%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG109+4 : 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 : n027.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 05:05:22 PM UTC 2026
% Result : Theorem 1.43s 1.77s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 178 ( 60 equ)
% Maximal formula atoms : 33 ( 5 avg)
% Number of connectives : 202 ( 58 ~; 60 |; 68 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 38 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xa))
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xa,X3) = X2 ) )
=> ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xb,X3) = X2 ) )
=> ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
& X1 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2203,hypothesis,
( ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = sz00 )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = xa )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xb,X1) = sz00 )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xb,X1) = xb )
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__2174,hypothesis,
( aSet0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,xI)
<=> ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(m__2110,hypothesis,
( xa != sz00
| xb != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2110) ).
fof(c_0_7,negated_conjecture,
~ ? [X1] :
( ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xa))
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xa,X3) = X2 ) )
=> ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xb,X3) = X2 ) )
=> ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
& X1 != sz00 ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,negated_conjecture,
! [X249,X250,X252,X253,X254,X256,X257,X258,X259] :
( ( aElement0(esk32_2(X249,X250))
| ~ aElementOf0(X250,slsdtgt0(xa))
| X249 = sz00 )
& ( sdtasdt0(xa,esk32_2(X249,X250)) = X250
| ~ aElementOf0(X250,slsdtgt0(xa))
| X249 = sz00 )
& ( ~ aElement0(X253)
| sdtasdt0(xa,X253) != X252
| aElementOf0(X252,slsdtgt0(xa))
| X249 = sz00 )
& ( aElement0(esk33_2(X249,X254))
| ~ aElementOf0(X254,slsdtgt0(xb))
| X249 = sz00 )
& ( sdtasdt0(xb,esk33_2(X249,X254)) = X254
| ~ aElementOf0(X254,slsdtgt0(xb))
| X249 = sz00 )
& ( ~ aElement0(X257)
| sdtasdt0(xb,X257) != X256
| aElementOf0(X256,slsdtgt0(xb))
| X249 = sz00 )
& ( ~ aElementOf0(X258,slsdtgt0(xa))
| ~ aElementOf0(X259,slsdtgt0(xb))
| sdtpldt0(X258,X259) != X249
| X249 = sz00 )
& ( ~ aElementOf0(X249,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| X249 = sz00 ) ),
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)],[c_0_7])])])])])]) ).
cnf(c_0_9,negated_conjecture,
( X3 = sz00
| ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_10,hypothesis,
( aElement0(esk28_0)
& sdtasdt0(xa,esk28_0) = sz00
& aElementOf0(sz00,slsdtgt0(xa))
& aElement0(esk29_0)
& sdtasdt0(xa,esk29_0) = xa
& aElementOf0(xa,slsdtgt0(xa))
& aElement0(esk30_0)
& sdtasdt0(xb,esk30_0) = sz00
& aElementOf0(sz00,slsdtgt0(xb))
& aElement0(esk31_0)
& sdtasdt0(xb,esk31_0) = xb
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2203])]) ).
fof(c_0_11,plain,
! [X128] :
( ( sdtpldt0(X128,sz00) = X128
| ~ aElement0(X128) )
& ( X128 = sdtpldt0(sz00,X128)
| ~ aElement0(X128) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_12,negated_conjecture,
( sdtpldt0(X1,X2) = sz00
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
aElementOf0(xb,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,hypothesis,
( sdtpldt0(X1,xb) = sz00
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_17,hypothesis,
aElementOf0(sz00,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,plain,
! [X121,X122] :
( ~ aElement0(X121)
| ~ aElement0(X122)
| aElement0(sdtasdt0(X121,X122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_19,hypothesis,
! [X228,X229,X230,X231,X233,X234,X235,X237,X238,X239,X242,X243,X244] :
( aSet0(xI)
& ( ~ aElementOf0(X229,xI)
| aElementOf0(sdtpldt0(X228,X229),xI)
| ~ aElementOf0(X228,xI) )
& ( ~ aElement0(X230)
| aElementOf0(sdtasdt0(X230,X228),xI)
| ~ aElementOf0(X228,xI) )
& aIdeal0(xI)
& ( aElement0(esk24_1(X231))
| ~ aElementOf0(X231,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk24_1(X231)) = X231
| ~ aElementOf0(X231,slsdtgt0(xa)) )
& ( ~ aElement0(X234)
| sdtasdt0(xa,X234) != X233
| aElementOf0(X233,slsdtgt0(xa)) )
& ( aElement0(esk25_1(X235))
| ~ aElementOf0(X235,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk25_1(X235)) = X235
| ~ aElementOf0(X235,slsdtgt0(xb)) )
& ( ~ aElement0(X238)
| sdtasdt0(xb,X238) != X237
| aElementOf0(X237,slsdtgt0(xb)) )
& ( aElementOf0(esk26_1(X239),slsdtgt0(xa))
| ~ aElementOf0(X239,xI) )
& ( aElementOf0(esk27_1(X239),slsdtgt0(xb))
| ~ aElementOf0(X239,xI) )
& ( sdtpldt0(esk26_1(X239),esk27_1(X239)) = X239
| ~ aElementOf0(X239,xI) )
& ( ~ aElementOf0(X243,slsdtgt0(xa))
| ~ aElementOf0(X244,slsdtgt0(xb))
| sdtpldt0(X243,X244) != X242
| aElementOf0(X242,xI) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
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)],[m__2174])])])])])]) ).
cnf(c_0_20,hypothesis,
sz00 = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_21,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,hypothesis,
( sdtasdt0(xa,esk24_1(X1)) = X1
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_25,hypothesis,
( aElement0(esk24_1(X1))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,hypothesis,
( sdtpldt0(X1,xb) = xb
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(rw,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_27,plain,
( sdtpldt0(X1,xb) = X1
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_28,hypothesis,
( aElement0(X1)
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_29,hypothesis,
( xa != sz00
| xb != sz00 ),
inference(split_conjunct,[status(thm)],[m__2110]) ).
cnf(c_0_30,hypothesis,
( X1 = xb
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_31,hypothesis,
aElementOf0(xa,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_32,hypothesis,
xb != xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_20]),c_0_20])]) ).
cnf(c_0_33,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG109+4 : 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
% 0.16/0.33 % Computer : n027.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 01:51:05 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.43/1.77 % Version : CSE_E---1.7
% 1.43/1.77 % Problem : theBenchmark.p
% 1.43/1.77 % SZS status Theorem for theBenchmark.p
% 1.43/1.77 % SZS output start CNFRefutation
% See solution above
% 1.43/1.77 % Total time : 1.372s
%------------------------------------------------------------------------------