%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM433+3 : 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 : n016.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 04:57:19 PM UTC 2026
% Result : Theorem 1.65s 1.84s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 98 ( 37 unt; 0 def)
% Number of atoms : 308 ( 81 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 357 ( 147 ~; 137 |; 57 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 50 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( sdtasdt0(xp,xq) != sz00
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(sdtasdt0(xp,xq),X1) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) )
=> ( ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
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(m__979,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__979) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mEquModSym,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).
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(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(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_14,negated_conjecture,
~ ( ( sdtasdt0(xp,xq) != sz00
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(sdtasdt0(xp,xq),X1) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) )
=> ( ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_15,negated_conjecture,
! [X92,X93] :
( sdtasdt0(xp,xq) != sz00
& aInteger0(esk2_0)
& sdtasdt0(sdtasdt0(xp,xq),esk2_0) = sdtpldt0(xa,smndt0(xb))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& ( ~ aInteger0(X93)
| sdtasdt0(xq,X93) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X92)
| sdtasdt0(xp,X92) != sdtpldt0(xa,smndt0(xb)) )
& ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(X92)
| sdtasdt0(xp,X92) != sdtpldt0(xa,smndt0(xb)) )
& ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ aInteger0(X92)
| sdtasdt0(xp,X92) != sdtpldt0(xa,smndt0(xb)) )
& ( ~ aInteger0(X93)
| sdtasdt0(xq,X93) != sdtpldt0(xa,smndt0(xb))
| ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) )
& ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) )
& ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) )
& ( ~ aInteger0(X93)
| sdtasdt0(xq,X93) != sdtpldt0(xa,smndt0(xb))
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
fof(c_0_16,plain,
! [X50,X51] :
( ~ aInteger0(X50)
| ~ aInteger0(X51)
| aInteger0(sdtpldt0(X50,X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
fof(c_0_17,plain,
! [X74,X75,X77,X78] :
( ( aInteger0(X75)
| ~ aDivisorOf0(X75,X74)
| ~ aInteger0(X74) )
& ( X75 != sz00
| ~ aDivisorOf0(X75,X74)
| ~ aInteger0(X74) )
& ( aInteger0(esk1_2(X74,X75))
| ~ aDivisorOf0(X75,X74)
| ~ aInteger0(X74) )
& ( sdtasdt0(X75,esk1_2(X74,X75)) = X74
| ~ aDivisorOf0(X75,X74)
| ~ aInteger0(X74) )
& ( ~ aInteger0(X77)
| X77 = sz00
| ~ aInteger0(X78)
| sdtasdt0(X77,X78) != X74
| aDivisorOf0(X77,X74)
| ~ aInteger0(X74) ) ),
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_18,negated_conjecture,
aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
sdtasdt0(sdtasdt0(xp,xq),esk2_0) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__979]) ).
fof(c_0_22,plain,
! [X49] :
( ~ aInteger0(X49)
| aInteger0(smndt0(X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_23,plain,
( aInteger0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
aDivisorOf0(sdtasdt0(xp,xq),sdtasdt0(sdtasdt0(xp,xq),esk2_0)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( aInteger0(sdtasdt0(sdtasdt0(xp,xq),esk2_0))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19]),c_0_21])]) ).
cnf(c_0_26,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__979]) ).
fof(c_0_28,plain,
! [X84,X85,X86] :
( ~ aInteger0(X84)
| ~ aInteger0(X85)
| ~ aInteger0(X86)
| X86 = sz00
| ~ sdteqdtlpzmzozddtrp0(X84,X85,X86)
| sdteqdtlpzmzozddtrp0(X85,X84,X86) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModSym])]) ).
cnf(c_0_29,negated_conjecture,
( aInteger0(sdtasdt0(xp,xq))
| ~ aInteger0(sdtasdt0(sdtasdt0(xp,xq),esk2_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
aInteger0(sdtasdt0(sdtasdt0(xp,xq),esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
fof(c_0_31,plain,
! [X79,X80,X81] :
( ( ~ sdteqdtlpzmzozddtrp0(X79,X80,X81)
| aDivisorOf0(X81,sdtpldt0(X79,smndt0(X80)))
| ~ aInteger0(X79)
| ~ aInteger0(X80)
| ~ aInteger0(X81)
| X81 = sz00 )
& ( ~ aDivisorOf0(X81,sdtpldt0(X79,smndt0(X80)))
| sdteqdtlpzmzozddtrp0(X79,X80,X81)
| ~ aInteger0(X79)
| ~ aInteger0(X80)
| ~ aInteger0(X81)
| X81 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_32,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,negated_conjecture,
aInteger0(sdtasdt0(xp,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_35,negated_conjecture,
sdtasdt0(xp,xq) != sz00,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_36,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_31]) ).
