%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM527+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 04:57:42 PM UTC 2026
% Result : Theorem 3.70s 3.14s
% Output : CNFRefutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 94 ( 26 unt; 0 def)
% Number of atoms : 333 ( 99 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 406 ( 167 ~; 160 |; 59 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 57 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__,conjecture,
( ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xm )
& sdtlseqdt0(xn,xm) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm) )
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__3046,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(m__3059,hypothesis,
( aNaturalNumber0(xq)
& xn = sdtasdt0(xp,xq)
& xq = sdtsldt0(xn,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(c_0_19,plain,
! [X158,X159,X161] :
( ( aNaturalNumber0(esk2_2(X158,X159))
| ~ doDivides0(X158,X159)
| ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159) )
& ( X159 = sdtasdt0(X158,esk2_2(X158,X159))
| ~ doDivides0(X158,X159)
| ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159) )
& ( ~ aNaturalNumber0(X161)
| X159 != sdtasdt0(X158,X161)
| doDivides0(X158,X159)
| ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_20,plain,
! [X104,X105] :
( ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105)
| aNaturalNumber0(sdtasdt0(X104,X105)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_21,negated_conjecture,
~ ( ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xm )
& sdtlseqdt0(xn,xm) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm) )
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_22,plain,
! [X162,X163,X164] :
( ( aNaturalNumber0(X164)
| X164 != sdtsldt0(X163,X162)
| X162 = sz00
| ~ doDivides0(X162,X163)
| ~ aNaturalNumber0(X162)
| ~ aNaturalNumber0(X163) )
& ( X163 = sdtasdt0(X162,X164)
| X164 != sdtsldt0(X163,X162)
| X162 = sz00
| ~ doDivides0(X162,X163)
| ~ aNaturalNumber0(X162)
| ~ aNaturalNumber0(X163) )
& ( ~ aNaturalNumber0(X164)
| X163 != sdtasdt0(X162,X164)
| X164 = sdtsldt0(X163,X162)
| X162 = sz00
| ~ doDivides0(X162,X163)
| ~ aNaturalNumber0(X162)
| ~ aNaturalNumber0(X163) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_23,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,plain,
! [X122,X123,X124] :
( ( sdtpldt0(X122,X123) != sdtpldt0(X122,X124)
| X123 = X124
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( sdtpldt0(X123,X122) != sdtpldt0(X124,X122)
| X123 = X124
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
fof(c_0_26,negated_conjecture,
! [X197] :
( aNaturalNumber0(esk9_0)
& sdtpldt0(xn,esk9_0) = xm
& sdtlseqdt0(xn,xm)
& ( ~ aNaturalNumber0(X197)
| sdtpldt0(sdtasdt0(xn,xn),X197) != sdtasdt0(xm,xm) )
& ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_27,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_24]) ).
cnf(c_0_29,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
sdtpldt0(xn,esk9_0) = xm,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_32,negated_conjecture,
aNaturalNumber0(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_33,plain,
! [X106,X107] :
( ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107)
| sdtpldt0(X106,X107) = sdtpldt0(X107,X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_34,hypothesis,
( aNaturalNumber0(esk7_0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0)
& doDivides0(xp,sdtasdt0(xn,xn))
& aNaturalNumber0(esk8_0)
& xn = sdtasdt0(xp,esk8_0)
& doDivides0(xp,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__3046])]) ).
cnf(c_0_35,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
cnf(c_0_36,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_37,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_24]),c_0_28]) ).
cnf(c_0_38,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_39,negated_conjecture,
( X1 = xn
| sdtpldt0(X1,esk9_0) != xm
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[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_40,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_41,plain,
! [X132,X133,X135] :
( ( aNaturalNumber0(esk1_2(X132,X133))
| ~ sdtlseqdt0(X132,X133)
| ~ aNaturalNumber0(X132)
| ~ aNaturalNumber0(X133) )
& ( sdtpldt0(X132,esk1_2(X132,X133)) = X133
| ~ sdtlseqdt0(X132,X133)
| ~ aNaturalNumber0(X132)
| ~ aNaturalNumber0(X133) )
& ( ~ aNaturalNumber0(X135)
| sdtpldt0(X132,X135) != X133
| sdtlseqdt0(X132,X133)
| ~ aNaturalNumber0(X132)
| ~ aNaturalNumber0(X133) ) ),
inference(distribute,[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_42,plain,
! [X102,X103] :
( ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| aNaturalNumber0(sdtpldt0(X102,X103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_43,hypothesis,
sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,hypothesis,
aNaturalNumber0(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,hypothesis,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_35]),c_0_36])]) ).
cnf(c_0_46,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_47,hypothesis,
( sdtsldt0(sdtasdt0(xp,X1),xp) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_36]),c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( X1 = xn
| sdtpldt0(esk9_0,X1) != xm
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_32])]) ).
cnf(c_0_49,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_51,plain,
! [X145,X146] :
( ( X146 != X145
| sdtlseqdt0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( sdtlseqdt0(X146,X145)
| sdtlseqdt0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_52,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_53,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sdtasdt0(xn,xn),X1) != sdtasdt0(xm,xm) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_55,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_43]),c_0_44]),c_0_36])]) ).
cnf(c_0_56,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_57,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_24]),c_0_46])]) ).
