%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM431+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 04:57:18 PM UTC 2026
% Result : Theorem 3.73s 3.18s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 22
% Syntax : Number of formulae : 124 ( 45 unt; 0 def)
% Number of atoms : 309 ( 110 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 316 ( 131 ~; 128 |; 40 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 58 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
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(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(m__899,hypothesis,
( aInteger0(xm)
& sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__899) ).
fof(m__818,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00
& aInteger0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
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(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__853,hypothesis,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__853) ).
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(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(m__876,hypothesis,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__876) ).
fof(m__,conjecture,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_22,plain,
! [X46,X47,X48] :
( ~ aInteger0(X46)
| ~ aInteger0(X47)
| ~ aInteger0(X48)
| sdtpldt0(X46,sdtpldt0(X47,X48)) = sdtpldt0(sdtpldt0(X46,X47),X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_23,plain,
! [X52] :
( ( sdtpldt0(X52,smndt0(X52)) = sz00
| ~ aInteger0(X52) )
& ( sz00 = sdtpldt0(smndt0(X52),X52)
| ~ aInteger0(X52) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
fof(c_0_24,plain,
! [X41] :
( ~ aInteger0(X41)
| aInteger0(smndt0(X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
fof(c_0_25,plain,
! [X51] :
( ( sdtpldt0(X51,sz00) = X51
| ~ aInteger0(X51) )
& ( X51 = sdtpldt0(sz00,X51)
| ~ aInteger0(X51) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_26,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_31,plain,
! [X42,X43] :
( ~ aInteger0(X42)
| ~ aInteger0(X43)
| aInteger0(sdtpldt0(X42,X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
cnf(c_0_32,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_33,hypothesis,
sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)),
inference(split_conjunct,[status(thm)],[m__899]) ).
cnf(c_0_34,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_35,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_26,c_0_29]),c_0_30])]) ).
cnf(c_0_36,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_37,plain,
! [X49,X50] :
( ~ aInteger0(X49)
| ~ aInteger0(X50)
| sdtpldt0(X49,X50) = sdtpldt0(X50,X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_38,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_39,hypothesis,
( sdtpldt0(smndt0(xb),sdtasdt0(xq,xm)) = sdtpldt0(sz00,smndt0(xc))
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_40,hypothesis,
aInteger0(xc),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_41,hypothesis,
( sdtpldt0(sz00,sdtasdt0(xq,xm)) = sdtasdt0(xq,xm)
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_34])]) ).
cnf(c_0_42,hypothesis,
( aInteger0(sdtasdt0(xq,xm))
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_34])]) ).
cnf(c_0_43,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
( sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_38]),c_0_28]) ).
cnf(c_0_45,hypothesis,
sdtpldt0(smndt0(xb),sdtasdt0(xq,xm)) = sdtpldt0(sz00,smndt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_28]),c_0_40])]) ).
cnf(c_0_46,hypothesis,
sdtpldt0(sz00,sdtasdt0(xq,xm)) = sdtasdt0(xq,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_28]),c_0_40])]) ).
cnf(c_0_47,hypothesis,
aInteger0(sdtasdt0(xq,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_28]),c_0_40])]) ).
cnf(c_0_48,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_43,c_0_26]),c_0_36]) ).
cnf(c_0_49,hypothesis,
sdtpldt0(xb,sdtpldt0(sz00,smndt0(xc))) = 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_46]),c_0_47]),c_0_34])]) ).
cnf(c_0_50,hypothesis,
( sdtpldt0(sz00,sdtpldt0(smndt0(xc),xb)) = sdtasdt0(xq,xm)
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_34]),c_0_30])]) ).
cnf(c_0_51,hypothesis,
sdtpldt0(sz00,sdtpldt0(smndt0(xc),xb)) = sdtasdt0(xq,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28]),c_0_40])]) ).
fof(c_0_52,plain,
! [X71,X72,X73] :
( ( ~ sdteqdtlpzmzozddtrp0(X71,X72,X73)
| aDivisorOf0(X73,sdtpldt0(X71,smndt0(X72)))
| ~ aInteger0(X71)
| ~ aInteger0(X72)
| ~ aInteger0(X73)
| X73 = sz00 )
& ( ~ aDivisorOf0(X73,sdtpldt0(X71,smndt0(X72)))
| sdteqdtlpzmzozddtrp0(X71,X72,X73)
| ~ aInteger0(X71)
| ~ aInteger0(X72)
| ~ aInteger0(X73)
| X73 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_53,hypothesis,
( sdtpldt0(smndt0(xc),xb) = sdtasdt0(xq,xm)
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_51]),c_0_34])]) ).
