%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM463+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 01:49:10 PM UTC 2026
% Result : Theorem 0.49s 0.56s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 87 ( 17 unt; 0 def)
% Number of atoms : 331 ( 125 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 400 ( 156 ~; 163 |; 51 &)
% ( 1 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 60 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__,conjecture,
( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X2 = sz00
& X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mLENTr,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( ( sdtlseqdt0(sz10,X1)
& sz10 != X1 )
| X1 = sz10
| X1 = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_17,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[mMulCanc]) ).
fof(c_0_18,plain,
! [X28,X29,X30] :
( ( ~ aNaturalNumber0(X28)
| X28 = sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X29)
| X29 = X30
| sdtasdt0(X29,X28) != sdtasdt0(X30,X28) )
& ( ~ aNaturalNumber0(X28)
| X28 = sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X29)
| X29 = X30
| sdtasdt0(X28,X29) != sdtasdt0(X28,X30) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).
fof(c_0_19,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_20,negated_conjecture,
~ ( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__987]) ).
fof(c_0_23,plain,
! [X20] :
( ( ~ aNaturalNumber0(X20)
| X20 = sdtasdt0(sz10,X20) )
& ( ~ aNaturalNumber0(X20)
| sdtasdt0(X20,sz10) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_24,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X31,X32] :
( ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X32 = sz00 )
& ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X31 = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])])]) ).
fof(c_0_26,plain,
! [X35,X36,X38] :
( ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| sdtlseqdt0(X35,X36)
| sdtpldt0(X35,X38) != X36
| ~ aNaturalNumber0(X38) )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| sdtpldt0(X35,esk1_2(X35,X36)) = X36 )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| aNaturalNumber0(esk1_2(X35,X36)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])])]) ).
fof(c_0_27,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( ( sdtlseqdt0(sz10,X1)
& sz10 != X1 )
| X1 = sz10
| X1 = sz00 ) ),
inference(fof_simplification,[status(thm)],[mLENTr]) ).
fof(c_0_28,negated_conjecture,
~ ( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
cnf(c_0_29,hypothesis,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X2,X1) != sdtasdt0(X2,xm)
| X2 = sz00
| X1 = xm ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_33,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_34,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_37,plain,
! [X5,X6] :
( aNaturalNumber0(sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
fof(c_0_38,plain,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
inference(fof_simplification,[status(thm)],[mMonMul]) ).
fof(c_0_39,plain,
! [X56] :
( ( ~ aNaturalNumber0(X56)
| X56 = sz10
| X56 = sz00
| sdtlseqdt0(sz10,X56) )
& ( ~ aNaturalNumber0(X56)
| X56 = sz10
| X56 = sz00
| sz10 != X56 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
fof(c_0_40,negated_conjecture,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& xm != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
cnf(c_0_41,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| X2 = sz00
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__987]) ).
fof(c_0_43,plain,
! [X17,X18,X19] :
( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_44,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(sz10,xm))
| sdtasdt0(sz10,xm) = xm ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32])]) ).
cnf(c_0_45,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_46,plain,
! [X21] :
( ( ~ aNaturalNumber0(X21)
| sz00 = sdtasdt0(sz00,X21) )
& ( ~ aNaturalNumber0(X21)
| sdtasdt0(X21,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_47,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk1_2(X1,sz00))
| ~ sdtlseqdt0(X1,sz00)
| esk1_2(X1,sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35])]),c_0_36])]) ).
cnf(c_0_48,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_49,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_50,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_51,plain,
! [X14] :
( ( ~ aNaturalNumber0(X14)
| X14 = sdtpldt0(sz00,X14) )
& ( ~ aNaturalNumber0(X14)
| sdtpldt0(X14,sz00) = X14 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
fof(c_0_52,plain,
! [X53,X54,X55] :
( ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtlseqdt0(sdtasdt0(X54,X53),sdtasdt0(X55,X53)) )
& ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtasdt0(X54,X53) != sdtasdt0(X55,X53) )
& ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtlseqdt0(sdtasdt0(X53,X54),sdtasdt0(X53,X55)) )
& ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtasdt0(X53,X54) != sdtasdt0(X53,X55) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| sdtlseqdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_54,negated_conjecture,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_55,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(xn,X2)
| X2 = sz00
| X1 = xn ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_56,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_57,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_58,hypothesis,
sdtasdt0(sz10,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_22]),c_0_31])]) ).
