1,X2),rd(unit,f(X2))) = rd(X1,mult(X2,f(X2))),
inference(spm,[status(thm)],[c_0_32,c_0_54]) ).
cnf(c_0_64,plain,
mult(X1,mult(ld(X1,X2),mult(X2,X1))) = mult(X2,mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_40]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_65,plain,
mult(mult(X1,mult(X2,X2)),f(X2)) = mult(X1,mult(X2,mult(X2,f(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_56]),c_0_57]),c_0_16]) ).
cnf(c_0_66,plain,
mult(rd(X1,f(X2)),mult(X2,X2)) = mult(mult(X1,X2),f(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_35]),c_0_58]) ).
cnf(c_0_67,plain,
ld(ld(X1,X2),ld(X1,mult(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_68,plain,
ld(rd(unit,f(X1)),X1) = mult(X1,f(X1)),
inference(spm,[status(thm)],[c_0_26,c_0_59]) ).
cnf(c_0_69,plain,
rd(X1,rd(unit,X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_24]),c_0_61]) ).
cnf(c_0_70,plain,
mult(mult(X1,mult(X2,X3)),ld(X3,X2)) = mult(mult(X1,X3),mult(ld(X3,X2),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_40]),c_0_32]),c_0_32]) ).
cnf(c_0_71,plain,
ld(f(X1),X1) = f(X1),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_72,plain,
mult(rd(X1,X2),f(X2)) = rd(X1,f(X2)),
inference(spm,[status(thm)],[c_0_51,c_0_18]) ).
cnf(c_0_73,plain,
mult(rd(X1,mult(X2,f(X2))),X2) = mult(X1,rd(unit,f(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_34]),c_0_35]),c_0_14]),c_0_18]),c_0_12]) ).
cnf(c_0_74,plain,
rd(mult(X1,X2),mult(X2,f(X2))) = mult(X1,rd(unit,f(X2))),
inference(spm,[status(thm)],[c_0_63,c_0_15]) ).
cnf(c_0_75,plain,
mult(mult(ld(X1,X2),X2),X1) = mult(ld(X1,X2),mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_32]),c_0_40]),c_0_32]) ).
cnf(c_0_76,plain,
mult(ld(X1,X2),mult(X2,X1)) = ld(X1,mult(X2,mult(X2,X1))),
inference(spm,[status(thm)],[c_0_26,c_0_64]) ).
cnf(c_0_77,plain,
mult(rd(X1,f(X2)),mult(X2,mult(X2,f(X2)))) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_16]),c_0_22]),c_0_16]) ).
cnf(c_0_78,plain,
ld(mult(X1,f(X1)),X1) = rd(unit,f(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_34]),c_0_61]),c_0_69]),c_0_22]) ).
cnf(c_0_79,plain,
mult(rd(X1,f(X2)),mult(X2,f(X2))) = rd(mult(X1,mult(X2,f(X2))),f(X2)),
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_70,c_0_44]),c_0_71]),c_0_72]),c_0_72]),c_0_71]),c_0_25]) ).
cnf(c_0_80,plain,
mult(mult(X1,rd(unit,f(X2))),X2) = mult(mult(X1,X2),rd(unit,f(X2))),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,plain,
mult(mult(ld(X1,X2),X2),X1) = ld(X1,mult(X2,mult(X2,X1))),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
mult(mult(X1,mult(X2,X2)),rd(unit,f(X2))) = mult(X1,mult(X2,f(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(spm,[status(thm)],[c_0_70,c_0_77]),c_0_78]),c_0_79]),c_0_78]),c_0_35]),c_0_14]),c_0_18]) ).
cnf(c_0_83,plain,
mult(rd(X1,mult(X2,f(X2))),mult(X2,X2)) = mult(mult(X1,X2),rd(unit,f(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_73]),c_0_80]) ).
cnf(c_0_84,plain,
mult(rd(unit,X1),rd(unit,X1)) = rd(unit,mult(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_53]),c_0_47]),c_0_20]),c_0_47]),c_0_47]) ).
cnf(c_0_85,plain,
mult(mult(X1,X2),ld(X2,X1)) = mult(X2,mult(ld(X2,X1),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_40]),c_0_32]),c_0_32]) ).
cnf(c_0_86,plain,
mult(X1,mult(ld(X1,X2),X2)) = rd(mult(X2,mult(X2,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_81]),c_0_32]) ).
