%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM424+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 : n013.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 04:57:17 PM UTC 2026
% Result : Theorem 30.25s 18.53s
% Output : CNFRefutation 30.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 16
% Syntax : Number of formulae : 140 ( 56 unt; 0 def)
% Number of atoms : 325 ( 120 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 322 ( 137 ~; 128 |; 42 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 5 ( 2 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 : 112 ( 0 sgn 49 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq) )
=> ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xb,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(m__704,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__704) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
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/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
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(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(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_16,negated_conjecture,
~ ( ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq) )
=> ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xb,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_17,plain,
! [X45,X46,X47] :
( ~ aInteger0(X45)
| ~ aInteger0(X46)
| ~ aInteger0(X47)
| sdtpldt0(X45,sdtpldt0(X46,X47)) = sdtpldt0(sdtpldt0(X45,X46),X47) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_18,negated_conjecture,
! [X76] :
( aInteger0(esk2_0)
& sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb))
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ( ~ aInteger0(X76)
| sdtasdt0(xq,X76) != sdtpldt0(xb,smndt0(xa)) )
& ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_19,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__704]) ).
fof(c_0_22,plain,
! [X40] :
( ~ aInteger0(X40)
| aInteger0(smndt0(X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
fof(c_0_23,plain,
! [X41,X42] :
( ~ aInteger0(X41)
| ~ aInteger0(X42)
| aInteger0(sdtpldt0(X41,X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
cnf(c_0_24,negated_conjecture,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,esk2_0),X1)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_25,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__704]) ).
fof(c_0_27,plain,
! [X50] :
( ( sdtpldt0(X50,sz00) = X50
| ~ aInteger0(X50) )
& ( X50 = sdtpldt0(sz00,X50)
| ~ aInteger0(X50) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(c_0_28,plain,
! [X51] :
( ( sdtpldt0(X51,smndt0(X51)) = sz00
| ~ aInteger0(X51) )
& ( sz00 = sdtpldt0(smndt0(X51),X51)
| ~ aInteger0(X51) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
cnf(c_0_29,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,esk2_0),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_33,plain,
! [X48,X49] :
( ~ aInteger0(X48)
| ~ aInteger0(X49)
| sdtpldt0(X48,X49) = sdtpldt0(X49,X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_34,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( aInteger0(sdtasdt0(xq,esk2_0))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_20]),c_0_21])]) ).
cnf(c_0_36,negated_conjecture,
( sdtpldt0(sdtasdt0(xq,esk2_0),sz00) = sdtasdt0(xq,esk2_0)
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_20]),c_0_32])]) ).
cnf(c_0_37,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk2_0),xb) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_34]),c_0_26])]) ).
cnf(c_0_39,negated_conjecture,
aInteger0(sdtasdt0(xq,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_25]),c_0_26])]) ).
cnf(c_0_40,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk2_0),sz00) = sdtasdt0(xq,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_25]),c_0_26])]) ).
cnf(c_0_41,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_34]),c_0_25]) ).
cnf(c_0_42,negated_conjecture,
sdtpldt0(xb,sdtasdt0(xq,esk2_0)) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_26]),c_0_39])]) ).
cnf(c_0_43,negated_conjecture,
sdtpldt0(sz00,sdtasdt0(xq,esk2_0)) = sdtasdt0(xq,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_40]),c_0_32]),c_0_39])]) ).
cnf(c_0_44,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_45,negated_conjecture,
sdtpldt0(smndt0(xb),sdtpldt0(xa,sz00)) = 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_41,c_0_42]),c_0_43]),c_0_39]),c_0_26])]) ).
cnf(c_0_46,plain,
( sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_44]),c_0_25]) ).
cnf(c_0_47,negated_conjecture,
sdtpldt0(smndt0(xb),xa) = sdtasdt0(xq,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_31]),c_0_21])]) ).
fof(c_0_48,plain,
! [X58,X59,X60] :
( ( sdtasdt0(X58,sdtpldt0(X59,X60)) = sdtpldt0(sdtasdt0(X58,X59),sdtasdt0(X58,X60))
| ~ aInteger0(X58)
| ~ aInteger0(X59)
| ~ aInteger0(X60) )
& ( sdtasdt0(sdtpldt0(X58,X59),X60) = sdtpldt0(sdtasdt0(X58,X60),sdtasdt0(X59,X60))
| ~ aInteger0(X58)
| ~ aInteger0(X59)
| ~ aInteger0(X60) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
fof(c_0_49,plain,
! [X43,X44] :
( ~ aInteger0(X43)
| ~ aInteger0(X44)
| aInteger0(sdtasdt0(X43,X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_50,negated_conjecture,
sdtpldt0(xa,sz00) = sdtpldt0(sz00,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42]),c_0_21]),c_0_26])]) ).
