%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG226+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 11:55:40 AM UTC 2026
% Result : Theorem 32.58s 5.65s
% Output : CNFRefutation 32.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 79 ( 21 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 80 ( 26 ~; 16 |; 20 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_closure3,conjecture,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> ! [X3] :
( ( m1_pboole(X3,X1)
& v2_relat_1(X3) )
=> ( ( k7_relat_1(X2,k1_closure3(X1,X2)) = k7_relat_1(X3,k1_closure3(X1,X3))
& k1_closure3(X1,X2) = k1_closure3(X1,X3) )
=> r6_pboole(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_closure3) ).
fof(t6_closure3,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> X2 = k1_funct_4(k1_pboole(X1),k7_relat_1(X2,k1_closure3(X1,X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_closure3) ).
fof(redefinition_r6_pboole,axiom,
! [X1,X2,X3] :
( ( m1_pboole(X3,X1)
& m1_pboole(X2,X1) )
=> ( r6_pboole(X1,X2,X3)
<=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+80.ax',redefinition_r6_pboole) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> ! [X3] :
( ( m1_pboole(X3,X1)
& v2_relat_1(X3) )
=> ( ( k7_relat_1(X2,k1_closure3(X1,X2)) = k7_relat_1(X3,k1_closure3(X1,X3))
& k1_closure3(X1,X2) = k1_closure3(X1,X3) )
=> r6_pboole(X1,X2,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t7_closure3]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> ! [X3] :
( ( m1_pboole(X3,X1)
& v2_relat_1(X3) )
=> ( ( k7_relat_1(X2,k1_closure3(X1,X2)) = k7_relat_1(X3,k1_closure3(X1,X3))
& k1_closure3(X1,X2) = k1_closure3(X1,X3) )
=> r6_pboole(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_5,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> X2 = k1_funct_4(k1_pboole(X1),k7_relat_1(X2,k1_closure3(X1,X2))) ) ),
inference(fof_simplification,[status(thm)],[t6_closure3]) ).
fof(c_0_6,negated_conjecture,
( ~ r6_pboole(esk1_0,esk2_0,esk3_0)
& k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)) = k7_relat_1(esk3_0,k1_closure3(esk1_0,esk3_0))
& k1_closure3(esk1_0,esk2_0) = k1_closure3(esk1_0,esk3_0)
& m1_pboole(esk3_0,esk1_0)
& v2_relat_1(esk3_0)
& m1_pboole(esk2_0,esk1_0)
& v2_relat_1(esk2_0)
& ~ v1_xboole_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,plain,
! [X153,X154] :
( X154 = k1_funct_4(k1_pboole(X153),k7_relat_1(X154,k1_closure3(X153,X154)))
| ~ m1_pboole(X154,X153)
| ~ v2_relat_1(X154)
| v1_xboole_0(X153) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_8,negated_conjecture,
k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)) = k7_relat_1(esk3_0,k1_closure3(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
k1_closure3(esk1_0,esk2_0) = k1_closure3(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ m1_pboole(X2,X1)
| ~ v2_relat_1(X2)
| X2 = k1_funct_4(k1_pboole(X1),k7_relat_1(X2,k1_closure3(X1,X2)))
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
k7_relat_1(esk3_0,k1_closure3(esk1_0,esk2_0)) = k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
m1_pboole(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
v2_relat_1(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
~ v1_xboole_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
k1_funct_4(k1_pboole(esk1_0),k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0))) = esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_11]),c_0_12]),c_0_13])]),c_0_14]) ).
cnf(c_0_16,negated_conjecture,
m1_pboole(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
v2_relat_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_18,plain,
! [X25,X26,X27] :
( ( ~ m1_pboole(X27,X25)
| ~ m1_pboole(X26,X25)
| r6_pboole(X25,X26,X27)
| X26 != X27 )
& ( ~ m1_pboole(X27,X25)
| ~ m1_pboole(X26,X25)
| X26 = X27
| ~ r6_pboole(X25,X26,X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r6_pboole])])])]) ).
cnf(c_0_19,negated_conjecture,
~ r6_pboole(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
esk3_0 = esk2_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_15]),c_0_16]),c_0_17])]),c_0_14]) ).
cnf(c_0_21,plain,
( ~ m1_pboole(X2,X3)
| ~ m1_pboole(X1,X3)
| X1 != X2
| r6_pboole(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
~ r6_pboole(esk1_0,esk2_0,esk2_0),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( ~ m1_pboole(X2,X1)
| r6_pboole(X1,X2,X2) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG226+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n002.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 13:09:02 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 32.58/5.65 % Version: 3.5.1
% 32.58/5.65 % Preprocessing class: FMLLSMLLSSSNFFN.
% 32.58/5.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 32.58/5.65 % Starting new_bool_3 with 900s (3) cores
% 32.58/5.65 % Starting new_bool_1 with 900s (3) cores
% 32.58/5.65 % Starting sh5l with 300s (1) cores
% 32.58/5.65 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 32.58/5.65 % new_bool_3 with pid 3349697 completed with status 0
% 32.58/5.65 % Result found by new_bool_3
% 32.58/5.65 % Preprocessing class: FMLLSMLLSSSNFFN.
