%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG114+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 : n003.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 05:05:23 PM UTC 2026
% Result : Theorem 1.41s 1.75s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 116 ( 34 equ)
% Maximal formula atoms : 33 ( 5 avg)
% Number of connectives : 138 ( 44 ~; 35 |; 51 &)
% ( 3 <=>; 5 =>; 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 : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 26 !; 16 ?)
% 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,X2] :
( aElement0(X1)
& aElement0(X2)
& xu = sdtpldt0(sdtasdt0(xa,X1),sdtasdt0(xb,X2)) ),
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(c_0_3,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_4,negated_conjecture,
~ ? [X1,X2] :
( aElement0(X1)
& aElement0(X2)
& xu = sdtpldt0(sdtasdt0(xa,X1),sdtasdt0(xb,X2)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_5,hypothesis,
! [X237,X238,X239,X240,X242,X243,X244,X246,X247,X248,X251,X252,X253] :
( aSet0(xI)
& ( ~ aElementOf0(X238,xI)
| aElementOf0(sdtpldt0(X237,X238),xI)
| ~ aElementOf0(X237,xI) )
& ( ~ aElement0(X239)
| aElementOf0(sdtasdt0(X239,X237),xI)
| ~ aElementOf0(X237,xI) )
& aIdeal0(xI)
& ( aElement0(esk24_1(X240))
| ~ aElementOf0(X240,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk24_1(X240)) = X240
| ~ aElementOf0(X240,slsdtgt0(xa)) )
& ( ~ aElement0(X243)
| sdtasdt0(xa,X243) != X242
| aElementOf0(X242,slsdtgt0(xa)) )
& ( aElement0(esk25_1(X244))
| ~ aElementOf0(X244,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk25_1(X244)) = X244
| ~ aElementOf0(X244,slsdtgt0(xb)) )
& ( ~ aElement0(X247)
| sdtasdt0(xb,X247) != X246
| aElementOf0(X246,slsdtgt0(xb)) )
& ( aElementOf0(esk26_1(X248),slsdtgt0(xa))
| ~ aElementOf0(X248,xI) )
& ( aElementOf0(esk27_1(X248),slsdtgt0(xb))
| ~ aElementOf0(X248,xI) )
& ( sdtpldt0(esk26_1(X248),esk27_1(X248)) = X248
| ~ aElementOf0(X248,xI) )
& ( ~ aElementOf0(X252,slsdtgt0(xa))
| ~ aElementOf0(X253,slsdtgt0(xb))
| sdtpldt0(X252,X253) != X251
| aElementOf0(X251,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_6,hypothesis,
! [X269,X270,X271] :
( aElementOf0(esk37_0,slsdtgt0(xa))
& aElementOf0(esk38_0,slsdtgt0(xb))
& sdtpldt0(esk37_0,esk38_0) = xu
& aElementOf0(xu,xI)
& xu != sz00
& ( ~ aElementOf0(X270,slsdtgt0(xa))
| ~ aElementOf0(X271,slsdtgt0(xb))
| sdtpldt0(X270,X271) != X269
| X269 = sz00
| ~ iLess0(sbrdtbr0(X269),sbrdtbr0(xu)) )
& ( ~ aElementOf0(X269,xI)
| X269 = sz00
| ~ iLess0(sbrdtbr0(X269),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_3])])])])]) ).
fof(c_0_7,negated_conjecture,
! [X274,X275] :
( ~ aElement0(X274)
| ~ aElement0(X275)
| xu != sdtpldt0(sdtasdt0(xa,X274),sdtasdt0(xb,X275)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
cnf(c_0_8,hypothesis,
( sdtasdt0(xa,esk24_1(X1)) = X1
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,hypothesis,
aElementOf0(esk37_0,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
( aElement0(esk24_1(X1))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( ~ aElement0(X1)
| ~ aElement0(X2)
| xu != sdtpldt0(sdtasdt0(xa,X1),sdtasdt0(xb,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
sdtasdt0(xa,esk24_1(esk37_0)) = esk37_0,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,hypothesis,
aElement0(esk24_1(esk37_0)),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_14,hypothesis,
( sdtasdt0(xb,esk25_1(X1)) = X1
| ~ aElementOf0(X1,slsdtgt0(xb)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,hypothesis,
aElementOf0(esk38_0,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,hypothesis,
( aElement0(esk25_1(X1))
| ~ aElementOf0(X1,slsdtgt0(xb)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
( sdtpldt0(esk37_0,sdtasdt0(xb,X1)) != xu
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_18,hypothesis,
sdtasdt0(xb,esk25_1(esk38_0)) = esk38_0,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,hypothesis,
sdtpldt0(esk37_0,esk38_0) = xu,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,hypothesis,
aElement0(esk25_1(esk38_0)),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG114+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:50:26 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.41/1.75 % Version : CSE_E---1.7
% 1.41/1.75 % Problem : theBenchmark.p
% 1.41/1.75 % SZS status Theorem for theBenchmark.p
% 1.41/1.75 % SZS output start CNFRefutation
% See solution above
% 1.41/1.76 % Total time : 1.371s
%------------------------------------------------------------------------------