%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM475+2 : 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 : n020.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 04:57:28 PM UTC 2026
% Result : Theorem 1.36s 1.76s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 102 ( 29 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 116 ( 47 ~; 44 |; 18 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__1459,hypothesis,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1459) ).
fof(m__1360,hypothesis,
( aNaturalNumber0(xp)
& xm = sdtasdt0(xl,xp)
& xp = sdtsldt0(xm,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
fof(m__1379,hypothesis,
( aNaturalNumber0(xq)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& xq = sdtsldt0(sdtpldt0(xm,xn),xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(m__,conjecture,
xn = sdtasdt0(xl,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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__1422,hypothesis,
( aNaturalNumber0(xr)
& sdtpldt0(xp,xr) = xq
& xr = sdtmndt0(xq,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1422) ).
fof(c_0_10,plain,
! [X107,X108,X110] :
( ( aNaturalNumber0(esk1_2(X107,X108))
| ~ sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) )
& ( sdtpldt0(X107,esk1_2(X107,X108)) = X108
| ~ sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) )
& ( ~ aNaturalNumber0(X110)
| sdtpldt0(X107,X110) != X108
| sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) ) ),
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_11,plain,
! [X77,X78] :
( ~ aNaturalNumber0(X77)
| ~ aNaturalNumber0(X78)
| aNaturalNumber0(sdtpldt0(X77,X78)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_12,plain,
! [X111,X112,X113] :
( ( aNaturalNumber0(X113)
| X113 != sdtmndt0(X112,X111)
| ~ sdtlseqdt0(X111,X112)
| ~ aNaturalNumber0(X111)
| ~ aNaturalNumber0(X112) )
& ( sdtpldt0(X111,X113) = X112
| X113 != sdtmndt0(X112,X111)
| ~ sdtlseqdt0(X111,X112)
| ~ aNaturalNumber0(X111)
| ~ aNaturalNumber0(X112) )
& ( ~ aNaturalNumber0(X113)
| sdtpldt0(X111,X113) != X112
| X113 = sdtmndt0(X112,X111)
| ~ sdtlseqdt0(X111,X112)
| ~ aNaturalNumber0(X111)
| ~ aNaturalNumber0(X112) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_13,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( X1 = sdtmndt0(X3,X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_14]) ).
cnf(c_0_17,hypothesis,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(split_conjunct,[status(thm)],[m__1459]) ).
cnf(c_0_18,hypothesis,
xm = sdtasdt0(xl,xp),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_19,hypothesis,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(split_conjunct,[status(thm)],[m__1379]) ).
cnf(c_0_20,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_14]),c_0_16]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1324]) ).
fof(c_0_23,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_24,hypothesis,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtasdt0(xl,xq),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]),c_0_19]) ).
cnf(c_0_25,hypothesis,
sdtmndt0(sdtasdt0(xl,xq),xm) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19]),c_0_21]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_27,plain,
! [X79,X80] :
( ~ aNaturalNumber0(X79)
| ~ aNaturalNumber0(X80)
| aNaturalNumber0(sdtasdt0(X79,X80)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_28,hypothesis,
~ aNaturalNumber0(sdtasdt0(xl,xr)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_24]),c_0_21])]),c_0_25]),c_0_26]) ).
cnf(c_0_29,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__1422]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_32,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM475+2 : 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
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:37:50 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.36/1.76 % Version : CSE_E---1.7
% 1.36/1.76 % Problem : theBenchmark.p
% 1.36/1.76 % SZS status Theorem for theBenchmark.p
% 1.36/1.76 % SZS output start CNFRefutation
% See solution above
% 1.36/1.76 % Total time : 1.374s
%------------------------------------------------------------------------------