% 32.58/5.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 32.58/5.65 % Starting new_bool_3 with 900s (3) cores
% 32.58/5.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 32.58/5.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 32.58/5.65 % Search class: FGHSM-SMLM32-MFFFFFNN
% 32.58/5.65 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 32.58/5.65 % Starting SubtermCWHack with 82s (1) cores
% 32.58/5.65 % Starting new_bool_3 with 91s (1) cores
% 32.58/5.65 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 32.58/5.65 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 3349708 completed with status 0
% 32.58/5.65 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 32.58/5.65 % Preprocessing class: FMLLSMLLSSSNFFN.
% 32.58/5.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 32.58/5.65 % Starting new_bool_3 with 900s (3) cores
% 32.58/5.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 32.58/5.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 32.58/5.65 % Search class: FGHSM-SMLM32-MFFFFFNN
% 32.58/5.65 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 32.58/5.65 % Starting SubtermCWHack with 82s (1) cores
% 32.58/5.65 % Starting new_bool_3 with 91s (1) cores
% 32.58/5.65 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 32.58/5.65 % Preprocessing time : 0.041 s
% 32.58/5.65 % Presaturation interreduction done
% 32.58/5.65
% 32.58/5.65 % Proof found!
% 32.58/5.65 % SZS status Theorem
% 32.58/5.65 % SZS output start CNFRefutation
% See solution above
% 32.58/5.65 % Parsed axioms : 4731
% 32.58/5.65 % Removed by relevancy pruning/SinE : 3749
% 32.58/5.65 % Initial clauses : 1789
% 32.58/5.65 % Removed in clause preprocessing : 32
% 32.58/5.65 % Initial clauses in saturation : 1757
% 32.58/5.65 % Processed clauses : 15753
% 32.58/5.65 % ...of these trivial : 159
% 32.58/5.65 % ...subsumed : 10305
% 32.58/5.65 % ...remaining for further processing : 5289
% 32.58/5.65 % Other redundant clauses eliminated : 666
% 32.58/5.65 % Clauses deleted for lack of memory : 0
% 32.58/5.65 % Backward-subsumed : 123
% 32.58/5.65 % Backward-rewritten : 411
% 32.58/5.65 % Generated clauses : 69869
% 32.58/5.65 % ...of the previous two non-redundant : 60807
% 32.58/5.65 % ...aggressively subsumed : 0
% 32.58/5.65 % Contextual simplify-reflections : 75
% 32.58/5.65 % Paramodulations : 69172
% 32.58/5.65 % Factorizations : 12
% 32.58/5.65 % NegExts : 0
% 32.58/5.65 % Equation resolutions : 692
% 32.58/5.65 % Disequality decompositions : 0
% 32.58/5.65 % Total rewrite steps : 32311
% 32.58/5.65 % ...of those cached : 29791
% 32.58/5.65 % Propositional unsat checks : 1
% 32.58/5.65 % Propositional check models : 0
% 32.58/5.65 % Propositional check unsatisfiable : 0
% 32.58/5.65 % Propositional clauses : 0
% 32.58/5.65 % Propositional clauses after purity: 0
% 32.58/5.65 % Propositional unsat core size : 0
% 32.58/5.65 % Propositional preprocessing time : 0.000
% 32.58/5.65 % Propositional encoding time : 0.149
% 32.58/5.65 % Propositional solver time : 0.163
% 32.58/5.65 % Success case prop preproc time : 0.000
% 32.58/5.65 % Success case prop encoding time : 0.000
% 32.58/5.65 % Success case prop solver time : 0.000
% 32.58/5.65 % Current number of processed clauses : 2957
% 32.58/5.65 % Positive orientable unit clauses : 370
% 32.58/5.65 % Positive unorientable unit clauses: 4
% 32.58/5.65 % Negative unit clauses : 470
% 32.58/5.65 % Non-unit-clauses : 2113
% 32.58/5.65 % Current number of unprocessed clauses: 48218
% 32.58/5.65 % ...number of literals in the above : 194013
% 32.58/5.65 % Current number of archived formulas : 0
% 32.58/5.65 % Current number of archived clauses : 2165
% 32.58/5.65 % Clause-clause subsumption calls (NU) : 2066194
% 32.58/5.65 % Rec. Clause-clause subsumption calls : 779919
% 32.58/5.65 % Non-unit clause-clause subsumptions : 4082
% 32.58/5.65 % Unit Clause-clause subsumption calls : 191893
% 32.58/5.65 % Rewrite failures with RHS unbound : 22
% 32.58/5.65 % BW rewrite match attempts : 344
% 32.58/5.65 % BW rewrite match successes : 248
% 32.58/5.65 % Condensation attempts : 0
% 32.58/5.65 % Condensation successes : 0
% 32.58/5.65 % Termbank termtop insertions : 1395033
% 32.58/5.65 % Search garbage collected termcells : 61136
% 32.58/5.65
% 32.58/5.65 % -------------------------------------------------
% 32.58/5.65 % User time : 4.490 s
% 32.58/5.65 % System time : 0.147 s
% 32.58/5.65 % Total time : 4.637 s
% 32.58/5.65 % Maximum resident set size: 16324 pages
% 32.58/5.65
% 32.58/5.65 % -------------------------------------------------
% 32.58/5.65 % User time : 13.359 s
% 32.58/5.65 % System time : 0.438 s
% 32.58/5.65 % Total time : 13.797 s
% 32.58/5.65 % Maximum resident set size: 10496 pages
% 32.58/5.65 % E exiting
%------------------------------------------------------------------------------