cnf(c_0_51,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_48]) ).
cnf(c_0_52,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
sdtpldt0(sz00,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_50]),c_0_21])]) ).
cnf(c_0_54,plain,
( aInteger0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_51]),c_0_52]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
sdtpldt0(xb,sdtasdt0(xq,esk2_0)) = xa,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_50]),c_0_53]) ).
fof(c_0_56,plain,
! [X62] :
( ( sdtasdt0(smndt0(sz10),X62) = smndt0(X62)
| ~ aInteger0(X62) )
& ( smndt0(X62) = sdtasdt0(X62,smndt0(sz10))
| ~ aInteger0(X62) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
cnf(c_0_57,plain,
( sdtpldt0(X1,sdtpldt0(X2,smndt0(sdtpldt0(X1,X2)))) = sz00
| ~ aInteger0(smndt0(sdtpldt0(X1,X2)))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_19]),c_0_29]) ).
cnf(c_0_58,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk2_0),xb) = xa,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_50]),c_0_53]) ).
cnf(c_0_59,negated_conjecture,
( aInteger0(sdtasdt0(X1,xa))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_39]),c_0_26])]) ).
cnf(c_0_60,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_61,negated_conjecture,
( sdtpldt0(sdtasdt0(xq,esk2_0),sdtpldt0(xb,smndt0(xa))) = sz00
| ~ aInteger0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_26]),c_0_39])]) ).
cnf(c_0_62,negated_conjecture,
( sdtpldt0(smndt0(xa),sdtasdt0(xq,esk2_0)) = sdtpldt0(sz00,smndt0(xb))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_20]),c_0_21])]) ).
cnf(c_0_63,negated_conjecture,
( aInteger0(smndt0(xa))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_21])]) ).
cnf(c_0_64,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_65,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_19]),c_0_29]) ).
cnf(c_0_66,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk2_0),sdtpldt0(xb,smndt0(xa))) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_25]),c_0_21])]) ).
cnf(c_0_67,negated_conjecture,
sdtpldt0(smndt0(xa),sdtasdt0(xq,esk2_0)) = sdtpldt0(sz00,smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_25]),c_0_26])]) ).
cnf(c_0_68,negated_conjecture,
aInteger0(smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_25]),c_0_64])]) ).
cnf(c_0_69,negated_conjecture,
sdtpldt0(xb,sdtpldt0(sz00,smndt0(xb))) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_39]),c_0_26])]),c_0_68])]) ).
cnf(c_0_70,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_71,negated_conjecture,
( sdtpldt0(sz00,sdtpldt0(smndt0(xb),xb)) = sz00
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_69]),c_0_26]),c_0_32])]) ).
cnf(c_0_72,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_19,c_0_70]),c_0_32])]) ).
cnf(c_0_73,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(smndt0(xb),xb)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_25]),c_0_26])]) ).
cnf(c_0_74,negated_conjecture,
( sdtpldt0(smndt0(xb),xb) = sz00
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_26])]) ).
cnf(c_0_75,negated_conjecture,
sdtpldt0(smndt0(xb),xb) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_25]),c_0_26])]) ).
cnf(c_0_76,negated_conjecture,
sdtpldt0(xb,sz00) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_75]),c_0_26])]) ).
cnf(c_0_77,plain,
( smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_34]),c_0_32])]) ).
cnf(c_0_78,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_19,c_0_31]),c_0_32])]) ).
cnf(c_0_79,negated_conjecture,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_76]),c_0_26])]) ).
cnf(c_0_80,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_25]),c_0_32])]) ).
cnf(c_0_81,negated_conjecture,
( sdtpldt0(sdtasdt0(xq,esk2_0),smndt0(smndt0(xb))) = sdtpldt0(xa,sz00)
| ~ aInteger0(smndt0(xb)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_44]),c_0_25]) ).
cnf(c_0_82,negated_conjecture,
( sdtpldt0(xb,smndt0(xb)) = sz00
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_69]),c_0_26])]) ).
cnf(c_0_83,negated_conjecture,
( aInteger0(sdtasdt0(X1,xb))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_79]),c_0_26]),c_0_32])]) ).
cnf(c_0_84,negated_conjecture,
sdtpldt0(xa,sz00) = xa,
inference(rw,[status(thm)],[c_0_50,c_0_53]) ).
cnf(c_0_85,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_80]),c_0_32])]) ).
cnf(c_0_86,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk2_0),smndt0(smndt0(xb))) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_25]),c_0_26])]) ).
