%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM462+2 : 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 : n012.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 277.88s 36.33s
% Output : CNFRefutation 277.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 17 unt; 0 def)
% Number of atoms : 261 ( 107 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 321 ( 128 ~; 124 |; 53 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 42 !; 9 ?)
% 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__897,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__897) ).
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(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
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__,conjecture,
( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X1] :
( sdtpldt0(sdtasdt0(xl,xm),X1) = sdtasdt0(xn,xm)
& aNaturalNumber0(X1) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X1] :
( sdtpldt0(sdtasdt0(xm,xl),X1) = sdtasdt0(xm,xn)
& aNaturalNumber0(X1) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__897_03,hypothesis,
( sdtlseqdt0(xl,xn)
& ? [X1] :
( sdtpldt0(xl,X1) = xn
& aNaturalNumber0(X1) )
& xl != xn
& xm != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__897_03) ).
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(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(c_0_12,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_13,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_12])])])])]) ).
fof(c_0_14,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
cnf(c_0_15,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__897]) ).
fof(c_0_17,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_18,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
cnf(c_0_19,hypothesis,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X2,X1) != sdtasdt0(X2,xn)
| X2 = sz00
| X1 = xn ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,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])])]) ).
fof(c_0_24,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])])]) ).
fof(c_0_25,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_26,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(sz10,xn))
| sdtasdt0(sz10,xn) = xn ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22])]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__897]) ).
cnf(c_0_29,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_16]),c_0_21])]) ).
cnf(c_0_32,hypothesis,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X2,X1) != sdtasdt0(X2,xm)
| X2 = sz00
| X1 = xm ),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
fof(c_0_33,negated_conjecture,
~ ( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X1] :
( sdtpldt0(sdtasdt0(xl,xm),X1) = sdtasdt0(xn,xm)
& aNaturalNumber0(X1) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X1] :
( sdtpldt0(sdtasdt0(xm,xl),X1) = sdtasdt0(xm,xn)
& aNaturalNumber0(X1) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__897]) ).
cnf(c_0_35,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27]) ).
cnf(c_0_36,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31]),c_0_16]),c_0_21])]) ).
cnf(c_0_37,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_32,c_0_20]),c_0_21])]),c_0_22])]) ).
fof(c_0_38,hypothesis,
( sdtlseqdt0(xl,xn)
& ? [X1] :
( sdtpldt0(xl,X1) = xn
& aNaturalNumber0(X1) )
& xl != xn
& xm != sz00 ),
inference(fof_simplification,[status(thm)],[m__897_03]) ).
fof(c_0_39,negated_conjecture,
~ ( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X1] :
( sdtpldt0(sdtasdt0(xl,xm),X1) = sdtasdt0(xn,xm)
& aNaturalNumber0(X1) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X1] :
( sdtpldt0(sdtasdt0(xm,xl),X1) = sdtasdt0(xm,xn)
& aNaturalNumber0(X1) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
cnf(c_0_40,hypothesis,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X2,X1) != sdtasdt0(X2,xl)
| X2 = sz00
| X1 = xl ),
inference(spm,[status(thm)],[c_0_15,c_0_34]) ).
cnf(c_0_41,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xn,sdtasdt0(sz10,X1)) = sdtasdt0(X1,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_21]),c_0_16])]) ).
cnf(c_0_42,hypothesis,
sdtasdt0(sz10,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_28]),c_0_21])]) ).
fof(c_0_43,hypothesis,
( sdtlseqdt0(xl,xn)
& sdtpldt0(xl,esk2_0) = xn
& aNaturalNumber0(esk2_0)
& xl != xn
& xm != sz00 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_38])])]) ).
cnf(c_0_44,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| X2 = sz00
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_45,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_46,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_47,negated_conjecture,
! [X54,X55] :
( ( sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) )
& ( sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| sdtpldt0(sdtasdt0(xl,xm),X55) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X55) )
& ( sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtpldt0(sdtasdt0(xm,xl),X54) != sdtasdt0(xm,xn)
| ~ aNaturalNumber0(X54)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) )
& ( sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtpldt0(sdtasdt0(xm,xl),X54) != sdtasdt0(xm,xn)
| ~ aNaturalNumber0(X54)
| sdtpldt0(sdtasdt0(xl,xm),X55) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X55) ) ),
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_39])])])])]) ).