fof(c_0_54,plain,
! [X66,X67,X69,X70] :
( ( aInteger0(X67)
| ~ aDivisorOf0(X67,X66)
| ~ aInteger0(X66) )
& ( X67 != sz00
| ~ aDivisorOf0(X67,X66)
| ~ aInteger0(X66) )
& ( aInteger0(esk1_2(X66,X67))
| ~ aDivisorOf0(X67,X66)
| ~ aInteger0(X66) )
& ( sdtasdt0(X67,esk1_2(X66,X67)) = X66
| ~ aDivisorOf0(X67,X66)
| ~ aInteger0(X66) )
& ( ~ aInteger0(X69)
| X69 = sz00
| ~ aInteger0(X70)
| sdtasdt0(X69,X70) != X66
| aDivisorOf0(X69,X66)
| ~ aInteger0(X66) ) ),
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_55,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_52]) ).
cnf(c_0_56,hypothesis,
sdteqdtlpzmzozddtrp0(xb,xc,xq),
inference(split_conjunct,[status(thm)],[m__853]) ).
cnf(c_0_57,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_58,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_59,hypothesis,
sdtpldt0(smndt0(xc),xb) = sdtasdt0(xq,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_28]),c_0_40])]) ).
fof(c_0_60,plain,
! [X53,X54,X55] :
( ~ aInteger0(X53)
| ~ aInteger0(X54)
| ~ aInteger0(X55)
| sdtasdt0(X53,sdtasdt0(X54,X55)) = sdtasdt0(sdtasdt0(X53,X54),X55) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_61,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,hypothesis,
aDivisorOf0(xq,sdtasdt0(xq,xm)),
inference(sr,[status(thm)],[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_55,c_0_56]),c_0_33]),c_0_57]),c_0_40]),c_0_34])]),c_0_58]) ).
cnf(c_0_63,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,hypothesis,
( sdtpldt0(smndt0(smndt0(xc)),sdtasdt0(xq,xm)) = sdtpldt0(sz00,xb)
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_59]),c_0_34])]) ).
cnf(c_0_65,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,hypothesis,
sdtasdt0(xq,esk1_2(sdtasdt0(xq,xm),xq)) = sdtasdt0(xq,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_47])]) ).
cnf(c_0_67,hypothesis,
aInteger0(esk1_2(sdtasdt0(xq,xm),xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_62]),c_0_47])]) ).
fof(c_0_68,plain,
! [X62] :
( ( sdtasdt0(X62,sz00) = sz00
| ~ aInteger0(X62) )
& ( sz00 = sdtasdt0(sz00,X62)
| ~ aInteger0(X62) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
cnf(c_0_69,hypothesis,
sdtpldt0(smndt0(smndt0(xc)),sdtasdt0(xq,xm)) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_28]),c_0_40])]) ).
cnf(c_0_70,hypothesis,
( sdtasdt0(xq,sdtasdt0(esk1_2(sdtasdt0(xq,xm),xq),X1)) = sdtasdt0(sdtasdt0(xq,xm),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_57])]),c_0_67])]) ).
cnf(c_0_71,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_72,hypothesis,
( sdtpldt0(sdtasdt0(xq,xm),smndt0(smndt0(xc))) = sdtpldt0(sz00,xb)
| ~ aInteger0(smndt0(smndt0(xc))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_69]),c_0_47])]) ).
cnf(c_0_73,hypothesis,
sdtpldt0(xc,sdtasdt0(xq,xm)) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_59]),c_0_34]),c_0_40])]) ).
cnf(c_0_74,hypothesis,
sdtasdt0(sdtasdt0(xq,xm),sz00) = sdtasdt0(xq,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_30]),c_0_67])]) ).
cnf(c_0_75,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_76,plain,
! [X59,X60,X61] :
( ( sdtasdt0(X59,sdtpldt0(X60,X61)) = sdtpldt0(sdtasdt0(X59,X60),sdtasdt0(X59,X61))
| ~ aInteger0(X59)
| ~ aInteger0(X60)
| ~ aInteger0(X61) )
& ( sdtasdt0(sdtpldt0(X59,X60),X61) = sdtpldt0(sdtasdt0(X59,X61),sdtasdt0(X60,X61))
| ~ aInteger0(X59)
| ~ aInteger0(X60)
| ~ aInteger0(X61) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
cnf(c_0_77,hypothesis,
( sdtpldt0(sdtasdt0(xq,xm),smndt0(smndt0(xc))) = sdtpldt0(sz00,xb)
| ~ aInteger0(smndt0(xc)) ),
inference(spm,[status(thm)],[c_0_72,c_0_28]) ).
cnf(c_0_78,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_35,c_0_73]),c_0_47]),c_0_40])]) ).
fof(c_0_79,plain,
! [X56,X57] :
( ~ aInteger0(X56)
| ~ aInteger0(X57)
| sdtasdt0(X56,X57) = sdtasdt0(X57,X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_80,hypothesis,
sdtasdt0(xq,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_74]),c_0_47])]) ).
