%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG108+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 : n007.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 1.18s 1.87s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 221 ( 63 equ)
% Maximal formula atoms : 96 ( 7 avg)
% Number of connectives : 328 ( 137 ~; 124 |; 59 &)
% ( 3 <=>; 5 =>; 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 : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 27 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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__,conjecture,
( ( ? [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__) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(c_0_7,hypothesis,
! [X221,X222,X223,X224,X226,X227,X228,X230,X231,X232,X235,X236,X237] :
( aSet0(xI)
& ( ~ aElementOf0(X222,xI)
| aElementOf0(sdtpldt0(X221,X222),xI)
| ~ aElementOf0(X221,xI) )
& ( ~ aElement0(X223)
| aElementOf0(sdtasdt0(X223,X221),xI)
| ~ aElementOf0(X221,xI) )
& aIdeal0(xI)
& ( aElement0(esk24_1(X224))
| ~ aElementOf0(X224,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk24_1(X224)) = X224
| ~ aElementOf0(X224,slsdtgt0(xa)) )
& ( ~ aElement0(X227)
| sdtasdt0(xa,X227) != X226
| aElementOf0(X226,slsdtgt0(xa)) )
& ( aElement0(esk25_1(X228))
| ~ aElementOf0(X228,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk25_1(X228)) = X228
| ~ aElementOf0(X228,slsdtgt0(xb)) )
& ( ~ aElement0(X231)
| sdtasdt0(xb,X231) != X230
| aElementOf0(X230,slsdtgt0(xb)) )
& ( aElementOf0(esk26_1(X232),slsdtgt0(xa))
| ~ aElementOf0(X232,xI) )
& ( aElementOf0(esk27_1(X232),slsdtgt0(xb))
| ~ aElementOf0(X232,xI) )
& ( sdtpldt0(esk26_1(X232),esk27_1(X232)) = X232
| ~ aElementOf0(X232,xI) )
& ( ~ aElementOf0(X236,slsdtgt0(xa))
| ~ aElementOf0(X237,slsdtgt0(xb))
| sdtpldt0(X236,X237) != X235
| aElementOf0(X235,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_8,negated_conjecture,
~ ( ( ? [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)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_9,hypothesis,
( aElementOf0(X2,slsdtgt0(xa))
| ~ aElement0(X1)
| sdtasdt0(xa,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X133] :
( ( sdtasdt0(X133,sz00) = sz00
| ~ aElement0(X133) )
& ( sz00 = sdtasdt0(sz00,X133)
| ~ aElement0(X133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(c_0_11,negated_conjecture,
! [X238,X239,X240,X241] :
( ( ~ aElement0(X241)
| sdtasdt0(xb,X241) != xb
| ~ aElement0(X240)
| sdtasdt0(xb,X240) != sz00
| ~ aElement0(X239)
| sdtasdt0(xa,X239) != xa
| ~ aElement0(X238)
| sdtasdt0(xa,X238) != sz00 )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(X240)
| sdtasdt0(xb,X240) != sz00
| ~ aElement0(X239)
| sdtasdt0(xa,X239) != xa
| ~ aElement0(X238)
| sdtasdt0(xa,X238) != sz00 )
& ( ~ aElement0(X241)
| sdtasdt0(xb,X241) != xb
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(X239)
| sdtasdt0(xa,X239) != xa
| ~ aElement0(X238)
| sdtasdt0(xa,X238) != sz00 )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(X239)
| sdtasdt0(xa,X239) != xa
| ~ aElement0(X238)
| sdtasdt0(xa,X238) != sz00 )
& ( ~ aElement0(X241)
| sdtasdt0(xb,X241) != xb
| ~ aElement0(X240)
| sdtasdt0(xb,X240) != sz00
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(X238)
| sdtasdt0(xa,X238) != sz00 )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(X240)
| sdtasdt0(xb,X240) != sz00
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(X238)
| sdtasdt0(xa,X238) != sz00 )
& ( ~ aElement0(X241)
| sdtasdt0(xb,X241) != xb
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(X238)
| sdtasdt0(xa,X238) != sz00 )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(X238)
| sdtasdt0(xa,X238) != sz00 )
& ( ~ aElement0(X241)
| sdtasdt0(xb,X241) != xb
| ~ aElement0(X240)
| sdtasdt0(xb,X240) != sz00
| ~ aElement0(X239)
| sdtasdt0(xa,X239) != xa
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(X240)
| sdtasdt0(xb,X240) != sz00
| ~ aElement0(X239)
| sdtasdt0(xa,X239) != xa
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElement0(X241)
| sdtasdt0(xb,X241) != xb
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(X239)
| sdtasdt0(xa,X239) != xa
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(X239)
| sdtasdt0(xa,X239) != xa
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElement0(X241)
| sdtasdt0(xb,X241) != xb
| ~ aElement0(X240)
| sdtasdt0(xb,X240) != sz00
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(X240)
| sdtasdt0(xb,X240) != sz00
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElement0(X241)
| sdtasdt0(xb,X241) != xb
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_12,hypothesis,
( aElementOf0(sdtasdt0(xa,X1),slsdtgt0(xa))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_15,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_16,hypothesis,
( aElementOf0(X2,slsdtgt0(xb))
| ~ aElement0(X1)
| sdtasdt0(xb,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_19,hypothesis,
( aElementOf0(sdtasdt0(xb,X1),slsdtgt0(xb))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_21,plain,
! [X128] :
( ( sdtasdt0(X128,sz10) = X128
| ~ aElement0(X128) )
& ( X128 = sdtasdt0(sz10,X128)
| ~ aElement0(X128) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).
cnf(c_0_22,negated_conjecture,
( ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_23,hypothesis,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13]),c_0_14]),c_0_20])]) ).
cnf(c_0_24,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_26,negated_conjecture,
( ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xb,slsdtgt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_24]),c_0_25]),c_0_20])]) ).
cnf(c_0_28,negated_conjecture,
~ aElementOf0(xa,slsdtgt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_29,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_24]),c_0_25]),c_0_15])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.20 % Problem : RNG108+4 : TPTP v9.2.1. Released v4.0.0.
% 0.02/0.20 % 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
% 0.11/0.43 % Computer : n007.cluster.edu
% 0.11/0.43 % Model : x86_64 x86_64
% 0.11/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.43 % Memory : 8042.1875MB
% 0.11/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.43 % CPULimit : 300
% 0.11/0.43 % WCLimit : 300
% 0.11/0.43 % DateTime : Tue May 5 01:50:08 EDT 2026
% 0.11/0.45 % CPUTime :
% 0.15/0.47 % start to proof: theBenchmark
% 1.18/1.87 % Version : CSE_E---1.7
% 1.18/1.87 % Problem : theBenchmark.p
% 1.18/1.87 % SZS status Theorem for theBenchmark.p
% 1.18/1.87 % SZS output start CNFRefutation
% See solution above
% 1.18/1.87 % Total time : 1.391s
%------------------------------------------------------------------------------