%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG126+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 : n005.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 05:05:26 PM UTC 2026
% Result : Theorem 1.64s 1.83s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 162 ( 42 equ)
% Maximal formula atoms : 33 ( 6 avg)
% Number of connectives : 194 ( 59 ~; 51 |; 65 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 44 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2273,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(m__,conjecture,
( ! [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,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xc )
| aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2744,hypothesis,
? [X1] :
( aElement0(X1)
& sdtasdt0(xu,X1) = xc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2744) ).
fof(c_0_6,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
fof(c_0_7,negated_conjecture,
~ ( ! [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,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xc )
| aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,hypothesis,
! [X242,X243,X244,X245,X247,X248,X249,X251,X252,X253,X256,X257,X258] :
( aSet0(xI)
& ( ~ aElementOf0(X243,xI)
| aElementOf0(sdtpldt0(X242,X243),xI)
| ~ aElementOf0(X242,xI) )
& ( ~ aElement0(X244)
| aElementOf0(sdtasdt0(X244,X242),xI)
| ~ aElementOf0(X242,xI) )
& aIdeal0(xI)
& ( aElement0(esk24_1(X245))
| ~ aElementOf0(X245,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk24_1(X245)) = X245
| ~ aElementOf0(X245,slsdtgt0(xa)) )
& ( ~ aElement0(X248)
| sdtasdt0(xa,X248) != X247
| aElementOf0(X247,slsdtgt0(xa)) )
& ( aElement0(esk25_1(X249))
| ~ aElementOf0(X249,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk25_1(X249)) = X249
| ~ aElementOf0(X249,slsdtgt0(xb)) )
& ( ~ aElement0(X252)
| sdtasdt0(xb,X252) != X251
| aElementOf0(X251,slsdtgt0(xb)) )
& ( aElementOf0(esk26_1(X253),slsdtgt0(xa))
| ~ aElementOf0(X253,xI) )
& ( aElementOf0(esk27_1(X253),slsdtgt0(xb))
| ~ aElementOf0(X253,xI) )
& ( sdtpldt0(esk26_1(X253),esk27_1(X253)) = X253
| ~ aElementOf0(X253,xI) )
& ( ~ aElementOf0(X257,slsdtgt0(xa))
| ~ aElementOf0(X258,slsdtgt0(xb))
| sdtpldt0(X257,X258) != X256
| aElementOf0(X256,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])])])])])]) ).
fof(c_0_9,plain,
! [X144,X145] :
( ~ aElement0(X144)
| ~ aElement0(X145)
| sdtasdt0(X144,X145) = sdtasdt0(X145,X144) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_10,plain,
! [X157,X158] :
( ~ aSet0(X157)
| ~ aElementOf0(X158,X157)
| aElement0(X158) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_11,hypothesis,
! [X274,X275,X276] :
( aElementOf0(esk37_0,slsdtgt0(xa))
& aElementOf0(esk38_0,slsdtgt0(xb))
& sdtpldt0(esk37_0,esk38_0) = xu
& aElementOf0(xu,xI)
& xu != sz00
& ( ~ aElementOf0(X275,slsdtgt0(xa))
| ~ aElementOf0(X276,slsdtgt0(xb))
| sdtpldt0(X275,X276) != X274
| X274 = sz00
| ~ iLess0(sbrdtbr0(X274),sbrdtbr0(xu)) )
& ( ~ aElementOf0(X274,xI)
| X274 = sz00
| ~ iLess0(sbrdtbr0(X274),sbrdtbr0(xu)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
fof(c_0_12,negated_conjecture,
! [X280,X282,X283,X284,X286,X287,X288,X289] :
( ( aElement0(esk42_1(X280))
| ~ aElementOf0(X280,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk42_1(X280)) = X280
| ~ aElementOf0(X280,slsdtgt0(xa)) )
& ( ~ aElement0(X283)
| sdtasdt0(xa,X283) != X282
| aElementOf0(X282,slsdtgt0(xa)) )
& ( aElement0(esk43_1(X284))
| ~ aElementOf0(X284,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk43_1(X284)) = X284
| ~ aElementOf0(X284,slsdtgt0(xb)) )
& ( ~ aElement0(X287)
| sdtasdt0(xb,X287) != X286
| aElementOf0(X286,slsdtgt0(xb)) )
& ( ~ aElementOf0(X288,slsdtgt0(xa))
| ~ aElementOf0(X289,slsdtgt0(xb))
| sdtpldt0(X288,X289) != xc )
& ~ aElementOf0(xc,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)],[c_0_7])])])])])]) ).
cnf(c_0_13,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,hypothesis,
( aElement0(esk41_0)
& sdtasdt0(xu,esk41_0) = xc ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2744])]) ).
cnf(c_0_16,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,hypothesis,
sdtasdt0(xu,esk41_0) = xc,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,hypothesis,
aElement0(esk41_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_25,negated_conjecture,
~ aElementOf0(xc,xI),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_17]),c_0_23]),c_0_24])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG126+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 : n005.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 01:52:15 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.64/1.83 % Version : CSE_E---1.7
% 1.64/1.83 % Problem : theBenchmark.p
% 1.64/1.83 % SZS status Theorem for theBenchmark.p
% 1.64/1.83 % SZS output start CNFRefutation
% See solution above
% 1.64/1.84 % Total time : 1.373s
%------------------------------------------------------------------------------