cnf(c_0_87,negated_conjecture,
sdtpldt0(xb,smndt0(xb)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_25]),c_0_26])]) ).
cnf(c_0_88,negated_conjecture,
( aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_60]),c_0_26])]) ).
cnf(c_0_89,negated_conjecture,
sdtpldt0(smndt0(xa),xa) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_84]),c_0_85]),c_0_32]),c_0_21])]) ).
cnf(c_0_90,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk2_0),smndt0(smndt0(xb))) = xa,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_50]),c_0_53]) ).
cnf(c_0_91,negated_conjecture,
sdtpldt0(smndt0(sdtasdt0(xq,esk2_0)),xa) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_58]),c_0_26]),c_0_39])]) ).
cnf(c_0_92,negated_conjecture,
( sdtpldt0(smndt0(xb),sz00) = sdtpldt0(sz00,smndt0(xb))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_87]),c_0_26])]) ).
cnf(c_0_93,negated_conjecture,
aInteger0(smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_25]),c_0_64])]) ).
cnf(c_0_94,negated_conjecture,
( sdtpldt0(xa,smndt0(xa)) = sz00
| ~ aInteger0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_89]),c_0_21])]) ).
cnf(c_0_95,negated_conjecture,
( sdtpldt0(sz00,smndt0(smndt0(xb))) = sdtpldt0(sz00,xb)
| ~ aInteger0(smndt0(smndt0(xb))) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_90]),c_0_39])]),c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( sdtpldt0(sdtasdt0(xq,esk2_0),smndt0(xa)) = sdtpldt0(sz00,smndt0(xb))
| ~ aInteger0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_67]),c_0_39])]) ).
cnf(c_0_97,negated_conjecture,
sdtpldt0(smndt0(xb),sz00) = sdtpldt0(sz00,smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
cnf(c_0_98,negated_conjecture,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_25]),c_0_21])]) ).
cnf(c_0_99,negated_conjecture,
( sdtpldt0(sz00,smndt0(smndt0(xb))) = sdtpldt0(sz00,xb)
| ~ aInteger0(smndt0(xb)) ),
inference(spm,[status(thm)],[c_0_95,c_0_25]) ).
cnf(c_0_100,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk2_0),smndt0(xa)) = sdtpldt0(sz00,smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_25]),c_0_21])]) ).
cnf(c_0_101,negated_conjecture,
sdtpldt0(sz00,smndt0(xb)) = smndt0(xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_97]),c_0_93])]) ).
cnf(c_0_102,negated_conjecture,
sdtpldt0(smndt0(xa),sz00) = sdtpldt0(sz00,smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_98]),c_0_21])]),c_0_68])]) ).
cnf(c_0_103,negated_conjecture,
( sdtpldt0(sz00,smndt0(smndt0(xb))) = xb
| ~ aInteger0(smndt0(xb)) ),
inference(rw,[status(thm)],[c_0_99,c_0_79]) ).
fof(c_0_104,plain,
! [X52,X53,X54] :
( ~ aInteger0(X52)
| ~ aInteger0(X53)
| ~ aInteger0(X54)
| sdtasdt0(X52,sdtasdt0(X53,X54)) = sdtasdt0(sdtasdt0(X52,X53),X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_105,plain,
! [X65,X66,X68,X69] :
( ( aInteger0(X66)
| ~ aDivisorOf0(X66,X65)
| ~ aInteger0(X65) )
& ( X66 != sz00
| ~ aDivisorOf0(X66,X65)
| ~ aInteger0(X65) )
& ( aInteger0(esk1_2(X65,X66))
| ~ aDivisorOf0(X66,X65)
| ~ aInteger0(X65) )
& ( sdtasdt0(X66,esk1_2(X65,X66)) = X65
| ~ aDivisorOf0(X66,X65)
| ~ aInteger0(X65) )
& ( ~ aInteger0(X68)
| X68 = sz00
| ~ aInteger0(X69)
| sdtasdt0(X68,X69) != X65
| aDivisorOf0(X68,X65)
| ~ aInteger0(X65) ) ),
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_106,negated_conjecture,
aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_107,plain,
! [X55,X56] :
( ~ aInteger0(X55)
| ~ aInteger0(X56)
| sdtasdt0(X55,X56) = sdtasdt0(X56,X55) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_108,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk2_0),smndt0(xa)) = smndt0(xb),
inference(rw,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_109,negated_conjecture,
sdtpldt0(sz00,smndt0(xa)) = smndt0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_102]),c_0_68])]) ).
cnf(c_0_110,negated_conjecture,
sdtpldt0(sz00,smndt0(smndt0(xb))) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_25]),c_0_26])]) ).
