%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG125+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 02:06:29 PM UTC 2026
% Result : ContradictoryAxioms 0.11s 0.53s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 105 ( 7 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 122 ( 49 ~; 40 |; 23 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2273,hypothesis,
( ! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) )
& ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) ) ) )
& aSet0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(mDefDvs,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( doDivides0(X2,X1)
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDvs) ).
fof(m__2612,hypothesis,
~ ~ doDivides0(xu,xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2612) ).
fof(m__2479,hypothesis,
~ ~ doDivides0(xu,xa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2479) ).
fof(m__2383,hypothesis,
~ ( aDivisorOf0(xu,xb)
& aDivisorOf0(xu,xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2383) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(c_0_9,hypothesis,
( ! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
fof(c_0_10,plain,
! [X50,X51,X52,X53,X54] :
( ( aIdeal0(X54)
| ~ aSet0(X54)
| ~ aElementOf0(sdtpldt0(esk13_1(X54),esk14_1(X54)),X54)
| ~ aElementOf0(sdtasdt0(esk15_1(X54),esk13_1(X54)),X54) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| ~ aElementOf0(sdtpldt0(esk13_1(X54),esk14_1(X54)),X54)
| aElement0(esk15_1(X54)) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| aElementOf0(esk14_1(X54),X54)
| ~ aElementOf0(sdtasdt0(esk15_1(X54),esk13_1(X54)),X54) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| aElementOf0(esk14_1(X54),X54)
| aElement0(esk15_1(X54)) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| aElementOf0(esk13_1(X54),X54) )
& ( ~ aIdeal0(X50)
| ~ aElementOf0(X51,X50)
| aElementOf0(sdtasdt0(X53,X51),X50)
| ~ aElement0(X53) )
& ( ~ aIdeal0(X50)
| ~ aElementOf0(X51,X50)
| aElementOf0(sdtpldt0(X51,X52),X50)
| ~ aElementOf0(X52,X50) )
& ( ~ aIdeal0(X50)
| aSet0(X50) ) ),
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)],[mDefIdeal])])])])])])]) ).
fof(c_0_11,plain,
! [X89,X90] :
( aElement0(X90)
| ~ aElementOf0(X90,X89)
| ~ aSet0(X89) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_12,hypothesis,
! [X8] :
( ( ~ iLess0(sbrdtbr0(X8),sbrdtbr0(xu))
| X8 = sz00
| ~ aElementOf0(X8,xI) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_13,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__2174]) ).
fof(c_0_15,plain,
! [X65,X66] :
( ( ~ aElement0(X65)
| aDivisorOf0(X66,X65)
| ~ doDivides0(X66,X65)
| ~ aElement0(X66) )
& ( ~ aElement0(X65)
| ~ aDivisorOf0(X66,X65)
| doDivides0(X66,X65) )
& ( ~ aElement0(X65)
| ~ aDivisorOf0(X66,X65)
| aElement0(X66) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDvs])])])])]) ).
fof(c_0_16,hypothesis,
doDivides0(xu,xb),
inference(fof_simplification,[status(thm)],[m__2612]) ).
cnf(c_0_17,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_20,hypothesis,
doDivides0(xu,xa),
inference(fof_simplification,[status(thm)],[m__2479]) ).
fof(c_0_21,hypothesis,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2383])]) ).
cnf(c_0_22,plain,
( ~ aElement0(X2)
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| aDivisorOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,hypothesis,
doDivides0(xu,xb),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_25,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_26,hypothesis,
doDivides0(xu,xa),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_28,hypothesis,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
aDivisorOf0(xu,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_30,hypothesis,
aDivisorOf0(xu,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_27]),c_0_25])]) ).
cnf(c_0_31,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG125+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:21:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.11/0.53 % Version: 3.5.1
% 0.11/0.53 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.53 % Starting sh5l with 300s (1) cores
% 0.11/0.53 % new_bool_3 with pid 2540566 completed with status 0
% 0.11/0.53 % Result found by new_bool_3
% 0.11/0.53 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.53 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.11/0.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.53 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.53 % SubtermCWHack with pid 2540571 completed with status 0
% 0.11/0.53 % Result found by SubtermCWHack
% 0.11/0.53 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.53 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.11/0.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.53 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.53 % Preprocessing time : 0.002 s
% 0.11/0.53
% 0.11/0.53 % Proof found!
