%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM426+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:02 PM UTC 2026
% Result : Theorem 0.72s 0.50s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 16
% Syntax : Number of formulae : 106 ( 53 unt; 0 def)
% Number of atoms : 220 ( 96 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 190 ( 76 ~; 70 |; 33 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__704,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__704) ).
fof(m__724,hypothesis,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__724) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__747,hypothesis,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__747) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(m__,conjecture,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_16,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_simplification,[status(thm)],[m__704]) ).
fof(c_0_17,hypothesis,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__724])]) ).
fof(c_0_18,plain,
! [X6,X7] :
( aInteger0(sdtpldt0(X6,X7))
| ~ aInteger0(X7)
| ~ aInteger0(X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])])]) ).
fof(c_0_19,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X17,X18,X19] :
( sdtasdt0(X17,sdtasdt0(X18,X19)) = sdtasdt0(sdtasdt0(X17,X18),X19)
| ~ aInteger0(X19)
| ~ aInteger0(X18)
| ~ aInteger0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_21,hypothesis,
sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,hypothesis,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[m__747]) ).
cnf(c_0_23,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X5] :
( aInteger0(smndt0(X5))
| ~ aInteger0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
fof(c_0_26,plain,
! [X27] :
( ( ~ aInteger0(X27)
| smndt0(X27) = sdtasdt0(X27,smndt0(sz10)) )
& ( ~ aInteger0(X27)
| sdtasdt0(smndt0(sz10),X27) = smndt0(X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])])]) ).
cnf(c_0_27,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,hypothesis,
sdtasdt0(xq,esk2_0) = sdtasdt0(xq,xn),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,hypothesis,
aInteger0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,hypothesis,
( ~ aInteger0(smndt0(xb))
| aInteger0(sdtasdt0(xq,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_24])]) ).
cnf(c_0_32,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_34,plain,
( ~ aInteger0(X1)
| smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,hypothesis,
( ~ aInteger0(X1)
| sdtasdt0(sdtasdt0(xq,xn),X1) = sdtasdt0(xq,sdtasdt0(esk2_0,X1)) ),
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_36,hypothesis,
aInteger0(sdtasdt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,hypothesis,
( ~ aInteger0(smndt0(sz10))
| sdtasdt0(xq,sdtasdt0(esk2_0,smndt0(sz10))) = smndt0(sdtasdt0(xq,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_38,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
fof(c_0_39,plain,
! [X16] :
( ( ~ aInteger0(X16)
| sz00 = sdtpldt0(smndt0(X16),X16) )
& ( ~ aInteger0(X16)
| sdtpldt0(X16,smndt0(X16)) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).
cnf(c_0_40,hypothesis,
sdtasdt0(xq,sdtasdt0(esk2_0,smndt0(sz10))) = smndt0(sdtasdt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_38])]) ).
fof(c_0_41,plain,
! [X23,X24,X25] :
( ( ~ aInteger0(X25)
| ~ aInteger0(X24)
| ~ aInteger0(X23)
| sdtasdt0(sdtpldt0(X23,X24),X25) = sdtpldt0(sdtasdt0(X23,X25),sdtasdt0(X24,X25)) )
& ( ~ aInteger0(X25)
| ~ aInteger0(X24)
| ~ aInteger0(X23)
| sdtasdt0(X23,sdtpldt0(X24,X25)) = sdtpldt0(sdtasdt0(X23,X24),sdtasdt0(X23,X25)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])])]) ).
cnf(c_0_42,plain,
( ~ aInteger0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,hypothesis,
smndt0(sdtasdt0(xq,xn)) = sdtasdt0(xq,smndt0(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_34]),c_0_29])]) ).
cnf(c_0_44,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,hypothesis,
sdtpldt0(sdtasdt0(xq,smndt0(esk2_0)),sdtasdt0(xq,xn)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_36])]) ).
cnf(c_0_46,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__747]) ).
fof(c_0_47,plain,
! [X28,X29] :
( X29 = sz00
| X28 = sz00
| sdtasdt0(X28,X29) != sz00
| ~ aInteger0(X29)
| ~ aInteger0(X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])])]) ).
cnf(c_0_48,hypothesis,
( ~ aInteger0(smndt0(esk2_0))
| sdtasdt0(xq,sdtpldt0(smndt0(esk2_0),xn)) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_30])]) ).