cnf(c_0_87,plain,
mult(mult(X1,X2),rd(unit,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_16]),c_0_84]),c_0_22]),c_0_18]) ).
cnf(c_0_88,plain,
mult(mult(X1,rd(unit,X2)),X2) = mult(mult(X1,X2),rd(unit,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(spm,[status(thm)],[c_0_80,c_0_16]),c_0_84]),c_0_22]),c_0_80]),c_0_16]),c_0_84]),c_0_22]) ).
cnf(c_0_89,plain,
mult(mult(X1,X2),ld(X2,X1)) = rd(mult(X1,mult(X1,X2)),X2),
inference(rw,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,plain,
ld(mult(X1,X2),X1) = rd(unit,X2),
inference(spm,[status(thm)],[c_0_26,c_0_87]) ).
cnf(c_0_91,plain,
rd(mult(mult(X1,X2),rd(unit,X2)),X2) = mult(X1,rd(unit,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_88]) ).
cnf(c_0_92,plain,
mult(rd(X1,X2),rd(mult(X2,X1),X2)) = mult(X1,rd(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_18]),c_0_27]) ).
cnf(c_0_93,plain,
ld(mult(X1,X2),rd(mult(X1,mult(X1,X2)),X2)) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_89]) ).
cnf(c_0_94,plain,
rd(X1,rd(unit,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_53,c_0_90]) ).
cnf(c_0_95,plain,
mult(X1,rd(unit,X2)) = rd(X1,X2),
inference(rw,[status(thm)],[c_0_91,c_0_87]) ).
cnf(c_0_96,plain,
mult(mult(X1,rd(X1,X2)),X2) = mult(rd(X1,X2),mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_27]),c_0_92]),c_0_18]) ).
cnf(c_0_97,plain,
ld(rd(unit,X1),X2) = 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_93,c_0_94]),c_0_95]),c_0_95]),c_0_96]),c_0_26]) ).
cnf(c_0_98,plain,
mult(rd(unit,X1),X2) = ld(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_94]),c_0_14]) ).
cnf(c_0_99,plain,
ld(rd(X1,X2),rd(mult(X1,X2),rd(X1,X2))) = rd(mult(X2,X2),rd(X1,X2)),
inference(spm,[status(thm)],[c_0_42,c_0_30]) ).
cnf(c_0_100,plain,
rd(ld(X1,X2),X2) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_15,c_0_98]) ).
cnf(c_0_101,plain,
mult(ld(X1,X2),X2) = ld(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_98]),c_0_98]) ).
cnf(c_0_102,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,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(spm,[status(thm)],[c_0_99,c_0_100]),c_0_94]),c_0_75]),c_0_76]),c_0_97]),c_0_32]),c_0_94]) ).
cnf(c_0_103,plain,
rd(rd(unit,X1),X2) = rd(unit,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_100,c_0_90]) ).
cnf(c_0_104,plain,
mult(mult(X1,mult(X2,X3)),ld(X3,X2)) = mult(mult(X1,X3),ld(X3,mult(X2,X2))),
inference(rw,[status(thm)],[c_0_70,c_0_101]) ).
cnf(c_0_105,plain,
mult(f(X1),mult(f(X1),X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_102,c_0_22]) ).
cnf(c_0_106,plain,
ld(mult(f(X1),X2),X1) = ld(X2,f(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_103]),c_0_98]),c_0_98]) ).
cnf(c_0_107,plain,
ld(X1,rd(unit,X2)) = rd(rd(unit,X1),X2),
inference(spm,[status(thm)],[c_0_95,c_0_98]) ).
cnf(c_0_108,plain,
rd(unit,rd(X1,X2)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_100,c_0_60]) ).
cnf(c_0_109,plain,
mult(mult(X1,X2),ld(X2,X3)) = rd(mult(X1,mult(X3,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(spm,[status(thm)],[c_0_104,c_0_105]),c_0_90]),c_0_95]),c_0_22]),c_0_106]),c_0_104]),c_0_22]) ).
cnf(c_0_110,plain,
ld(X1,rd(unit,X2)) = rd(unit,mult(X2,X1)),
inference(rw,[status(thm)],[c_0_107,c_0_103]) ).
cnf(c_0_111,plain,
rd(X1,rd(X2,X3)) = mult(X1,rd(X3,X2)),
inference(spm,[status(thm)],[c_0_95,c_0_108]) ).
