%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG116+1 : 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 : n006.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 1.42s 1.77s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 81 ( 26 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 98 ( 40 ~; 40 |; 15 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn 12 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( X2 = slsdtgt0(X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(X1,X4) = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(m__,conjecture,
? [X1,X2] :
( aElement0(X1)
& aElement0(X2)
& xu = sdtpldt0(sdtasdt0(xa,X1),sdtasdt0(xb,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2456,hypothesis,
( aElementOf0(xk,slsdtgt0(xa))
& aElementOf0(xl,slsdtgt0(xb))
& xu = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2456) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(c_0_4,plain,
! [X188,X189,X190,X192,X193,X194,X196] :
( ( aSet0(X189)
| X189 != slsdtgt0(X188)
| ~ aElement0(X188) )
& ( aElement0(esk18_3(X188,X189,X190))
| ~ aElementOf0(X190,X189)
| X189 != slsdtgt0(X188)
| ~ aElement0(X188) )
& ( sdtasdt0(X188,esk18_3(X188,X189,X190)) = X190
| ~ aElementOf0(X190,X189)
| X189 != slsdtgt0(X188)
| ~ aElement0(X188) )
& ( ~ aElement0(X193)
| sdtasdt0(X188,X193) != X192
| aElementOf0(X192,X189)
| X189 != slsdtgt0(X188)
| ~ aElement0(X188) )
& ( ~ aElementOf0(esk19_2(X188,X194),X194)
| ~ aElement0(X196)
| sdtasdt0(X188,X196) != esk19_2(X188,X194)
| ~ aSet0(X194)
| X194 = slsdtgt0(X188)
| ~ aElement0(X188) )
& ( aElement0(esk20_2(X188,X194))
| aElementOf0(esk19_2(X188,X194),X194)
| ~ aSet0(X194)
| X194 = slsdtgt0(X188)
| ~ aElement0(X188) )
& ( sdtasdt0(X188,esk20_2(X188,X194)) = esk19_2(X188,X194)
| aElementOf0(esk19_2(X188,X194),X194)
| ~ aSet0(X194)
| X194 = slsdtgt0(X188)
| ~ aElement0(X188) ) ),
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)],[mDefPrIdeal])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ? [X1,X2] :
( aElement0(X1)
& aElement0(X2)
& xu = sdtpldt0(sdtasdt0(xa,X1),sdtasdt0(xb,X2)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_6,plain,
( sdtasdt0(X1,esk18_3(X1,X2,X3)) = X3
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( aElement0(esk18_3(X1,X2,X3))
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
! [X201,X202] :
( ~ aElement0(X201)
| ~ aElement0(X202)
| xu != sdtpldt0(sdtasdt0(xa,X201),sdtasdt0(xb,X202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).
cnf(c_0_9,plain,
( sdtasdt0(X1,esk18_3(X1,slsdtgt0(X1),X2)) = X2
| ~ aElementOf0(X2,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
aElementOf0(xl,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2456]) ).
cnf(c_0_11,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_12,plain,
( aElement0(esk18_3(X1,slsdtgt0(X1),X2))
| ~ aElementOf0(X2,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( ~ aElement0(X1)
| ~ aElement0(X2)
| xu != sdtpldt0(sdtasdt0(xa,X1),sdtasdt0(xb,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,hypothesis,
sdtasdt0(xb,esk18_3(xb,slsdtgt0(xb),xl)) = xl,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
cnf(c_0_15,hypothesis,
aElement0(esk18_3(xb,slsdtgt0(xb),xl)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_11])]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xk,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[m__2456]) ).
cnf(c_0_17,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_18,negated_conjecture,
( sdtpldt0(sdtasdt0(xa,X1),xl) != xu
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_19,hypothesis,
sdtasdt0(xa,esk18_3(xa,slsdtgt0(xa),xk)) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_16]),c_0_17])]) ).
cnf(c_0_20,hypothesis,
xu = sdtpldt0(xk,xl),
inference(split_conjunct,[status(thm)],[m__2456]) ).
cnf(c_0_21,hypothesis,
aElement0(esk18_3(xa,slsdtgt0(xa),xk)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_17])]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG116+1 : 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
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:50:16 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.42/1.77 % Version : CSE_E---1.7
% 1.42/1.77 % Problem : theBenchmark.p
% 1.42/1.77 % SZS status Theorem for theBenchmark.p
% 1.42/1.77 % SZS output start CNFRefutation
% See solution above
% 1.42/1.77 % Total time : 1.370s
%------------------------------------------------------------------------------