%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM435+3 : 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 : n027.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 04:57:20 PM UTC 2026
% Result : Theorem 1.64s 1.84s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 25 unt; 0 def)
% Number of atoms : 123 ( 34 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 123 ( 50 ~; 40 |; 26 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1003,hypothesis,
( 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1003) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(m__1032,hypothesis,
( aInteger0(xm)
& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1032) ).
fof(m__979,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__979) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__,conjecture,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(c_0_10,hypothesis,
( 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)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1003])]) ).
fof(c_0_11,plain,
! [X48,X49] :
( ~ aInteger0(X48)
| ~ aInteger0(X49)
| aInteger0(sdtpldt0(X48,X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
fof(c_0_12,plain,
! [X72,X73,X75,X76] :
( ( aInteger0(X73)
| ~ aDivisorOf0(X73,X72)
| ~ aInteger0(X72) )
& ( X73 != sz00
| ~ aDivisorOf0(X73,X72)
| ~ aInteger0(X72) )
& ( aInteger0(esk1_2(X72,X73))
| ~ aDivisorOf0(X73,X72)
| ~ aInteger0(X72) )
& ( sdtasdt0(X73,esk1_2(X72,X73)) = X72
| ~ aDivisorOf0(X73,X72)
| ~ aInteger0(X72) )
& ( ~ aInteger0(X75)
| X75 = sz00
| ~ aInteger0(X76)
| sdtasdt0(X75,X76) != X72
| aDivisorOf0(X75,X72)
| ~ aInteger0(X72) ) ),
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_13,hypothesis,
aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,hypothesis,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[m__1032]) ).
cnf(c_0_15,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__979]) ).
fof(c_0_17,plain,
! [X47] :
( ~ aInteger0(X47)
| aInteger0(smndt0(X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_18,plain,
( aInteger0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
aDivisorOf0(sdtasdt0(xp,xq),sdtasdt0(sdtasdt0(xp,xq),xm)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,hypothesis,
( aInteger0(sdtasdt0(sdtasdt0(xp,xq),xm))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_16])]) ).
cnf(c_0_21,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_23,hypothesis,
sdtasdt0(sdtasdt0(xp,xq),esk2_0) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_24,plain,
! [X62,X63] :
( ~ aInteger0(X62)
| ~ aInteger0(X63)
| sdtasdt0(X62,X63) = sdtasdt0(X63,X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_25,hypothesis,
( aInteger0(sdtasdt0(xp,xq))
| ~ aInteger0(sdtasdt0(sdtasdt0(xp,xq),xm)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,hypothesis,
aInteger0(sdtasdt0(sdtasdt0(xp,xq),xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_27,hypothesis,
sdtasdt0(sdtasdt0(xp,xq),esk2_0) = sdtasdt0(sdtasdt0(xp,xq),xm),
inference(rw,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_28,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,hypothesis,
aInteger0(sdtasdt0(xp,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_30,hypothesis,
aInteger0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_31,hypothesis,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtasdt0(esk2_0,sdtasdt0(xp,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_32,hypothesis,
aInteger0(xm),
inference(split_conjunct,[status(thm)],[m__1032]) ).
fof(c_0_33,negated_conjecture,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_34,hypothesis,
sdtasdt0(esk2_0,sdtasdt0(xp,xq)) = sdtasdt0(xm,sdtasdt0(xp,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_32]),c_0_29])]) ).
fof(c_0_35,plain,
! [X59,X60,X61] :
( ~ aInteger0(X59)
| ~ aInteger0(X60)
| ~ aInteger0(X61)
| sdtasdt0(X59,sdtasdt0(X60,X61)) = sdtasdt0(sdtasdt0(X59,X60),X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_36,plain,
! [X50,X51] :
( ~ aInteger0(X50)
| ~ aInteger0(X51)
| aInteger0(sdtasdt0(X50,X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_37,negated_conjecture,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,hypothesis,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtasdt0(xm,sdtasdt0(xp,xq)),
inference(rw,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_39,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_41,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_42,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,negated_conjecture,
sdtasdt0(sdtasdt0(xp,xq),xm) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(rw,[status(thm)],[c_0_37,c_0_14]) ).
cnf(c_0_44,hypothesis,
sdtasdt0(xm,sdtasdt0(xp,xq)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32]),c_0_40]),c_0_41])]) ).
cnf(c_0_45,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_28,c_0_39]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
sdtasdt0(xm,sdtasdt0(xp,xq)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_28]),c_0_29]),c_0_32])]) ).
cnf(c_0_47,hypothesis,
sdtasdt0(xq,sdtasdt0(xm,xp)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_40]),c_0_41]),c_0_32])]) ).
cnf(c_0_48,negated_conjecture,
sdtasdt0(xq,sdtasdt0(xp,xm)) != sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(rw,[status(thm)],[c_0_46,c_0_44]) ).
cnf(c_0_49,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_28]),c_0_41]),c_0_32])]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM435+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n027.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 : Tue May 5 00:34:19 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.64/1.84 % Version : CSE_E---1.7
% 1.64/1.84 % Problem : theBenchmark.p
% 1.64/1.84 % SZS status Theorem for theBenchmark.p
% 1.64/1.84 % SZS output start CNFRefutation
% See solution above
% 1.64/1.84 % Total time : 1.372s
%------------------------------------------------------------------------------