cnf(c_0_112,plain,
rd(mult(X1,ld(X2,X3)),X3) = rd(mult(X1,X3),mult(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_95]),c_0_98]) ).
cnf(c_0_113,plain,
rd(X1,unit) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_114,plain,
rd(unit,ld(X1,X2)) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_90,c_0_32]) ).
cnf(c_0_115,plain,
rd(unit,mult(X1,rd(X2,X3))) = rd(rd(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_111]),c_0_14]) ).
cnf(c_0_116,plain,
mult(rd(X1,X2),rd(X2,X3)) = mult(rd(X1,mult(X2,X3)),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(spm,[status(thm)],[c_0_112,c_0_110]),c_0_95]),c_0_111]),c_0_113]),c_0_95]),c_0_95]),c_0_111]) ).
cnf(c_0_117,plain,
rd(unit,mult(rd(X1,X2),X3)) = ld(X3,rd(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_103]),c_0_98]) ).
cnf(c_0_118,plain,
rd(X1,ld(X2,X3)) = mult(X1,ld(X3,X2)),
inference(spm,[status(thm)],[c_0_95,c_0_114]) ).
cnf(c_0_119,plain,
ld(X1,rd(mult(X1,X2),X3)) = mult(rd(X2,mult(X1,X3)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]),c_0_111]),c_0_116]) ).
cnf(c_0_120,plain,
ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
inference(spm,[status(thm)],[c_0_97,c_0_108]) ).
cnf(c_0_121,plain,
mult(X1,rd(ld(X2,X3),X4)) = rd(X1,mult(X4,ld(X3,X2))),
inference(spm,[status(thm)],[c_0_111,c_0_118]) ).
cnf(c_0_122,plain,
rd(X1,mult(X2,ld(X3,X1))) = rd(mult(X3,X1),mult(X2,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(spm,[status(thm)],[c_0_119,c_0_98]),c_0_120]),c_0_113]),c_0_121]),c_0_98]),c_0_118]),c_0_95]),c_0_112]) ).
cnf(c_0_123,plain,
ld(ld(X1,X2),X3) = mult(ld(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_118]),c_0_14]) ).
cnf(c_0_124,plain,
mult(X1,mult(ld(X1,X2),X3)) = rd(mult(X2,mult(X3,X1)),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_122,c_0_98]),c_0_118]),c_0_123]),c_0_98]),c_0_118]),c_0_109]) ).
cnf(c_0_125,plain,
ld(X1,rd(mult(X2,mult(X3,X1)),X1)) = mult(ld(X1,X2),X3),
inference(spm,[status(thm)],[c_0_26,c_0_124]) ).
cnf(c_0_126,plain,
mult(mult(ld(X1,X2),X3),X1) = ld(X1,mult(X2,mult(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_125]),c_0_18]) ).
cnf(c_0_127,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
goals ).
cnf(c_0_128,plain,
mult(X1,mult(X2,rd(X3,X1))) = rd(mult(mult(X1,X2),X3),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_95,c_0_126]),c_0_95]),c_0_120]),c_0_113]),c_0_120]),c_0_113]) ).
cnf(c_0_129,plain,
rd(mult(X1,mult(X2,mult(X3,X2))),X2) = mult(mult(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_26]),c_0_11]) ).
cnf(c_0_130,negated_conjecture,
mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))),
inference(rw,[status(thm)],[c_0_127,c_0_11]) ).
cnf(c_0_131,plain,
mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_23]),c_0_129]),c_0_11]) ).
cnf(c_0_132,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP667-2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % 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
% 0.14/0.30 % Computer : n026.cluster.edu
% 0.14/0.30 % Model : x86_64 x86_64
% 0.14/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.30 % Memory : 8042.1875MB
% 0.14/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.30 % CPULimit : 300
% 0.14/0.30 % WCLimit : 300
% 0.14/0.30 % DateTime : Mon May 4 19:01:08 EDT 2026
% 0.14/0.30 % CPUTime :
% 0.14/0.31 % start to proof: theBenchmark
% 139.87/58.12 % Version : CSE_E---1.7
% 139.87/58.12 % Problem : theBenchmark.p
% 139.87/58.12 % SZS status Unsatisfiable for theBenchmark.p
% 139.87/58.12 % SZS output start CNFRefutation
% See solution above
% 140.25/58.46 % Total time : 45.595s
%------------------------------------------------------------------------------