cnf(c_0_48,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X2,X1) != sdtasdt0(X1,xl)
| X2 = xl
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_40,c_0_29]) ).
cnf(c_0_49,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_28])]) ).
cnf(c_0_50,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,hypothesis,
xl != xn,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(xl,X2)
| X2 = sz00
| X1 = xl ),
inference(spm,[status(thm)],[c_0_44,c_0_34]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_55,plain,
! [X22,X23,X24] :
( ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| sdtasdt0(sdtpldt0(X23,X24),X22) = sdtpldt0(sdtasdt0(X23,X22),sdtasdt0(X24,X22)) )
& ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| sdtasdt0(X22,sdtpldt0(X23,X24)) = sdtpldt0(sdtasdt0(X22,X23),sdtasdt0(X22,X24)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])])]) ).
cnf(c_0_56,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,hypothesis,
sdtasdt0(xm,xn) != sdtasdt0(xm,xl),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_16]),c_0_28])]),c_0_50]),c_0_51]) ).
cnf(c_0_58,hypothesis,
sdtasdt0(xl,xm) != sdtasdt0(xm,xn),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_49]),c_0_28]),c_0_16])]),c_0_51]),c_0_50]) ).
cnf(c_0_59,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_53]),c_0_54]) ).
cnf(c_0_60,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xm,xn))
| ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_49]),c_0_49]),c_0_57]),c_0_58]) ).
cnf(c_0_62,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,sdtpldt0(X2,X3))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_27]),c_0_27]) ).
cnf(c_0_63,hypothesis,
sdtpldt0(xl,esk2_0) = xn,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_64,hypothesis,
aNaturalNumber0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_65,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_29]),c_0_28]),c_0_34])]) ).
cnf(c_0_66,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(X1,xl),sdtasdt0(X1,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_34])]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM462+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 02:31:52 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.06/0.32 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
% 277.88/36.33 % Version: 3.5.1
% 277.88/36.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 277.88/36.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 277.88/36.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 277.88/36.33 % Starting new_bool_3 with 300s (1) cores
% 277.88/36.33 % Starting new_bool_1 with 300s (1) cores
% 277.88/36.33 % Starting sh5l with 300s (1) cores
% 277.88/36.33 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1383999 completed with status 0
% 277.88/36.33 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 277.88/36.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 277.88/36.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 277.88/36.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 277.88/36.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 277.88/36.33 % No SInE strategy applied
% 277.88/36.33 % Search class: FGUSF-FFMM22-SFFFFFNN
% 277.88/36.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 277.88/36.33 % Starting SubtermCWHack with 136s (1) cores
% 277.88/36.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 277.88/36.33 % Starting G-E--_107_B42_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 277.88/36.33 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 277.88/36.33 % Starting new_bool_3 with 136s (1) cores
% 277.88/36.33 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1384006 completed with status 0
% 277.88/36.33 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 277.88/36.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 277.88/36.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 277.88/36.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 277.88/36.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 277.88/36.33 % No SInE strategy applied
% 277.88/36.33 % Search class: FGUSF-FFMM22-SFFFFFNN
% 277.88/36.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 277.88/36.33 % Starting SubtermCWHack with 136s (1) cores
% 277.88/36.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 277.88/36.33 % Preprocessing time : 0.001 s
% 277.88/36.33 % Presaturation interreduction done
% 277.88/36.33
% 277.88/36.33 % Proof found!
