%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG112+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:05:54 PM UTC 2026
% Result : Theorem 0.23s 0.59s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 92 ( 42 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 112 ( 47 ~; 33 |; 25 &)
% ( 0 <=>; 7 =>; 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 : 26 ( 0 sgn 10 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2228,hypothesis,
? [X1] :
( X1 != sz00
& aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
fof(m__,conjecture,
? [X1] :
( ! [X2] :
( ( X2 != sz00
& aElementOf0(X2,xI) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& X1 != sz00
& aElementOf0(X1,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2351,hypothesis,
! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ? [X2] :
( ! [X3] :
( ( X3 != sz00
& aElementOf0(X3,xI) )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
& X2 != sz00
& aElementOf0(X2,xI) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2351) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(c_0_4,hypothesis,
? [X1] :
( X1 != sz00
& aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(fof_simplification,[status(thm)],[m__2228]) ).
fof(c_0_5,negated_conjecture,
~ ? [X1] :
( ! [X2] :
( ( X2 != sz00
& aElementOf0(X2,xI) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& X1 != sz00
& aElementOf0(X1,xI) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,hypothesis,
! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ? [X2] :
( ! [X3] :
( ( X3 != sz00
& aElementOf0(X3,xI) )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
& X2 != sz00
& aElementOf0(X2,xI) ) ),
inference(fof_simplification,[status(thm)],[m__2351]) ).
fof(c_0_7,hypothesis,
( esk1_0 != sz00
& aElementOf0(esk1_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,negated_conjecture,
~ ? [X1] :
( ! [X2] :
( ( X2 != sz00
& aElementOf0(X2,xI) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& X1 != sz00
& aElementOf0(X1,xI) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_9,hypothesis,
! [X8,X10] :
( ( X8 = sz00
| ~ aElementOf0(X8,xI)
| ~ iLess0(sbrdtbr0(X10),sbrdtbr0(esk2_0))
| X10 = sz00
| ~ aElementOf0(X10,xI) )
& ( X8 = sz00
| ~ aElementOf0(X8,xI)
| esk2_0 != sz00 )
& ( X8 = sz00
| ~ aElementOf0(X8,xI)
| aElementOf0(esk2_0,xI) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_6])])])])])])]) ).
cnf(c_0_10,hypothesis,
aElementOf0(esk1_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2174]) ).
fof(c_0_12,negated_conjecture,
! [X11] :
( ( X11 = sz00
| ~ aElementOf0(X11,xI)
| iLess0(sbrdtbr0(esk3_1(X11)),sbrdtbr0(X11)) )
& ( X11 = sz00
| ~ aElementOf0(X11,xI)
| esk3_1(X11) != sz00 )
& ( X11 = sz00
| ~ aElementOf0(X11,xI)
| aElementOf0(esk3_1(X11),xI) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
cnf(c_0_13,hypothesis,
( ~ aElementOf0(X1,xI)
| X1 = sz00
| aElementOf0(esk2_0,xI) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aElementOf0(esk1_0,xI),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,hypothesis,
esk1_0 != sz00,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,hypothesis,
( ~ aElementOf0(X1,xI)
| esk2_0 != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,hypothesis,
( ~ aElementOf0(X2,xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk2_0))
| ~ aElementOf0(X1,xI)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( ~ aElementOf0(X1,xI)
| X1 = sz00
| iLess0(sbrdtbr0(esk3_1(X1)),sbrdtbr0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
aElementOf0(esk2_0,xI),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_20,hypothesis,
esk2_0 != sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_14]),c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( ~ aElementOf0(X1,xI)
| ~ aElementOf0(esk3_1(esk2_0),xI)
| X1 = sz00
| esk3_1(esk2_0) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( ~ aElementOf0(X1,xI)
| X1 = sz00
| aElementOf0(esk3_1(X1),xI) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,negated_conjecture,
( ~ aElementOf0(X1,xI)
| X1 = sz00
| esk3_1(esk2_0) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_19])]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElementOf0(X1,xI)
| esk3_1(X1) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,hypothesis,
esk3_1(esk2_0) = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_20]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG112+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:22:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.59 % Version: 3.5.1
% 0.23/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.59 % Starting sh5l with 300s (1) cores
% 0.23/0.59 % new_bool_3 with pid 957282 completed with status 0
% 0.23/0.59 % Result found by new_bool_3
% 0.23/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.59 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.23/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.59 % SubtermCWHack with pid 957286 completed with status 0
% 0.23/0.59 % Result found by SubtermCWHack
% 0.23/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.59 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.23/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.59 % Preprocessing time : 0.003 s
% 0.23/0.59
% 0.23/0.59 % Proof found!
