%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM454+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 : n011.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 04:57:23 PM UTC 2026
% Result : Theorem 3.69s 3.18s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 86 ( 30 unt; 0 def)
% Number of atoms : 237 ( 93 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 251 ( 100 ~; 107 |; 30 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 44 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(m__2171,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModRef) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(c_0_15,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_16,plain,
! [X105] :
( ( sdtpldt0(X105,smndt0(X105)) = sz00
| ~ aInteger0(X105) )
& ( sz00 = sdtpldt0(smndt0(X105),X105)
| ~ aInteger0(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
fof(c_0_17,negated_conjecture,
( sdtpldt0(sz10,xp) = smndt0(sz10)
& sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X94] :
( ~ aInteger0(X94)
| aInteger0(smndt0(X94)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
fof(c_0_19,plain,
! [X99,X100,X101] :
( ~ aInteger0(X99)
| ~ aInteger0(X100)
| ~ aInteger0(X101)
| sdtpldt0(X99,sdtpldt0(X100,X101)) = sdtpldt0(sdtpldt0(X99,X100),X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_20,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_23,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
aInteger0(sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
( sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,X1)) = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_22]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_27,c_0_21]) ).
fof(c_0_30,plain,
! [X104] :
( ( sdtpldt0(X104,sz00) = X104
| ~ aInteger0(X104) )
& ( X104 = sdtpldt0(sz00,X104)
| ~ aInteger0(X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_31,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,negated_conjecture,
( sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtpldt0(sz00,smndt0(xp))
| ~ aInteger0(smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[m__2171]) ).
cnf(c_0_34,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz00) = sdtpldt0(sz00,sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_21]),c_0_21]),c_0_26]),c_0_22])]) ).
fof(c_0_36,plain,
! [X127,X128] :
( ~ aInteger0(X127)
| ~ aInteger0(X128)
| X128 = sz00
| sdteqdtlpzmzozddtrp0(X127,X127,X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModRef])]) ).
cnf(c_0_37,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,negated_conjecture,
( sdtpldt0(sz00,smndt0(xp)) = sdtpldt0(sz00,xp)
| ~ aInteger0(smndt0(xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_32]),c_0_33])]) ).
cnf(c_0_39,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz10,xp)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_26])]) ).
fof(c_0_40,plain,
! [X124,X125,X126] :
( ( ~ sdteqdtlpzmzozddtrp0(X124,X125,X126)
| aDivisorOf0(X126,sdtpldt0(X124,smndt0(X125)))
| ~ aInteger0(X124)
| ~ aInteger0(X125)
| ~ aInteger0(X126)
| X126 = sz00 )
& ( ~ aDivisorOf0(X126,sdtpldt0(X124,smndt0(X125)))
| sdteqdtlpzmzozddtrp0(X124,X125,X126)
| ~ aInteger0(X124)
| ~ aInteger0(X125)
| ~ aInteger0(X126)
| X126 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_41,plain,
( X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__2171]) ).
cnf(c_0_43,negated_conjecture,
( smndt0(xp) = sdtpldt0(sz00,xp)
| ~ aInteger0(smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz00) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_45,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_46,plain,
! [X102,X103] :
( ~ aInteger0(X102)
| ~ aInteger0(X103)
| sdtpldt0(X102,X103) = sdtpldt0(X103,X102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_47,plain,
! [X119,X120,X122,X123] :
( ( aInteger0(X120)
| ~ aDivisorOf0(X120,X119)
| ~ aInteger0(X119) )
& ( X120 != sz00
| ~ aDivisorOf0(X120,X119)
| ~ aInteger0(X119) )
& ( aInteger0(esk1_2(X119,X120))
| ~ aDivisorOf0(X120,X119)
| ~ aInteger0(X119) )
& ( sdtasdt0(X120,esk1_2(X119,X120)) = X119
| ~ aDivisorOf0(X120,X119)
| ~ aInteger0(X119) )
& ( ~ aInteger0(X122)
| X122 = sz00
| ~ aInteger0(X123)
| sdtasdt0(X122,X123) != X119
| aDivisorOf0(X122,X119)
| ~ aInteger0(X119) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivisor])])])])])]) ).
cnf(c_0_48,plain,
( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
| X3 = sz00
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,hypothesis,
( sdteqdtlpzmzozddtrp0(X1,X1,xp)
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_33]),c_0_42]) ).
cnf(c_0_50,negated_conjecture,
smndt0(xp) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_23]),c_0_33])]) ).
cnf(c_0_51,negated_conjecture,
sdtpldt0(sz10,sdtpldt0(xp,sz00)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_44]),c_0_45]),c_0_33]),c_0_22])]) ).
cnf(c_0_52,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,hypothesis,
( aDivisorOf0(xp,sdtpldt0(X1,smndt0(X1)))
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_33])]),c_0_42]) ).
cnf(c_0_55,negated_conjecture,
sdtpldt0(xp,sdtpldt0(sz00,xp)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_50]),c_0_33])]) ).
cnf(c_0_56,negated_conjecture,
sdtpldt0(sz10,sdtpldt0(sz00,xp)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_45]),c_0_33])]) ).