% 277.88/36.33 % SZS status Theorem
% 277.88/36.33 % SZS output start CNFRefutation
% See solution above
% 277.88/36.33 % Parsed axioms : 27
% 277.88/36.33 % Removed by relevancy pruning/SinE : 0
% 277.88/36.33 % Initial clauses : 52
% 277.88/36.33 % Removed in clause preprocessing : 1
% 277.88/36.33 % Initial clauses in saturation : 51
% 277.88/36.33 % Processed clauses : 40090
% 277.88/36.33 % ...of these trivial : 564
% 277.88/36.33 % ...subsumed : 32807
% 277.88/36.33 % ...remaining for further processing : 6719
% 277.88/36.33 % Other redundant clauses eliminated : 15718
% 277.88/36.33 % Clauses deleted for lack of memory : 0
% 277.88/36.33 % Backward-subsumed : 696
% 277.88/36.33 % Backward-rewritten : 1131
% 277.88/36.33 % Generated clauses : 1409676
% 277.88/36.33 % ...of the previous two non-redundant : 1364414
% 277.88/36.33 % ...aggressively subsumed : 0
% 277.88/36.33 % Contextual simplify-reflections : 1430
% 277.88/36.33 % Paramodulations : 1393747
% 277.88/36.33 % Factorizations : 0
% 277.88/36.33 % NegExts : 0
% 277.88/36.33 % Equation resolutions : 15917
% 277.88/36.33 % Disequality decompositions : 0
% 277.88/36.33 % Total rewrite steps : 1128448
% 277.88/36.33 % ...of those cached : 1127825
% 277.88/36.33 % Propositional unsat checks : 1
% 277.88/36.33 % Propositional check models : 0
% 277.88/36.33 % Propositional check unsatisfiable : 0
% 277.88/36.33 % Propositional clauses : 0
% 277.88/36.33 % Propositional clauses after purity: 0
% 277.88/36.33 % Propositional unsat core size : 0
% 277.88/36.33 % Propositional preprocessing time : 0.000
% 277.88/36.33 % Propositional encoding time : 2.837
% 277.88/36.33 % Propositional solver time : 1.503
% 277.88/36.33 % Success case prop preproc time : 0.000
% 277.88/36.33 % Success case prop encoding time : 0.000
% 277.88/36.33 % Success case prop solver time : 0.000
% 277.88/36.33 % Current number of processed clauses : 4827
% 277.88/36.33 % Positive orientable unit clauses : 533
% 277.88/36.33 % Positive unorientable unit clauses: 0
% 277.88/36.33 % Negative unit clauses : 1059
% 277.88/36.33 % Non-unit-clauses : 3235
% 277.88/36.33 % Current number of unprocessed clauses: 1322935
% 277.88/36.33 % ...number of literals in the above : 9373680
% 277.88/36.33 % Current number of archived formulas : 0
% 277.88/36.33 % Current number of archived clauses : 1887
% 277.88/36.33 % Clause-clause subsumption calls (NU) : 1830954
% 277.88/36.33 % Rec. Clause-clause subsumption calls : 439089
% 277.88/36.33 % Non-unit clause-clause subsumptions : 13546
% 277.88/36.33 % Unit Clause-clause subsumption calls : 223059
% 277.88/36.33 % Rewrite failures with RHS unbound : 0
% 277.88/36.33 % BW rewrite match attempts : 709
% 277.88/36.33 % BW rewrite match successes : 184
% 277.88/36.33 % Condensation attempts : 0
% 277.88/36.33 % Condensation successes : 0
% 277.88/36.33 % Termbank termtop insertions : 48199820
% 277.88/36.33 % Search garbage collected termcells : 756
% 277.88/36.33
% 277.88/36.33 % -------------------------------------------------
% 277.88/36.33 % User time : 34.231 s
% 277.88/36.33 % System time : 1.225 s
% 277.88/36.33 % Total time : 35.456 s
% 277.88/36.33 % Maximum resident set size: 3612 pages
% 277.88/36.33
% 277.88/36.33 % -------------------------------------------------
% 277.88/36.33 % User time : 171.756 s
% 277.88/36.33 % System time : 6.274 s
% 277.88/36.33 % Total time : 178.030 s
% 277.88/36.33 % Maximum resident set size: 4608 pages
% 277.88/36.33 % E exiting
%------------------------------------------------------------------------------