cnf(c_0_49,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,hypothesis,
sdtasdt0(xq,sdtpldt0(smndt0(esk2_0),xn)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_32]),c_0_29])]) ).
cnf(c_0_51,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_52,hypothesis,
( ~ aInteger0(sdtpldt0(smndt0(esk2_0),xn))
| sdtpldt0(smndt0(esk2_0),xn) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_30])]),c_0_51]) ).
fof(c_0_53,plain,
! [X13,X14] :
( sdtpldt0(X13,X14) = sdtpldt0(X14,X13)
| ~ aInteger0(X14)
| ~ aInteger0(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_54,hypothesis,
( ~ aInteger0(smndt0(esk2_0))
| sdtpldt0(smndt0(esk2_0),xn) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_23]),c_0_46])]) ).
fof(c_0_55,plain,
! [X10,X11,X12] :
( sdtpldt0(X10,sdtpldt0(X11,X12)) = sdtpldt0(sdtpldt0(X10,X11),X12)
| ~ aInteger0(X12)
| ~ aInteger0(X11)
| ~ aInteger0(X10) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_56,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,hypothesis,
sdtpldt0(smndt0(esk2_0),xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_32]),c_0_29])]) ).
cnf(c_0_58,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_59,hypothesis,
( ~ aInteger0(smndt0(esk2_0))
| sdtpldt0(xn,smndt0(esk2_0)) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_46])]) ).
cnf(c_0_60,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_42]),c_0_32]) ).
cnf(c_0_61,hypothesis,
sdtpldt0(xn,smndt0(esk2_0)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_32]),c_0_29])]) ).
fof(c_0_62,plain,
! [X15] :
( ( ~ aInteger0(X15)
| X15 = sdtpldt0(sz00,X15) )
& ( ~ aInteger0(X15)
| sdtpldt0(X15,sz00) = X15 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
cnf(c_0_63,hypothesis,
( ~ aInteger0(smndt0(esk2_0))
| sdtpldt0(smndt0(xn),sz00) = sdtpldt0(sz00,smndt0(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_46])]) ).
cnf(c_0_64,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_65,hypothesis,
sdtpldt0(smndt0(xn),sz00) = sdtpldt0(sz00,smndt0(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_32]),c_0_29])]) ).
cnf(c_0_66,hypothesis,
( ~ aInteger0(smndt0(xn))
| sdtpldt0(sz00,smndt0(esk2_0)) = smndt0(xn) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_67,hypothesis,
( ~ aInteger0(X1)
| ~ aInteger0(smndt0(xb))
| sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,xn),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_22]),c_0_24])]) ).
cnf(c_0_68,plain,
( ~ aInteger0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,hypothesis,
sdtpldt0(sz00,smndt0(esk2_0)) = smndt0(xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_32]),c_0_46])]) ).
cnf(c_0_70,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_71,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,xn),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_32]),c_0_33])]) ).
cnf(c_0_72,hypothesis,
( ~ aInteger0(smndt0(esk2_0))
| smndt0(esk2_0) = smndt0(xn) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,hypothesis,
( ~ aInteger0(smndt0(xn))
| aInteger0(sdtpldt0(sz00,smndt0(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_65]),c_0_70])]) ).
cnf(c_0_74,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),xb) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_42]),c_0_33])]) ).
cnf(c_0_75,hypothesis,
smndt0(esk2_0) = smndt0(xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_32]),c_0_29])]) ).
cnf(c_0_76,hypothesis,
aInteger0(sdtpldt0(sz00,smndt0(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_32]),c_0_46])]) ).
cnf(c_0_77,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_68]),c_0_70])]) ).
cnf(c_0_78,hypothesis,
sdtpldt0(xb,sdtasdt0(xq,xn)) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_74]),c_0_33]),c_0_36])]) ).
cnf(c_0_79,hypothesis,
sdtpldt0(smndt0(xn),xn) = sz00,
inference(rw,[status(thm)],[c_0_57,c_0_75]) ).
cnf(c_0_80,hypothesis,
aInteger0(smndt0(xn)),
inference(rw,[status(thm)],[c_0_76,c_0_69]) ).
