%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KRS251+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 01:01:12 PM UTC 2026
% Result : Theorem 196.74s 33.96s
% Output : CNFRefutation 196.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 11 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 92 ( 34 ~; 40 |; 9 &)
% ( 6 <=>; 1 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 37 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(completeness,axiom,
! [X9,X10] :
( model(X9,X10)
<~> model(X9,not(X10)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',completeness) ).
fof(csa,axiom,
! [X1,X2] :
( ? [X3] :
( model(X3,not(X2))
& model(X3,X1) )
<=> status(X1,X2,csa) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax',csa) ).
fof(thm,axiom,
! [X1,X2] :
( ! [X3] :
( model(X3,X1)
=> model(X3,X2) )
<=> status(X1,X2,thm) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax',thm) ).
fof(xora,axiom,
! [X7,X8] :
( ! [X1,X2] :
( status(X1,X2,X7)
<~> status(X1,X2,X8) )
<=> xora(X7,X8) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',xora) ).
fof(xora_csa_thm,conjecture,
xora(csa,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xora_csa_thm) ).
fof(c_0_5,plain,
! [X9,X10] :
~ ( model(X9,X10)
<=> model(X9,not(X10)) ),
inference(fof_simplification,[status(thm)],[completeness]) ).
fof(c_0_6,plain,
! [X27,X28,X29,X30,X31] :
( ( ~ status(X30,X31,csa)
| model(esk4_2(X30,X31),not(X31)) )
& ( ~ status(X30,X31,csa)
| model(esk4_2(X30,X31),X30) )
& ( status(X27,X28,csa)
| ~ model(X29,not(X28))
| ~ model(X29,X27) ) ),
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)],[csa])])])])])])]) ).
fof(c_0_7,plain,
! [X54,X55] :
( ( model(X54,not(X55))
| model(X54,X55) )
& ( ~ model(X54,not(X55))
| ~ model(X54,X55) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_8,plain,
( ~ model(X1,not(X3))
| ~ model(X1,X2)
| status(X2,X3,csa) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( model(X1,not(X2))
| model(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X21,X22,X24,X25,X26] :
( ( model(X26,X25)
| ~ model(X26,X24)
| ~ status(X24,X25,thm) )
& ( status(X21,X22,thm)
| ~ model(esk3_2(X21,X22),X22) )
& ( status(X21,X22,thm)
| model(esk3_2(X21,X22),X21) ) ),
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)],[thm])])])])])])]) ).
fof(c_0_11,plain,
! [X7,X8] :
( ! [X1,X2] :
~ ( status(X1,X2,X7)
<=> status(X1,X2,X8) )
<=> xora(X7,X8) ),
inference(fof_simplification,[status(thm)],[xora]) ).
cnf(c_0_12,plain,
( ~ model(X3,X1)
| model(X3,X2)
| status(X1,X2,csa) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( status(X1,X2,thm)
| model(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,negated_conjecture,
~ xora(csa,thm),
inference(assume_negation,[status(cth)],[xora_csa_thm]) ).
fof(c_0_15,plain,
! [X11,X12,X15,X16,X17,X18,X19,X20] :
( ( ~ xora(X15,X16)
| status(X19,X20,X16)
| status(X19,X20,X15) )
& ( ~ xora(X15,X16)
| ~ status(X17,X18,X16)
| ~ status(X17,X18,X15) )
& ( xora(X11,X12)
| status(esk1_2(X11,X12),esk2_2(X11,X12),X11)
| ~ status(esk1_2(X11,X12),esk2_2(X11,X12),X12) )
& ( xora(X11,X12)
| status(esk1_2(X11,X12),esk2_2(X11,X12),X12)
| ~ status(esk1_2(X11,X12),esk2_2(X11,X12),X11) ) ),
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_11])])])])])])]) ).
