%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG112+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 : 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 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 85 ( 39 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 102 ( 42 ~; 33 |; 21 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 9 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2351,hypothesis,
! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( aElementOf0(X3,xI)
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2351) ).
fof(m__2228,hypothesis,
? [X1] :
( aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X1 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
fof(m__,conjecture,
? [X1] :
( aElementOf0(X1,xI)
& X1 != sz00
& ! [X2] :
( ( aElementOf0(X2,xI)
& X2 != sz00 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2174,hypothesis,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(c_0_4,hypothesis,
! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( aElementOf0(X3,xI)
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ),
inference(fof_simplification,[status(thm)],[m__2351]) ).
fof(c_0_5,hypothesis,
( aElementOf0(esk21_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& esk21_0 != sz00 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2228])]) ).
fof(c_0_6,negated_conjecture,
~ ? [X1] :
( aElementOf0(X1,xI)
& X1 != sz00
& ! [X2] :
( ( aElementOf0(X2,xI)
& X2 != sz00 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_7,hypothesis,
! [X202,X204] :
( ( aElementOf0(esk22_0,xI)
| ~ aElementOf0(X202,xI)
| X202 = sz00 )
& ( esk22_0 != sz00
| ~ aElementOf0(X202,xI)
| X202 = sz00 )
& ( ~ aElementOf0(X204,xI)
| X204 = sz00
| ~ iLess0(sbrdtbr0(X204),sbrdtbr0(esk22_0))
| ~ aElementOf0(X202,xI)
| X202 = sz00 ) ),
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_4])])])])])]) ).
cnf(c_0_8,hypothesis,
aElementOf0(esk21_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2174]) ).
fof(c_0_10,negated_conjecture,
! [X205] :
( ( aElementOf0(esk23_1(X205),xI)
| ~ aElementOf0(X205,xI)
| X205 = sz00 )
& ( esk23_1(X205) != sz00
| ~ aElementOf0(X205,xI)
| X205 = sz00 )
& ( iLess0(sbrdtbr0(esk23_1(X205)),sbrdtbr0(X205))
| ~ aElementOf0(X205,xI)
| X205 = sz00 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_11,hypothesis,
( aElementOf0(esk22_0,xI)
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
aElementOf0(esk21_0,xI),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,hypothesis,
esk21_0 != sz00,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,hypothesis,
( X1 = sz00
| esk22_0 != sz00
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,hypothesis,
( X1 = sz00
| X2 = sz00
| ~ aElementOf0(X1,xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk22_0))
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( iLess0(sbrdtbr0(esk23_1(X1)),sbrdtbr0(X1))
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,hypothesis,
aElementOf0(esk22_0,xI),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_18,hypothesis,
esk22_0 != sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( esk23_1(esk22_0) = sz00
| X1 = sz00
| ~ aElementOf0(esk23_1(esk22_0),xI)
| ~ aElementOf0(X1,xI) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]) ).
cnf(c_0_20,negated_conjecture,
( aElementOf0(esk23_1(X1),xI)
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
( esk23_1(esk22_0) = sz00
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17])]),c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( X1 = sz00
| esk23_1(X1) != sz00
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,hypothesis,
esk23_1(esk22_0) = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_18]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_17])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG112+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n003.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:50:26 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Theorem for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------