cnf(c_0_37,negated_conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,sdtasdt0(xp,xq)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_27]),c_0_21])]),c_0_35]) ).
fof(c_0_38,plain,
! [X54,X55,X56] :
( ~ aInteger0(X54)
| ~ aInteger0(X55)
| ~ aInteger0(X56)
| sdtpldt0(X54,sdtpldt0(X55,X56)) = sdtpldt0(sdtpldt0(X54,X55),X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_39,plain,
! [X60] :
( ( sdtpldt0(X60,smndt0(X60)) = sz00
| ~ aInteger0(X60) )
& ( sz00 = sdtpldt0(smndt0(X60),X60)
| ~ aInteger0(X60) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
fof(c_0_40,plain,
! [X59] :
( ( sdtpldt0(X59,sz00) = X59
| ~ aInteger0(X59) )
& ( X59 = sdtpldt0(sz00,X59)
| ~ aInteger0(X59) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_41,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_42,negated_conjecture,
aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xb,smndt0(xa))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_34]),c_0_21]),c_0_27])]),c_0_35]) ).
cnf(c_0_43,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_44,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_48,negated_conjecture,
( sdtasdt0(sdtasdt0(xp,xq),esk1_2(sdtpldt0(xb,smndt0(xa)),sdtasdt0(xp,xq))) = sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(sdtpldt0(xb,smndt0(xa))) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( aInteger0(esk1_2(sdtpldt0(xb,smndt0(xa)),sdtasdt0(xp,xq)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xa))) ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_50,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_26]) ).
cnf(c_0_51,plain,
( sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_46]),c_0_47])]) ).
fof(c_0_52,plain,
! [X52,X53] :
( ~ aInteger0(X52)
| ~ aInteger0(X53)
| aInteger0(sdtasdt0(X52,X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
fof(c_0_53,plain,
! [X61,X62,X63] :
( ~ aInteger0(X61)
| ~ aInteger0(X62)
| ~ aInteger0(X63)
| sdtasdt0(X61,sdtasdt0(X62,X63)) = sdtasdt0(sdtasdt0(X61,X62),X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_54,negated_conjecture,
( sdtasdt0(sdtasdt0(xp,xq),esk1_2(sdtpldt0(xb,smndt0(xa)),sdtasdt0(xp,xq))) = sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_20]),c_0_27])]) ).
cnf(c_0_55,negated_conjecture,
( aInteger0(esk1_2(sdtpldt0(xb,smndt0(xa)),sdtasdt0(xp,xq)))
| ~ aInteger0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_20]),c_0_27])]) ).
cnf(c_0_56,negated_conjecture,
( sdtpldt0(smndt0(xa),sdtasdt0(sdtasdt0(xp,xq),esk2_0)) = sdtpldt0(sz00,smndt0(xb))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_19]),c_0_21])]) ).
fof(c_0_57,plain,
! [X64,X65] :
( ~ aInteger0(X64)
| ~ aInteger0(X65)
| sdtasdt0(X64,X65) = sdtasdt0(X65,X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_58,negated_conjecture,
( sdtpldt0(sz00,sdtasdt0(sdtasdt0(xp,xq),esk2_0)) = sdtasdt0(sdtasdt0(xp,xq),esk2_0)
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_19]),c_0_21])]) ).
cnf(c_0_59,plain,
( X1 = sz00
| aDivisorOf0(X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_60,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,negated_conjecture,
sdtasdt0(sdtasdt0(xp,xq),esk1_2(sdtpldt0(xb,smndt0(xa)),sdtasdt0(xp,xq))) = sdtpldt0(xb,smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_26]),c_0_21])]) ).
cnf(c_0_63,negated_conjecture,
aInteger0(esk1_2(sdtpldt0(xb,smndt0(xa)),sdtasdt0(xp,xq))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_26]),c_0_21])]) ).
cnf(c_0_64,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_65,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_66,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_67,negated_conjecture,
sdtpldt0(smndt0(xa),sdtasdt0(sdtasdt0(xp,xq),esk2_0)) = sdtpldt0(sz00,smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_26]),c_0_27])]) ).
cnf(c_0_68,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,negated_conjecture,
aInteger0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_70,negated_conjecture,
sdtpldt0(sz00,sdtasdt0(sdtasdt0(xp,xq),esk2_0)) = sdtasdt0(sdtasdt0(xp,xq),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_26]),c_0_27])]) ).