% 0.23/0.59 % SZS status Theorem
% 0.23/0.59 % SZS output start CNFRefutation
% See solution above
% 0.23/0.59 % Parsed axioms : 46
% 0.23/0.59 % Removed by relevancy pruning/SinE : 11
% 0.23/0.59 % Initial clauses : 84
% 0.23/0.59 % Removed in clause preprocessing : 4
% 0.23/0.59 % Initial clauses in saturation : 80
% 0.23/0.59 % Processed clauses : 514
% 0.23/0.59 % ...of these trivial : 3
% 0.23/0.59 % ...subsumed : 329
% 0.23/0.59 % ...remaining for further processing : 182
% 0.23/0.59 % Other redundant clauses eliminated : 13
% 0.23/0.59 % Clauses deleted for lack of memory : 0
% 0.23/0.59 % Backward-subsumed : 7
% 0.23/0.59 % Backward-rewritten : 6
% 0.23/0.59 % Generated clauses : 1298
% 0.23/0.59 % ...of the previous two non-redundant : 1033
% 0.23/0.59 % ...aggressively subsumed : 0
% 0.23/0.59 % Contextual simplify-reflections : 10
% 0.23/0.59 % Paramodulations : 1287
% 0.23/0.59 % Factorizations : 0
% 0.23/0.59 % NegExts : 0
% 0.23/0.59 % Equation resolutions : 13
% 0.23/0.59 % Disequality decompositions : 0
% 0.23/0.59 % Total rewrite steps : 1048
% 0.23/0.59 % ...of those cached : 1031
% 0.23/0.59 % Propositional unsat checks : 0
% 0.23/0.59 % Propositional check models : 0
% 0.23/0.59 % Propositional check unsatisfiable : 0
% 0.23/0.59 % Propositional clauses : 0
% 0.23/0.59 % Propositional clauses after purity: 0
% 0.23/0.59 % Propositional unsat core size : 0
% 0.23/0.59 % Propositional preprocessing time : 0.000
% 0.23/0.59 % Propositional encoding time : 0.000
% 0.23/0.59 % Propositional solver time : 0.000
% 0.23/0.59 % Success case prop preproc time : 0.000
% 0.23/0.59 % Success case prop encoding time : 0.000
% 0.23/0.59 % Success case prop solver time : 0.000
% 0.23/0.59 % Current number of processed clauses : 159
% 0.23/0.59 % Positive orientable unit clauses : 25
% 0.23/0.59 % Positive unorientable unit clauses: 0
% 0.23/0.59 % Negative unit clauses : 2
% 0.23/0.59 % Non-unit-clauses : 132
% 0.23/0.59 % Current number of unprocessed clauses: 530
% 0.23/0.59 % ...number of literals in the above : 2259
% 0.23/0.59 % Current number of archived formulas : 0
% 0.23/0.59 % Current number of archived clauses : 13
% 0.23/0.59 % Clause-clause subsumption calls (NU) : 5144
% 0.23/0.59 % Rec. Clause-clause subsumption calls : 4017
% 0.23/0.59 % Non-unit clause-clause subsumptions : 345
% 0.23/0.59 % Unit Clause-clause subsumption calls : 92
% 0.23/0.59 % Rewrite failures with RHS unbound : 0
% 0.23/0.59 % BW rewrite match attempts : 6
% 0.23/0.59 % BW rewrite match successes : 6
% 0.23/0.59 % Condensation attempts : 0
% 0.23/0.59 % Condensation successes : 0
% 0.23/0.59 % Termbank termtop insertions : 23671
% 0.23/0.59 % Search garbage collected termcells : 1632
% 0.23/0.59
% 0.23/0.59 % -------------------------------------------------
% 0.23/0.59 % User time : 0.057 s
% 0.23/0.59 % System time : 0.006 s
% 0.23/0.59 % Total time : 0.063 s
% 0.23/0.59 % Maximum resident set size: 3952 pages
% 0.23/0.59
% 0.23/0.59 % -------------------------------------------------
% 0.23/0.59 % User time : 0.061 s
% 0.23/0.59 % System time : 0.013 s
% 0.23/0.59 % Total time : 0.073 s
% 0.23/0.59 % Maximum resident set size: 4864 pages
% 0.23/0.59 % E exiting
%------------------------------------------------------------------------------