% 0.11/0.53 % SZS status ContradictoryAxioms
% 0.11/0.53 % SZS output start CNFRefutation
% See solution above
% 0.11/0.53 % Parsed axioms : 50
% 0.11/0.53 % Removed by relevancy pruning/SinE : 11
% 0.11/0.53 % Initial clauses : 88
% 0.11/0.53 % Removed in clause preprocessing : 5
% 0.11/0.53 % Initial clauses in saturation : 83
% 0.11/0.53 % Processed clauses : 48
% 0.11/0.53 % ...of these trivial : 0
% 0.11/0.53 % ...subsumed : 1
% 0.11/0.53 % ...remaining for further processing : 46
% 0.11/0.53 % Other redundant clauses eliminated : 1
% 0.11/0.53 % Clauses deleted for lack of memory : 0
% 0.11/0.53 % Backward-subsumed : 0
% 0.11/0.53 % Backward-rewritten : 1
% 0.11/0.53 % Generated clauses : 23
% 0.11/0.53 % ...of the previous two non-redundant : 10
% 0.11/0.53 % ...aggressively subsumed : 0
% 0.11/0.53 % Contextual simplify-reflections : 0
% 0.11/0.53 % Paramodulations : 22
% 0.11/0.53 % Factorizations : 0
% 0.11/0.53 % NegExts : 0
% 0.11/0.53 % Equation resolutions : 1
% 0.11/0.53 % Disequality decompositions : 0
% 0.11/0.53 % Total rewrite steps : 26
% 0.11/0.53 % ...of those cached : 17
% 0.11/0.53 % Propositional unsat checks : 0
% 0.11/0.53 % Propositional check models : 0
% 0.11/0.53 % Propositional check unsatisfiable : 0
% 0.11/0.53 % Propositional clauses : 0
% 0.11/0.53 % Propositional clauses after purity: 0
% 0.11/0.53 % Propositional unsat core size : 0
% 0.11/0.53 % Propositional preprocessing time : 0.000
% 0.11/0.53 % Propositional encoding time : 0.000
% 0.11/0.53 % Propositional solver time : 0.000
% 0.11/0.53 % Success case prop preproc time : 0.000
% 0.11/0.53 % Success case prop encoding time : 0.000
% 0.11/0.53 % Success case prop solver time : 0.000
% 0.11/0.53 % Current number of processed clauses : 44
% 0.11/0.53 % Positive orientable unit clauses : 22
% 0.11/0.53 % Positive unorientable unit clauses: 0
% 0.11/0.53 % Negative unit clauses : 2
% 0.11/0.53 % Non-unit-clauses : 20
% 0.11/0.53 % Current number of unprocessed clauses: 45
% 0.11/0.53 % ...number of literals in the above : 212
% 0.11/0.53 % Current number of archived formulas : 0
% 0.11/0.53 % Current number of archived clauses : 1
% 0.11/0.53 % Clause-clause subsumption calls (NU) : 60
% 0.11/0.53 % Rec. Clause-clause subsumption calls : 53
% 0.11/0.53 % Non-unit clause-clause subsumptions : 1
% 0.11/0.53 % Unit Clause-clause subsumption calls : 3
% 0.11/0.53 % Rewrite failures with RHS unbound : 0
% 0.11/0.53 % BW rewrite match attempts : 1
% 0.11/0.53 % BW rewrite match successes : 1
% 0.11/0.53 % Condensation attempts : 0
% 0.11/0.53 % Condensation successes : 0
% 0.11/0.53 % Termbank termtop insertions : 6363
% 0.11/0.53 % Search garbage collected termcells : 1553
% 0.11/0.53
% 0.11/0.53 % -------------------------------------------------
% 0.11/0.53 % User time : 0.016 s
% 0.11/0.53 % System time : 0.002 s
% 0.11/0.53 % Total time : 0.017 s
% 0.11/0.53 % Maximum resident set size: 3696 pages
% 0.11/0.53
% 0.11/0.53 % -------------------------------------------------
% 0.11/0.53 % User time : 0.020 s
% 0.11/0.53 % System time : 0.008 s
% 0.11/0.53 % Total time : 0.028 s
% 0.11/0.53 % Maximum resident set size: 4608 pages
% 0.11/0.53 % E exiting
%------------------------------------------------------------------------------