cnf(c_0_16,plain,
( ~ model(esk3_2(X1,X2),X2)
| status(X1,X2,thm) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( model(esk3_2(X1,X2),X3)
| status(X1,X3,csa)
| status(X1,X2,thm) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,negated_conjecture,
~ xora(csa,thm),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( ~ status(esk1_2(X1,X2),esk2_2(X1,X2),X1)
| xora(X1,X2)
| status(esk1_2(X1,X2),esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( status(X1,X2,thm)
| status(X1,X2,csa) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,negated_conjecture,
~ xora(csa,thm),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( status(esk1_2(csa,X1),esk2_2(csa,X1),X1)
| status(esk1_2(csa,X1),esk2_2(csa,X1),thm)
| xora(csa,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
~ xora(csa,thm),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,plain,
( ~ status(esk1_2(X1,X2),esk2_2(X1,X2),X2)
| xora(X1,X2)
| status(esk1_2(X1,X2),esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
status(esk1_2(csa,thm),esk2_2(csa,thm),thm),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_22]),c_0_23]) ).
cnf(c_0_26,plain,
( ~ model(X3,X1)
| ~ status(X1,X2,thm)
| model(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,plain,
( ~ status(X1,X2,csa)
| model(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,plain,
status(esk1_2(csa,thm),esk2_2(csa,thm),csa),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_23]) ).
cnf(c_0_29,plain,
( ~ status(X1,X2,csa)
| model(esk4_2(X1,X2),not(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_30,plain,
( ~ model(X1,esk1_2(csa,thm))
| model(X1,esk2_2(csa,thm)) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_31,plain,
model(esk4_2(esk1_2(csa,thm),esk2_2(csa,thm)),esk1_2(csa,thm)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( ~ model(X1,not(X2))
| ~ model(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,plain,
model(esk4_2(esk1_2(csa,thm),esk2_2(csa,thm)),not(esk2_2(csa,thm))),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_34,plain,
model(esk4_2(esk1_2(csa,thm),esk2_2(csa,thm)),esk2_2(csa,thm)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS251+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n005.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 22:59:33 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 196.74/33.96 % Version: 3.5.1
% 196.74/33.96 % Preprocessing class: FSMSSMSMSSSNFFN.
% 196.74/33.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 196.74/33.96 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 196.74/33.96 % Starting new_bool_3 with 300s (1) cores
% 196.74/33.96 % Starting new_bool_1 with 300s (1) cores
% 196.74/33.96 % Starting sh5l with 300s (1) cores
% 196.74/33.96 % new_bool_3 with pid 1949971 completed with status 0
% 196.74/33.96 % Result found by new_bool_3
% 196.74/33.96 % Preprocessing class: FSMSSMSMSSSNFFN.
% 196.74/33.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 196.74/33.96 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 196.74/33.96 % Starting new_bool_3 with 300s (1) cores
% 196.74/33.96 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 196.74/33.96 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 196.74/33.96 % Search class: FGHNF-FFMM21-SFFFFFNN
% 196.74/33.96 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 196.74/33.96 % Starting SubtermCWHack with 31s (1) cores
% 196.74/33.96 % SubtermCWHack with pid 1949974 completed with status 8
% 196.74/33.96 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 131s (1) cores
% 196.74/33.96 % G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with pid 1950395 completed with status 0
% 196.74/33.96 % Result found by G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S
% 196.74/33.96 % Preprocessing class: FSMSSMSMSSSNFFN.
% 196.74/33.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 196.74/33.96 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 196.74/33.96 % Starting new_bool_3 with 300s (1) cores
% 196.74/33.96 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 196.74/33.96 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 196.74/33.96 % Search class: FGHNF-FFMM21-SFFFFFNN
% 196.74/33.96 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 196.74/33.96 % Starting SubtermCWHack with 31s (1) cores
% 196.74/33.96 % SubtermCWHack with pid 1949974 completed with status 8
% 196.74/33.96 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 131s (1) cores
% 196.74/33.96 % Preprocessing time : 0.002 s
% 196.74/33.96 % Presaturation interreduction done
% 196.74/33.96
% 196.74/33.96 % Proof found!