cnf(c_0_111,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_112,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_113,negated_conjecture,
aDivisorOf0(xq,sdtasdt0(xq,esk2_0)),
inference(rw,[status(thm)],[c_0_106,c_0_20]) ).
cnf(c_0_114,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_115,negated_conjecture,
( ~ aInteger0(X1)
| sdtasdt0(xq,X1) != sdtpldt0(xb,smndt0(xa)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_116,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_117,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_118,negated_conjecture,
sdtpldt0(smndt0(sdtasdt0(xq,esk2_0)),smndt0(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_41,c_0_108]),c_0_109]),c_0_68]),c_0_39])]) ).
cnf(c_0_119,negated_conjecture,
( smndt0(smndt0(xb)) = xb
| ~ aInteger0(smndt0(smndt0(xb))) ),
inference(spm,[status(thm)],[c_0_70,c_0_110]) ).
cnf(c_0_120,plain,
( aInteger0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_111]),c_0_52]) ).
cnf(c_0_121,negated_conjecture,
sdtasdt0(xq,esk1_2(sdtasdt0(xq,esk2_0),xq)) = sdtasdt0(xq,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_39])]) ).
cnf(c_0_122,negated_conjecture,
aInteger0(esk1_2(sdtasdt0(xq,esk2_0),xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_113]),c_0_39])]) ).
cnf(c_0_123,negated_conjecture,
( sdtasdt0(X1,xq) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117])]) ).
cnf(c_0_124,negated_conjecture,
( sdtpldt0(smndt0(xb),smndt0(sdtasdt0(xq,esk2_0))) = smndt0(xa)
| ~ aInteger0(smndt0(sdtasdt0(xq,esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_118]),c_0_93])]) ).
cnf(c_0_125,negated_conjecture,
( smndt0(smndt0(xb)) = xb
| ~ aInteger0(smndt0(xb)) ),
inference(spm,[status(thm)],[c_0_119,c_0_25]) ).
cnf(c_0_126,negated_conjecture,
( aInteger0(sdtasdt0(X1,sdtasdt0(xq,esk2_0)))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]),c_0_117])]) ).
cnf(c_0_127,negated_conjecture,
( sdtasdt0(X1,sdtasdt0(X2,xq)) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_111]),c_0_117])]),c_0_52]) ).
cnf(c_0_128,negated_conjecture,
sdtpldt0(smndt0(xb),smndt0(sdtasdt0(xq,esk2_0))) = smndt0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_25]),c_0_39])]) ).
cnf(c_0_129,negated_conjecture,
smndt0(smndt0(xb)) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_25]),c_0_26])]) ).
cnf(c_0_130,negated_conjecture,
( aInteger0(smndt0(sdtasdt0(xq,esk2_0)))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_60]),c_0_39])]) ).
cnf(c_0_131,negated_conjecture,
( sdtasdt0(X1,sdtasdt0(xq,X2)) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_116]),c_0_117])]) ).
cnf(c_0_132,negated_conjecture,
( sdtpldt0(sz00,smndt0(sdtasdt0(xq,esk2_0))) = sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(smndt0(sdtasdt0(xq,esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_128]),c_0_129]),c_0_93])]) ).
cnf(c_0_133,negated_conjecture,
aInteger0(smndt0(sdtasdt0(xq,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_25]),c_0_64])]) ).
cnf(c_0_134,negated_conjecture,
( sdtasdt0(X1,sdtasdt0(xq,esk2_0)) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_121]),c_0_122])]) ).
cnf(c_0_135,negated_conjecture,
sdtpldt0(sz00,smndt0(sdtasdt0(xq,esk2_0))) = sdtpldt0(xb,smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133])]) ).
cnf(c_0_136,negated_conjecture,
( sdtpldt0(xb,smndt0(xa)) != smndt0(sdtasdt0(xq,esk2_0))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_60]),c_0_39])]) ).
cnf(c_0_137,negated_conjecture,
sdtpldt0(xb,smndt0(xa)) = smndt0(sdtasdt0(xq,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_135]),c_0_133])]) ).
cnf(c_0_138,negated_conjecture,
~ aInteger0(smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137])]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_25]),c_0_64])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM424+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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 : n013.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 00:31:56 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 30.25/18.53 % Version : CSE_E---1.7
% 30.25/18.53 % Problem : theBenchmark.p
% 30.25/18.53 % SZS status Theorem for theBenchmark.p
% 30.25/18.53 % SZS output start CNFRefutation
% See solution above
% 30.35/18.66 % Total time : 13.393s
%------------------------------------------------------------------------------