cnf(c_0_71,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_60]) ).
cnf(c_0_72,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xq,esk1_2(sdtpldt0(xb,smndt0(xa)),sdtasdt0(xp,xq)))) = sdtpldt0(xb,smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_64]),c_0_65])]) ).
cnf(c_0_73,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_74,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_75,plain,
( sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_66]),c_0_26]) ).
cnf(c_0_76,negated_conjecture,
sdtpldt0(smndt0(xa),sdtasdt0(esk2_0,sdtasdt0(xp,xq))) = sdtpldt0(sz00,smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_34])]) ).
cnf(c_0_77,negated_conjecture,
sdtpldt0(sz00,sdtasdt0(esk2_0,sdtasdt0(xp,xq))) = sdtasdt0(esk2_0,sdtasdt0(xp,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_68]),c_0_69]),c_0_34])]) ).
cnf(c_0_78,negated_conjecture,
aInteger0(sdtasdt0(esk2_0,sdtasdt0(xp,xq))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_68]),c_0_34]),c_0_69])]) ).
cnf(c_0_79,negated_conjecture,
( aDivisorOf0(xp,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(sdtasdt0(xq,esk1_2(sdtpldt0(xb,smndt0(xa)),sdtasdt0(xp,xq)))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_65])]),c_0_73]) ).
cnf(c_0_80,plain,
( sdtpldt0(X1,sdtpldt0(sz00,X2)) = sdtpldt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_74]),c_0_47])]) ).
cnf(c_0_81,negated_conjecture,
sdtpldt0(xa,sdtpldt0(sz00,smndt0(xb))) = sdtasdt0(esk2_0,sdtasdt0(xp,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78]),c_0_21])]) ).
cnf(c_0_82,plain,
( sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_83,negated_conjecture,
aDivisorOf0(xp,sdtpldt0(xb,smndt0(xa))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_60]),c_0_63]),c_0_64])]) ).
cnf(c_0_84,negated_conjecture,
( sdtasdt0(sdtasdt0(xp,xq),esk2_0) = sdtasdt0(esk2_0,sdtasdt0(xp,xq))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_19]),c_0_21])]) ).
cnf(c_0_85,negated_conjecture,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_86,negated_conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xp),
inference(sr,[status(thm)],[inference(cn,[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_21]),c_0_27]),c_0_65])]),c_0_73]) ).
cnf(c_0_87,negated_conjecture,
sdtasdt0(sdtasdt0(xp,xq),esk2_0) = sdtasdt0(esk2_0,sdtasdt0(xp,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_26]),c_0_27])]) ).
cnf(c_0_88,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
| ~ aDivisorOf0(xq,sdtasdt0(sdtasdt0(xp,xq),esk2_0)) ),
inference(rw,[status(thm)],[c_0_85,c_0_19]) ).
cnf(c_0_89,negated_conjecture,
sdteqdtlpzmzozddtrp0(xa,xb,xp),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_86]),c_0_65]),c_0_21]),c_0_27])]),c_0_73]) ).
cnf(c_0_90,negated_conjecture,
sdtasdt0(esk2_0,sdtasdt0(xp,xq)) = sdtasdt0(xp,sdtasdt0(xq,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_87]),c_0_69]),c_0_64]),c_0_65])]) ).
cnf(c_0_91,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_61]),c_0_60]) ).
cnf(c_0_92,negated_conjecture,
~ aDivisorOf0(xq,sdtasdt0(sdtasdt0(xp,xq),esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89])]) ).
cnf(c_0_93,negated_conjecture,
sdtasdt0(xq,sdtasdt0(esk2_0,xp)) = sdtasdt0(xp,sdtasdt0(xq,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_64]),c_0_65]),c_0_69])]) ).
cnf(c_0_94,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_95,negated_conjecture,
~ aDivisorOf0(xq,sdtasdt0(xp,sdtasdt0(xq,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_61]),c_0_69]),c_0_64]),c_0_65])]) ).
cnf(c_0_96,negated_conjecture,
~ aInteger0(sdtasdt0(esk2_0,xp)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_93]),c_0_64])]),c_0_94]),c_0_95]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_60]),c_0_65]),c_0_69])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM433+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n016.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:35:21 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.65/1.84 % Version : CSE_E---1.7
% 1.65/1.84 % Problem : theBenchmark.p
% 1.65/1.84 % SZS status Theorem for theBenchmark.p
% 1.65/1.84 % SZS output start CNFRefutation
% See solution above
% 1.65/1.85 % Total time : 1.371s
%------------------------------------------------------------------------------