cnf(c_0_57,negated_conjecture,
aInteger0(sdtpldt0(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_50]),c_0_33])]) ).
cnf(c_0_58,plain,
( esk1_2(X1,X2) = sz00
| sdteqdtlpzmzozddtrp0(X3,X3,esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X3)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
aDivisorOf0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_55]),c_0_33])]) ).
cnf(c_0_60,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtpldt0(sz00,sdtpldt0(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_56]),c_0_57])]) ).
cnf(c_0_61,negated_conjecture,
( esk1_2(sz00,xp) = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,esk1_2(sz00,xp))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_45])]) ).
cnf(c_0_62,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz00,xp)) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_60]),c_0_33])]) ).
cnf(c_0_63,negated_conjecture,
sdtpldt0(sdtpldt0(sz00,xp),xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_50]),c_0_33])]) ).
cnf(c_0_64,hypothesis,
( esk1_2(sz00,xp) = sz00
| sdteqdtlpzmzozddtrp0(xp,xp,esk1_2(sz00,xp)) ),
inference(spm,[status(thm)],[c_0_61,c_0_33]) ).
cnf(c_0_65,negated_conjecture,
sdtpldt0(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_37]),c_0_33])]) ).
cnf(c_0_66,negated_conjecture,
sdtpldt0(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_37]),c_0_33])]) ).
fof(c_0_67,plain,
! [X117,X118] :
( ~ aInteger0(X117)
| ~ aInteger0(X118)
| sdtasdt0(X117,X118) != sz00
| X117 = sz00
| X118 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).
cnf(c_0_68,hypothesis,
( esk1_2(sz00,xp) = sz00
| aDivisorOf0(esk1_2(sz00,xp),sz00)
| ~ aInteger0(esk1_2(sz00,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_64]),c_0_50]),c_0_65]),c_0_66]),c_0_33])]) ).
fof(c_0_69,plain,
! [X116] :
( ( sdtasdt0(smndt0(sz10),X116) = smndt0(X116)
| ~ aInteger0(X116) )
& ( smndt0(X116) = sdtasdt0(X116,smndt0(sz10))
| ~ aInteger0(X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
cnf(c_0_70,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_71,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_72,plain,
( aInteger0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_73,hypothesis,
( esk1_2(sz00,xp) = sz00
| aDivisorOf0(esk1_2(sz00,xp),sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_53]),c_0_59]),c_0_45])]) ).
fof(c_0_74,plain,
! [X112,X113,X114] :
( ( sdtasdt0(X112,sdtpldt0(X113,X114)) = sdtpldt0(sdtasdt0(X112,X113),sdtasdt0(X112,X114))
| ~ aInteger0(X112)
| ~ aInteger0(X113)
| ~ aInteger0(X114) )
& ( sdtasdt0(sdtpldt0(X112,X113),X114) = sdtpldt0(sdtasdt0(X112,X114),sdtasdt0(X113,X114))
| ~ aInteger0(X112)
| ~ aInteger0(X113)
| ~ aInteger0(X114) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
cnf(c_0_75,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,plain,
( esk1_2(sz00,X1) = sz00
| X1 = sz00
| ~ aDivisorOf0(X1,sz00)
| ~ aInteger0(esk1_2(sz00,X1))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71])]),c_0_45])]) ).
cnf(c_0_77,hypothesis,
( esk1_2(sz00,xp) = sz00
| aInteger0(esk1_2(sz00,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_45])]) ).
cnf(c_0_78,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_79,plain,
( sdtasdt0(X1,sdtpldt0(sz10,xp)) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(rw,[status(thm)],[c_0_75,c_0_21]) ).
cnf(c_0_80,hypothesis,
esk1_2(sz00,xp) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_59]),c_0_33])]),c_0_42]) ).
cnf(c_0_81,plain,
( sdtpldt0(sdtasdt0(X1,X2),smndt0(X1)) = sdtasdt0(X1,sdtpldt0(X2,sdtpldt0(sz10,xp)))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_26])]) ).
cnf(c_0_82,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_80]),c_0_59]),c_0_45])]) ).
cnf(c_0_83,hypothesis,
sdtasdt0(xp,sdtpldt0(sz10,xp)) = xp,
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(spm,[status(thm)],[c_0_81,c_0_82]),c_0_50]),c_0_65]),c_0_65]),c_0_39]),c_0_45]),c_0_33])]) ).
cnf(c_0_84,hypothesis,
sdtasdt0(xp,xp) = sz00,
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(spm,[status(thm)],[c_0_81,c_0_83]),c_0_50]),c_0_65]),c_0_66]),c_0_60]),c_0_65]),c_0_65]),c_0_26]),c_0_33])]) ).
cnf(c_0_85,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_84]),c_0_33])]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM454+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
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:35:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.69/3.18 % Version : CSE_E---1.7
% 3.69/3.18 % Problem : theBenchmark.p
% 3.69/3.18 % SZS status Theorem for theBenchmark.p
% 3.69/3.18 % SZS output start CNFRefutation
% See solution above
% 3.69/3.19 % Total time : 2.374s
%------------------------------------------------------------------------------