cnf(c_0_81,hypothesis,
sdtpldt0(sz00,sdtpldt0(xa,sz00)) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_36]),c_0_33])]) ).
cnf(c_0_82,hypothesis,
sdtpldt0(smndt0(xn),esk2_0) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_75]),c_0_29])]) ).
cnf(c_0_83,hypothesis,
sdtpldt0(smndt0(smndt0(xn)),sz00) = sdtpldt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_79]),c_0_46]),c_0_80])]) ).
cnf(c_0_84,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_58]),c_0_70])]),c_0_23]) ).
cnf(c_0_85,hypothesis,
sdtpldt0(sz00,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_64]),c_0_24])]) ).
cnf(c_0_86,hypothesis,
sdtpldt0(sz00,esk2_0) = sdtpldt0(sz00,xn),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_82]),c_0_29]),c_0_80])]),c_0_83]) ).
cnf(c_0_87,hypothesis,
sdtpldt0(xa,sz00) = xa,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_81]),c_0_24]),c_0_70])]),c_0_85]) ).
cnf(c_0_88,hypothesis,
sdtpldt0(sz00,xn) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_86]),c_0_29])]) ).
cnf(c_0_89,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),xb) = xa,
inference(rw,[status(thm)],[c_0_74,c_0_87]) ).
cnf(c_0_90,hypothesis,
esk2_0 = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_88]),c_0_46])]) ).
cnf(c_0_91,hypothesis,
aInteger0(sdtasdt0(xq,smndt0(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_43]),c_0_36])]) ).
cnf(c_0_92,hypothesis,
sdtpldt0(sdtasdt0(xq,smndt0(xn)),xa) = sdtpldt0(sz00,xb),
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_60,c_0_89]),c_0_43]),c_0_90]),c_0_33]),c_0_36])]) ).
cnf(c_0_93,hypothesis,
aInteger0(sdtasdt0(xq,smndt0(xn))),
inference(spm,[status(thm)],[c_0_91,c_0_75]) ).
cnf(c_0_94,hypothesis,
sdtpldt0(sz00,sdtpldt0(sz00,xb)) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_92]),c_0_24]),c_0_93])]) ).
cnf(c_0_95,hypothesis,
sdtpldt0(xa,sdtasdt0(xq,smndt0(xn))) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_92]),c_0_24]),c_0_93])]) ).
cnf(c_0_96,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_68]),c_0_33])]) ).
fof(c_0_97,negated_conjecture,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_98,hypothesis,
sdtpldt0(xa,sdtasdt0(xq,smndt0(xn))) = xb,
inference(rw,[status(thm)],[c_0_95,c_0_96]) ).
fof(c_0_99,negated_conjecture,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
cnf(c_0_100,hypothesis,
sdtpldt0(sz00,sdtasdt0(xq,smndt0(xn))) = sdtpldt0(smndt0(xa),xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_98]),c_0_93]),c_0_24])]) ).
fof(c_0_101,negated_conjecture,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(fof_nnf,[status(thm)],[c_0_99]) ).
cnf(c_0_102,hypothesis,
sdtpldt0(smndt0(xa),xb) = sdtasdt0(xq,smndt0(xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_100]),c_0_93])]) ).
cnf(c_0_103,negated_conjecture,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_104,hypothesis,
~ aInteger0(smndt0(xa)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_102]),c_0_33])]),c_0_103]) ).
cnf(c_0_105,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_32]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM426+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:28:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.72/0.50 % Version: 3.5.1
% 0.72/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.72/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.72/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.72/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.72/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.72/0.50 % Starting sh5l with 300s (1) cores
% 0.72/0.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4040387 completed with status 0
% 0.72/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.72/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.72/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.72/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.72/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.72/0.50 % No SInE strategy applied
% 0.72/0.50 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.72/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.72/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.72/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.72/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.72/0.50 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.72/0.50 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.72/0.50 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 4040398 completed with status 0
% 0.72/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 0.72/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.72/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.72/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.72/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.72/0.50 % No SInE strategy applied
% 0.72/0.50 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.72/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.72/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.72/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.72/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.72/0.50 % Preprocessing time : 0.002 s
% 0.72/0.50 % Presaturation interreduction done
% 0.72/0.50
% 0.72/0.50 % Proof found!