cnf(c_0_59,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_60,plain,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,sz00)
| esk1_2(X1,sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_36])]) ).
cnf(c_0_61,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_49]),c_0_50]) ).
cnf(c_0_62,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_63,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
cnf(c_0_64,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| X2 = X3
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_65,hypothesis,
( sdtlseqdt0(sz10,xm)
| xm = sz10 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_22]),c_0_54]) ).
cnf(c_0_66,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,sz10))
| sdtasdt0(xn,sz10) = xn ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_31])]),c_0_32])]) ).
fof(c_0_67,plain,
! [X15,X16] :
( sdtasdt0(X15,X16) = sdtasdt0(X16,X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_68,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,sdtasdt0(xm,X1)) = sdtasdt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_22]),c_0_31])]) ).
cnf(c_0_69,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_57]),c_0_36])]),c_0_45]) ).
cnf(c_0_70,plain,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,sz00)
| sdtpldt0(X1,sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_60]),c_0_36])]) ).
cnf(c_0_71,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_36])]) ).
fof(c_0_72,plain,
! [X48,X49] :
( ( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| sdtlseqdt0(X48,X49)
| sdtlseqdt0(X49,X48) )
& ( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| sdtlseqdt0(X48,X49)
| X49 != X48 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])])]) ).
cnf(c_0_73,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,xm))
| X1 = sz00
| xm = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_22]),c_0_31])]) ).
cnf(c_0_74,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_45]),c_0_31]),c_0_42])]) ).
cnf(c_0_75,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_76,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,hypothesis,
sdtasdt0(xm,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_36]),c_0_22]),c_0_31])]) ).
cnf(c_0_78,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_36])]) ).
cnf(c_0_79,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_80,hypothesis,
( xm = sz10
| xn = sz00 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_42]),c_0_74]),c_0_75]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(sz00,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_36]),c_0_22])]) ).
cnf(c_0_82,plain,
sdtlseqdt0(sz00,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_78]),c_0_36])]) ).
cnf(c_0_83,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(xn,X1)
| sdtlseqdt0(X1,xn) ),
inference(spm,[status(thm)],[c_0_79,c_0_42]) ).
cnf(c_0_84,negated_conjecture,
xm = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_80]),c_0_81]),c_0_82])]) ).
cnf(c_0_85,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_83,c_0_42]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_84]),c_0_74]),c_0_85])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM463+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.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 02:32:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.49/0.56 % Version: 3.5.1
% 0.49/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.49/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.49/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.49/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.49/0.56 % Starting sh5l with 300s (1) cores
% 0.49/0.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1497524 completed with status 0
% 0.49/0.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.49/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.49/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.49/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.49/0.56 % No SInE strategy applied
% 0.49/0.56 % Search class: FGUSF-FFMS22-SFFFFFNN
% 0.49/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.49/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.49/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.49/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.49/0.56 % Starting new_bool_3 with 136s (1) cores
% 0.49/0.56 % Starting new_bool_1 with 136s (1) cores
% 0.49/0.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1497530 completed with status 0
% 0.49/0.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.49/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.49/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.49/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.49/0.56 % No SInE strategy applied
% 0.49/0.56 % Search class: FGUSF-FFMS22-SFFFFFNN
% 0.49/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.49/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.49/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.49/0.56 % Preprocessing time : 0.002 s
% 0.49/0.56 % Presaturation interreduction done
% 0.49/0.56
% 0.49/0.56 % Proof found!