cnf(c_0_58,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xp) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_43]),c_0_44])]) ).
cnf(c_0_59,negated_conjecture,
( esk1_2(esk9_0,xm) = xn
| ~ sdtlseqdt0(esk9_0,xm)
| ~ aNaturalNumber0(esk1_2(esk9_0,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_32])])]),c_0_50])]) ).
cnf(c_0_60,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_61,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_62,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_52]),c_0_53]) ).
fof(c_0_63,plain,
! [X111] :
( ( sdtpldt0(X111,sz00) = X111
| ~ aNaturalNumber0(X111) )
& ( X111 = sdtpldt0(sz00,X111)
| ~ aNaturalNumber0(X111) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_64,negated_conjecture,
( sdtpldt0(X1,sdtasdt0(xn,xn)) != sdtasdt0(xm,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_55])]) ).
cnf(c_0_65,hypothesis,
sdtasdt0(xm,xm) = esk7_0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_56]),c_0_57])]),c_0_58]) ).
fof(c_0_66,plain,
! [X108,X109,X110] :
( ~ aNaturalNumber0(X108)
| ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X110)
| sdtpldt0(sdtpldt0(X108,X109),X110) = sdtpldt0(X108,sdtpldt0(X109,X110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_67,negated_conjecture,
( esk1_2(esk9_0,xm) = xn
| ~ sdtlseqdt0(esk9_0,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_50]),c_0_32])]) ).
cnf(c_0_68,negated_conjecture,
( sdtlseqdt0(X1,esk9_0)
| sdtlseqdt0(esk9_0,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_32]) ).
fof(c_0_69,plain,
! [X140,X141] :
( ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141)
| ~ sdtlseqdt0(X140,X141)
| ~ sdtlseqdt0(X141,X140)
| X140 = X141 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_70,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_40]) ).
cnf(c_0_71,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_73,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_74,negated_conjecture,
( sdtpldt0(X1,sdtasdt0(xn,xn)) != esk7_0
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_75,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_76,plain,
! [X119,X120,X121] :
( ( sdtasdt0(X119,sdtpldt0(X120,X121)) = sdtpldt0(sdtasdt0(X119,X120),sdtasdt0(X119,X121))
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120)
| ~ aNaturalNumber0(X121) )
& ( sdtasdt0(sdtpldt0(X120,X121),X119) = sdtpldt0(sdtasdt0(X120,X119),sdtasdt0(X121,X119))
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120)
| ~ aNaturalNumber0(X121) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_77,negated_conjecture,
( sdtpldt0(esk9_0,xn) = xm
| ~ sdtlseqdt0(esk9_0,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_67]),c_0_50]),c_0_32])]) ).
cnf(c_0_78,hypothesis,
( sdtlseqdt0(esk9_0,xm)
| sdtlseqdt0(xm,esk9_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_50]) ).
cnf(c_0_79,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_80,negated_conjecture,
sdtlseqdt0(esk9_0,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_30]),c_0_32]),c_0_31])]) ).
cnf(c_0_81,negated_conjecture,
esk9_0 != xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_71]),c_0_72]),c_0_32])]),c_0_73]) ).
cnf(c_0_82,negated_conjecture,
( sdtpldt0(X1,sdtpldt0(X2,sdtasdt0(xn,xn))) != esk7_0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_55])]),c_0_53]) ).
cnf(c_0_83,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( sdtpldt0(esk9_0,xn) = xm
| sdtlseqdt0(xm,esk9_0) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,negated_conjecture,
~ sdtlseqdt0(xm,esk9_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_32]),c_0_50])]),c_0_81]) ).
cnf(c_0_86,negated_conjecture,
( sdtpldt0(X1,sdtasdt0(xn,sdtpldt0(X2,xn))) != esk7_0
| ~ aNaturalNumber0(sdtasdt0(xn,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_31])]) ).
cnf(c_0_87,negated_conjecture,
sdtpldt0(esk9_0,xn) = xm,
inference(sr,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
( sdtpldt0(X1,sdtasdt0(xn,xm)) != esk7_0
| ~ aNaturalNumber0(sdtasdt0(xn,esk9_0))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_32])]) ).
cnf(c_0_89,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_90,negated_conjecture,
( sdtasdt0(sdtpldt0(X1,xn),xm) != esk7_0
| ~ aNaturalNumber0(sdtasdt0(xn,esk9_0))
| ~ aNaturalNumber0(sdtasdt0(X1,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_50]),c_0_31])]) ).
cnf(c_0_91,negated_conjecture,
( ~ aNaturalNumber0(sdtasdt0(xn,esk9_0))
| ~ aNaturalNumber0(sdtasdt0(esk9_0,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_87]),c_0_65]),c_0_32])]) ).
cnf(c_0_92,negated_conjecture,
~ aNaturalNumber0(sdtasdt0(xn,esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_24]),c_0_50]),c_0_32])]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_24]),c_0_32]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM527+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n004.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 00:41:32 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 3.70/3.14 % Version : CSE_E---1.7
% 3.70/3.14 % Problem : theBenchmark.p
% 3.70/3.14 % SZS status Theorem for theBenchmark.p
% 3.70/3.14 % SZS output start CNFRefutation
% See solution above
% 3.70/3.15 % Total time : 2.374s
%------------------------------------------------------------------------------