% 0.72/0.50 % SZS status Theorem
% 0.72/0.50 % SZS output start CNFRefutation
% See solution above
% 0.72/0.50 % Parsed axioms : 24
% 0.72/0.50 % Removed by relevancy pruning/SinE : 0
% 0.72/0.50 % Initial clauses : 42
% 0.72/0.50 % Removed in clause preprocessing : 1
% 0.72/0.50 % Initial clauses in saturation : 41
% 0.72/0.50 % Processed clauses : 575
% 0.72/0.50 % ...of these trivial : 48
% 0.72/0.50 % ...subsumed : 158
% 0.72/0.50 % ...remaining for further processing : 369
% 0.72/0.50 % Other redundant clauses eliminated : 2
% 0.72/0.50 % Clauses deleted for lack of memory : 0
% 0.72/0.50 % Backward-subsumed : 4
% 0.72/0.50 % Backward-rewritten : 124
% 0.72/0.50 % Generated clauses : 2702
% 0.72/0.50 % ...of the previous two non-redundant : 2117
% 0.72/0.50 % ...aggressively subsumed : 0
% 0.72/0.50 % Contextual simplify-reflections : 21
% 0.72/0.50 % Paramodulations : 2700
% 0.72/0.50 % Factorizations : 0
% 0.72/0.50 % NegExts : 0
% 0.72/0.50 % Equation resolutions : 2
% 0.72/0.50 % Disequality decompositions : 0
% 0.72/0.50 % Total rewrite steps : 4128
% 0.72/0.50 % ...of those cached : 3996
% 0.72/0.50 % Propositional unsat checks : 0
% 0.72/0.50 % Propositional check models : 0
% 0.72/0.50 % Propositional check unsatisfiable : 0
% 0.72/0.50 % Propositional clauses : 0
% 0.72/0.50 % Propositional clauses after purity: 0
% 0.72/0.50 % Propositional unsat core size : 0
% 0.72/0.50 % Propositional preprocessing time : 0.000
% 0.72/0.50 % Propositional encoding time : 0.000
% 0.72/0.50 % Propositional solver time : 0.000
% 0.72/0.50 % Success case prop preproc time : 0.000
% 0.72/0.50 % Success case prop encoding time : 0.000
% 0.72/0.50 % Success case prop solver time : 0.000
% 0.72/0.50 % Current number of processed clauses : 198
% 0.72/0.50 % Positive orientable unit clauses : 103
% 0.72/0.50 % Positive unorientable unit clauses: 0
% 0.72/0.50 % Negative unit clauses : 3
% 0.72/0.50 % Non-unit-clauses : 92
% 0.72/0.50 % Current number of unprocessed clauses: 1586
% 0.72/0.50 % ...number of literals in the above : 5532
% 0.72/0.50 % Current number of archived formulas : 0
% 0.72/0.50 % Current number of archived clauses : 169
% 0.72/0.50 % Clause-clause subsumption calls (NU) : 2018
% 0.72/0.50 % Rec. Clause-clause subsumption calls : 1378
% 0.72/0.50 % Non-unit clause-clause subsumptions : 183
% 0.72/0.50 % Unit Clause-clause subsumption calls : 187
% 0.72/0.50 % Rewrite failures with RHS unbound : 0
% 0.72/0.50 % BW rewrite match attempts : 89
% 0.72/0.50 % BW rewrite match successes : 55
% 0.72/0.50 % Condensation attempts : 0
% 0.72/0.50 % Condensation successes : 0
% 0.72/0.50 % Termbank termtop insertions : 51215
% 0.72/0.50 % Search garbage collected termcells : 438
% 0.72/0.50
% 0.72/0.50 % -------------------------------------------------
% 0.72/0.50 % User time : 0.064 s
% 0.72/0.50 % System time : 0.005 s
% 0.72/0.50 % Total time : 0.069 s
% 0.72/0.50 % Maximum resident set size: 3400 pages
% 0.72/0.50
% 0.72/0.50 % -------------------------------------------------
% 0.72/0.50 % User time : 0.298 s
% 0.72/0.50 % System time : 0.033 s
% 0.72/0.50 % Total time : 0.331 s
% 0.72/0.50 % Maximum resident set size: 4608 pages
% 0.72/0.50 % E exiting
%------------------------------------------------------------------------------