% 0.49/0.56 % SZS status Theorem
% 0.49/0.56 % SZS output start CNFRefutation
% See solution above
% 0.49/0.57 % Parsed axioms : 28
% 0.49/0.57 % Removed by relevancy pruning/SinE : 0
% 0.49/0.57 % Initial clauses : 50
% 0.49/0.57 % Removed in clause preprocessing : 2
% 0.49/0.57 % Initial clauses in saturation : 48
% 0.49/0.57 % Processed clauses : 1119
% 0.49/0.57 % ...of these trivial : 18
% 0.49/0.57 % ...subsumed : 673
% 0.49/0.57 % ...remaining for further processing : 428
% 0.49/0.57 % Other redundant clauses eliminated : 74
% 0.49/0.57 % Clauses deleted for lack of memory : 0
% 0.49/0.57 % Backward-subsumed : 21
% 0.49/0.57 % Backward-rewritten : 124
% 0.49/0.57 % Generated clauses : 5818
% 0.49/0.57 % ...of the previous two non-redundant : 5049
% 0.49/0.57 % ...aggressively subsumed : 0
% 0.49/0.57 % Contextual simplify-reflections : 35
% 0.49/0.57 % Paramodulations : 5725
% 0.49/0.57 % Factorizations : 0
% 0.49/0.57 % NegExts : 0
% 0.49/0.57 % Equation resolutions : 93
% 0.49/0.57 % Disequality decompositions : 0
% 0.49/0.57 % Total rewrite steps : 5363
% 0.49/0.57 % ...of those cached : 5320
% 0.49/0.57 % Propositional unsat checks : 0
% 0.49/0.57 % Propositional check models : 0
% 0.49/0.57 % Propositional check unsatisfiable : 0
% 0.49/0.57 % Propositional clauses : 0
% 0.49/0.57 % Propositional clauses after purity: 0
% 0.49/0.57 % Propositional unsat core size : 0
% 0.49/0.57 % Propositional preprocessing time : 0.000
% 0.49/0.57 % Propositional encoding time : 0.000
% 0.49/0.57 % Propositional solver time : 0.000
% 0.49/0.57 % Success case prop preproc time : 0.000
% 0.49/0.57 % Success case prop encoding time : 0.000
% 0.49/0.57 % Success case prop solver time : 0.000
% 0.49/0.57 % Current number of processed clauses : 235
% 0.49/0.57 % Positive orientable unit clauses : 29
% 0.49/0.57 % Positive unorientable unit clauses: 0
% 0.49/0.57 % Negative unit clauses : 4
% 0.49/0.57 % Non-unit-clauses : 202
% 0.49/0.57 % Current number of unprocessed clauses: 3947
% 0.49/0.57 % ...number of literals in the above : 20851
% 0.49/0.57 % Current number of archived formulas : 0
% 0.49/0.57 % Current number of archived clauses : 188
% 0.49/0.57 % Clause-clause subsumption calls (NU) : 10195
% 0.49/0.57 % Rec. Clause-clause subsumption calls : 5526
% 0.49/0.57 % Non-unit clause-clause subsumptions : 685
% 0.49/0.57 % Unit Clause-clause subsumption calls : 444
% 0.49/0.57 % Rewrite failures with RHS unbound : 0
% 0.49/0.57 % BW rewrite match attempts : 17
% 0.49/0.57 % BW rewrite match successes : 17
% 0.49/0.57 % Condensation attempts : 0
% 0.49/0.57 % Condensation successes : 0
% 0.49/0.57 % Termbank termtop insertions : 108522
% 0.49/0.57 % Search garbage collected termcells : 777
% 0.49/0.57
% 0.49/0.57 % -------------------------------------------------
% 0.49/0.57 % User time : 0.120 s
% 0.49/0.57 % System time : 0.012 s
% 0.49/0.57 % Total time : 0.132 s
% 0.49/0.57 % Maximum resident set size: 3660 pages
% 0.49/0.57
% 0.49/0.57 % -------------------------------------------------
% 0.49/0.57 % User time : 0.585 s
% 0.49/0.57 % System time : 0.040 s
% 0.49/0.57 % Total time : 0.625 s
% 0.49/0.57 % Maximum resident set size: 4864 pages
% 0.49/0.57 % E exiting
%------------------------------------------------------------------------------