%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG123+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 : n013.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 05:05:25 PM UTC 2026
% Result : Theorem 1.36s 1.75s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 98 ( 24 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 104 ( 26 ~; 24 |; 48 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 21 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2690,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = smndt0(sdtasdt0(xq,xu)) )
& aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2690) ).
fof(m__2699,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xb )
& ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xb )
& aElementOf0(xb,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2699) ).
fof(m__,conjecture,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xr )
| aElementOf0(xr,xI) ),
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(m__2718,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2718) ).
fof(c_0_5,hypothesis,
( aElementOf0(esk42_0,slsdtgt0(xa))
& aElementOf0(esk43_0,slsdtgt0(xb))
& sdtpldt0(esk42_0,esk43_0) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2690])]) ).
fof(c_0_6,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xb )
& aElementOf0(xb,xI) ),
inference(fof_simplification,[status(thm)],[m__2699]) ).
fof(c_0_7,negated_conjecture,
~ ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xr )
| aElementOf0(xr,xI) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,hypothesis,
! [X247,X248,X249,X250,X252,X253,X254,X256,X257,X258,X261,X262,X263] :
( aSet0(xI)
& ( ~ aElementOf0(X248,xI)
| aElementOf0(sdtpldt0(X247,X248),xI)
| ~ aElementOf0(X247,xI) )
& ( ~ aElement0(X249)
| aElementOf0(sdtasdt0(X249,X247),xI)
| ~ aElementOf0(X247,xI) )
& aIdeal0(xI)
& ( aElement0(esk24_1(X250))
| ~ aElementOf0(X250,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk24_1(X250)) = X250
| ~ aElementOf0(X250,slsdtgt0(xa)) )
& ( ~ aElement0(X253)
| sdtasdt0(xa,X253) != X252
| aElementOf0(X252,slsdtgt0(xa)) )
& ( aElement0(esk25_1(X254))
| ~ aElementOf0(X254,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk25_1(X254)) = X254
| ~ aElementOf0(X254,slsdtgt0(xb)) )
& ( ~ aElement0(X257)
| sdtasdt0(xb,X257) != X256
| aElementOf0(X256,slsdtgt0(xb)) )
& ( aElementOf0(esk26_1(X258),slsdtgt0(xa))
| ~ aElementOf0(X258,xI) )
& ( aElementOf0(esk27_1(X258),slsdtgt0(xb))
| ~ aElementOf0(X258,xI) )
& ( sdtpldt0(esk26_1(X258),esk27_1(X258)) = X258
| ~ aElementOf0(X258,xI) )
& ( ~ aElementOf0(X262,slsdtgt0(xa))
| ~ aElementOf0(X263,slsdtgt0(xb))
| sdtpldt0(X262,X263) != X261
| aElementOf0(X261,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_9,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(split_conjunct,[status(thm)],[m__2718]) ).
cnf(c_0_10,hypothesis,
sdtpldt0(esk42_0,esk43_0) = smndt0(sdtasdt0(xq,xu)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_12,hypothesis,
( aElementOf0(esk44_0,slsdtgt0(xa))
& aElementOf0(esk45_0,slsdtgt0(xb))
& sdtpldt0(esk44_0,esk45_0) = xb
& aElementOf0(xb,xI) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
fof(c_0_13,negated_conjecture,
! [X292,X293] :
( ( ~ aElementOf0(X292,slsdtgt0(xa))
| ~ aElementOf0(X293,slsdtgt0(xb))
| sdtpldt0(X292,X293) != xr )
& ~ aElementOf0(xr,xI) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_14,hypothesis,
( aElementOf0(sdtpldt0(X2,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,hypothesis,
sdtpldt0(sdtpldt0(esk42_0,esk43_0),xb) = xr,
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,hypothesis,
aElementOf0(sdtpldt0(esk42_0,esk43_0),xI),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xb,xI),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
~ aElementOf0(xr,xI),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
$false,
inference(sr,[status(thm)],[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])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG123+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 : n013.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 01:51:56 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.36/1.75 % Version : CSE_E---1.7
% 1.36/1.75 % Problem : theBenchmark.p
% 1.36/1.75 % SZS status Theorem for theBenchmark.p
% 1.36/1.75 % SZS output start CNFRefutation
% See solution above
% 1.36/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------