cnf(c_0_81,plain,
( smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_27]),c_0_30])]) ).
cnf(c_0_82,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_76]) ).
cnf(c_0_83,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_84,hypothesis,
sdtpldt0(sdtasdt0(xq,xm),smndt0(smndt0(xc))) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_28]),c_0_40])]) ).
cnf(c_0_85,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_29]),c_0_34])]) ).
cnf(c_0_86,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_87,hypothesis,
sdtasdt0(sdtasdt0(xq,xm),sz00) = sz00,
inference(rw,[status(thm)],[c_0_74,c_0_80]) ).
cnf(c_0_88,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_28]),c_0_30])]) ).
cnf(c_0_89,plain,
( sdtpldt0(sdtasdt0(sz00,X1),sz00) = sdtasdt0(sz00,sdtpldt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_30])]) ).
cnf(c_0_90,hypothesis,
sdtpldt0(sdtasdt0(xq,xm),smndt0(smndt0(xc))) = xb,
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,hypothesis,
sdtasdt0(sz00,sdtasdt0(xq,xm)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_30]),c_0_47])]) ).
cnf(c_0_92,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_88]),c_0_30])]) ).
fof(c_0_93,plain,
! [X58] :
( ( sdtasdt0(X58,sz10) = X58
| ~ aInteger0(X58) )
& ( X58 = sdtasdt0(sz10,X58)
| ~ aInteger0(X58) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
cnf(c_0_94,hypothesis,
( sdtasdt0(sz00,xb) = sz00
| ~ aInteger0(smndt0(smndt0(xc))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_92]),c_0_47])]) ).
cnf(c_0_95,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_96,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_97,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_98,hypothesis,
( sdtasdt0(sz00,xb) = sz00
| ~ aInteger0(smndt0(xc)) ),
inference(spm,[status(thm)],[c_0_94,c_0_28]) ).
fof(c_0_99,plain,
! [X44,X45] :
( ~ aInteger0(X44)
| ~ aInteger0(X45)
| aInteger0(sdtasdt0(X44,X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_100,plain,
( sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_101,hypothesis,
sdtasdt0(sz00,xb) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_28]),c_0_40])]) ).
cnf(c_0_102,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_103,hypothesis,
sdtasdt0(sdtpldt0(sz00,sz10),xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_85]),c_0_34]),c_0_30])]) ).
cnf(c_0_104,plain,
( aInteger0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_65]),c_0_102]) ).
cnf(c_0_105,hypothesis,
sdtasdt0(sz10,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_29]),c_0_97])]) ).
fof(c_0_106,plain,
! [X63] :
( ( sdtasdt0(smndt0(sz10),X63) = smndt0(X63)
| ~ aInteger0(X63) )
& ( smndt0(X63) = sdtasdt0(X63,smndt0(sz10))
| ~ aInteger0(X63) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
cnf(c_0_107,hypothesis,
( aInteger0(sdtasdt0(X1,xb))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_34]),c_0_97])]) ).
cnf(c_0_108,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_109,hypothesis,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[m__876]) ).
cnf(c_0_110,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_111,hypothesis,
( aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_34])]) ).
cnf(c_0_112,hypothesis,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,xn),X1)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_109]),c_0_110])]) ).
cnf(c_0_113,hypothesis,
aInteger0(smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_28]),c_0_97])]) ).
cnf(c_0_114,hypothesis,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,xn),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_113])]) ).
cnf(c_0_115,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_26,c_0_75]),c_0_30])]) ).
cnf(c_0_116,hypothesis,
sdtpldt0(xa,sdtpldt0(sz00,smndt0(xc))) = sdtpldt0(sdtasdt0(xq,xn),sdtasdt0(xq,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_45]),c_0_47])]) ).
cnf(c_0_117,hypothesis,
( sdtpldt0(sdtasdt0(xq,xn),sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xc))
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_110])]) ).
fof(c_0_118,negated_conjecture,
sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_119,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_28]),c_0_40])]) ).
cnf(c_0_120,hypothesis,
aInteger0(xm),
inference(split_conjunct,[status(thm)],[m__899]) ).
cnf(c_0_121,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__876]) ).
cnf(c_0_122,negated_conjecture,
sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_123,hypothesis,
$false,
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_119]),c_0_120]),c_0_121]),c_0_57])]),c_0_122]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM431+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 00:33:33 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.35 % start to proof: theBenchmark
% 3.73/3.18 % Version : CSE_E---1.7
% 3.73/3.18 % Problem : theBenchmark.p
% 3.73/3.18 % SZS status Theorem for theBenchmark.p
% 3.73/3.18 % SZS output start CNFRefutation
% See solution above
% 3.73/3.19 % Total time : 2.374s
%------------------------------------------------------------------------------