% 196.74/33.96 % SZS status Theorem
% 196.74/33.96 % SZS output start CNFRefutation
% See solution above
% 196.74/33.96 % Parsed axioms : 33
% 196.74/33.96 % Removed by relevancy pruning/SinE : 21
% 196.74/33.96 % Initial clauses : 30
% 196.74/33.96 % Removed in clause preprocessing : 0
% 196.74/33.96 % Initial clauses in saturation : 30
% 196.74/33.96 % Processed clauses : 5034
% 196.74/33.96 % ...of these trivial : 527
% 196.74/33.96 % ...subsumed : 2565
% 196.74/33.96 % ...remaining for further processing : 1942
% 196.74/33.96 % Other redundant clauses eliminated : 0
% 196.74/33.96 % Clauses deleted for lack of memory : 0
% 196.74/33.96 % Backward-subsumed : 22
% 196.74/33.96 % Backward-rewritten : 4
% 196.74/33.96 % Generated clauses : 52380
% 196.74/33.96 % ...of the previous two non-redundant : 46478
% 196.74/33.96 % ...aggressively subsumed : 0
% 196.74/33.96 % Contextual simplify-reflections : 0
% 196.74/33.96 % Paramodulations : 52292
% 196.74/33.96 % Factorizations : 88
% 196.74/33.96 % NegExts : 0
% 196.74/33.96 % Equation resolutions : 0
% 196.74/33.96 % Disequality decompositions : 0
% 196.74/33.96 % Total rewrite steps : 6557
% 196.74/33.96 % ...of those cached : 5963
% 196.74/33.96 % Propositional unsat checks : 0
% 196.74/33.96 % Propositional check models : 0
% 196.74/33.96 % Propositional check unsatisfiable : 0
% 196.74/33.96 % Propositional clauses : 0
% 196.74/33.96 % Propositional clauses after purity: 0
% 196.74/33.96 % Propositional unsat core size : 0
% 196.74/33.96 % Propositional preprocessing time : 0.000
% 196.74/33.96 % Propositional encoding time : 0.000
% 196.74/33.96 % Propositional solver time : 0.000
% 196.74/33.96 % Success case prop preproc time : 0.000
% 196.74/33.96 % Success case prop encoding time : 0.000
% 196.74/33.96 % Success case prop solver time : 0.000
% 196.74/33.96 % Current number of processed clauses : 1888
% 196.74/33.96 % Positive orientable unit clauses : 346
% 196.74/33.96 % Positive unorientable unit clauses: 0
% 196.74/33.96 % Negative unit clauses : 66
% 196.74/33.96 % Non-unit-clauses : 1476
% 196.74/33.96 % Current number of unprocessed clauses: 41187
% 196.74/33.96 % ...number of literals in the above : 121592
% 196.74/33.96 % Current number of archived formulas : 0
% 196.74/33.96 % Current number of archived clauses : 54
% 196.74/33.96 % Clause-clause subsumption calls (NU) : 194946
% 196.74/33.96 % Rec. Clause-clause subsumption calls : 122510
% 196.74/33.96 % Non-unit clause-clause subsumptions : 2582
% 196.74/33.96 % Unit Clause-clause subsumption calls : 5474
% 196.74/33.96 % Rewrite failures with RHS unbound : 0
% 196.74/33.96 % BW rewrite match attempts : 2145
% 196.74/33.96 % BW rewrite match successes : 4
% 196.74/33.96 % Condensation attempts : 0
% 196.74/33.96 % Condensation successes : 0
% 196.74/33.96 % Termbank termtop insertions : 663483
% 196.74/33.96 % Search garbage collected termcells : 585
% 196.74/33.96
% 196.74/33.96 % -------------------------------------------------
% 196.74/33.96 % User time : 31.240 s
% 196.74/33.96 % System time : 1.315 s
% 196.74/33.96 % Total time : 32.555 s
% 196.74/33.96 % Maximum resident set size: 3680 pages
% 196.74/33.96
% 196.74/33.96 % -------------------------------------------------
% 196.74/33.96 % User time : 31.242 s
% 196.74/33.96 % System time : 1.325 s
% 196.74/33.96 % Total time : 32.567 s
% 196.74/33.96 % Maximum resident set size: 4864 pages
% 196.74/33.96 % E exiting
%------------------------------------------------------------------------------