%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG227+1 : 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 : n013.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 11:55:41 AM UTC 2026
% Result : Theorem 0.04s 0.46s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 94 ( 28 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 116 ( 44 ~; 36 |; 14 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 43 ( 0 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fraenkel_a_2_0_closure3,axiom,
! [X1,X2,X3] :
( ( m1_pboole(X3,X2)
& ~ v1_xboole_0(X2) )
=> ( r2_hidden(X1,a_2_0_closure3(X2,X3))
<=> ? [X4] :
( k1_funct_1(X3,X4) != k1_xboole_0
& X1 = X4
& m1_subset_1(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(t8_closure3,conjecture,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,X1)
=> ( ~ r2_hidden(X3,k1_closure3(X1,X2))
=> k1_funct_1(X2,X3) = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_closure3) ).
fof(d3_closure3,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( X3 = k1_closure3(X1,X2)
<=> X3 = a_2_0_closure3(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_closure3) ).
fof(c_0_3,plain,
! [X1,X2,X3] :
( ( m1_pboole(X3,X2)
& ~ v1_xboole_0(X2) )
=> ( r2_hidden(X1,a_2_0_closure3(X2,X3))
<=> ? [X4] :
( k1_funct_1(X3,X4) != k1_xboole_0
& X1 = X4
& m1_subset_1(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_closure3]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,X1)
=> ( ~ r2_hidden(X3,k1_closure3(X1,X2))
=> k1_funct_1(X2,X3) = k1_xboole_0 ) ) ) ),
inference(assume_negation,[status(cth)],[t8_closure3]) ).
fof(c_0_5,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( X3 = k1_closure3(X1,X2)
<=> X3 = a_2_0_closure3(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d3_closure3]) ).
fof(c_0_6,plain,
! [X9,X10,X11,X13] :
( ( ~ m1_pboole(X11,X10)
| v1_xboole_0(X10)
| r2_hidden(X9,a_2_0_closure3(X10,X11))
| k1_funct_1(X11,X13) = k1_xboole_0
| X9 != X13
| ~ m1_subset_1(X13,X10) )
& ( ~ m1_pboole(X11,X10)
| v1_xboole_0(X10)
| ~ r2_hidden(X9,a_2_0_closure3(X10,X11))
| k1_funct_1(X11,esk4_3(X9,X10,X11)) != k1_xboole_0 )
& ( ~ m1_pboole(X11,X10)
| v1_xboole_0(X10)
| ~ r2_hidden(X9,a_2_0_closure3(X10,X11))
| X9 = esk4_3(X9,X10,X11) )
& ( ~ m1_pboole(X11,X10)
| v1_xboole_0(X10)
| ~ r2_hidden(X9,a_2_0_closure3(X10,X11))
| m1_subset_1(esk4_3(X9,X10,X11),X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,X1)
=> ( ~ r2_hidden(X3,k1_closure3(X1,X2))
=> k1_funct_1(X2,X3) = k1_xboole_0 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_8,plain,
! [X25,X26,X27] :
( ( v1_xboole_0(X25)
| ~ m1_pboole(X26,X25)
| X27 = k1_closure3(X25,X26)
| X27 != a_2_0_closure3(X25,X26) )
& ( v1_xboole_0(X25)
| ~ m1_pboole(X26,X25)
| X27 = a_2_0_closure3(X25,X26)
| X27 != k1_closure3(X25,X26) ) ),
inference(distribute,[status(thm)],[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_9,plain,
( ~ m1_pboole(X4,X2)
| X3 != X1
| ~ m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| r2_hidden(X3,a_2_0_closure3(X2,X4))
| k1_funct_1(X4,X1) = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
( k1_funct_1(esk2_0,esk3_0) != k1_xboole_0
& ~ r2_hidden(esk3_0,k1_closure3(esk1_0,esk2_0))
& m1_subset_1(esk3_0,esk1_0)
& m1_pboole(esk2_0,esk1_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_7])])])]) ).
cnf(c_0_11,plain,
( ~ m1_pboole(X3,X2)
| X1 != a_2_0_closure3(X2,X3)
| v1_xboole_0(X2)
| X1 = k1_closure3(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( ~ m1_pboole(X1,X3)
| ~ m1_subset_1(X2,X3)
| v1_xboole_0(X3)
| r2_hidden(X2,a_2_0_closure3(X3,X1))
| k1_funct_1(X1,X2) = k1_xboole_0 ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
m1_subset_1(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
~ v1_xboole_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
~ r2_hidden(esk3_0,k1_closure3(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| k1_closure3(X1,X2) = a_2_0_closure3(X1,X2) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
m1_pboole(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
k1_funct_1(esk2_0,esk3_0) != k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
( ~ m1_pboole(X1,esk1_0)
| r2_hidden(esk3_0,a_2_0_closure3(esk1_0,X1))
| k1_funct_1(X1,esk3_0) = k1_xboole_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ r2_hidden(esk3_0,a_2_0_closure3(esk1_0,esk2_0)),
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_14]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 13:06:21 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.43 Running first-order theorem proving
% 0.04/0.43 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
% 0.04/0.46 % Version: 3.5.1
% 0.04/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.04/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.04/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.04/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.04/0.46 % Starting sh5l with 300s (1) cores
% 0.04/0.46 % new_bool_3 with pid 827196 completed with status 0
% 0.04/0.46 % Result found by new_bool_3
% 0.04/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.04/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.04/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.04/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.04/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.04/0.46 % Search class: FGHSS-FFMM31-SFFFFFNN
% 0.04/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.04/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.04/0.46 % SubtermCWHack with pid 827200 completed with status 0
% 0.04/0.46 % Result found by SubtermCWHack
% 0.04/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.04/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.04/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.04/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.04/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.04/0.46 % Search class: FGHSS-FFMM31-SFFFFFNN
% 0.04/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.04/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.04/0.46 % Preprocessing time : 0.002 s
% 0.04/0.46
% 0.04/0.46 % Proof found!
% 0.04/0.46 % SZS status Theorem
% 0.04/0.46 % SZS output start CNFRefutation
% See solution above
% 0.04/0.46 % Parsed axioms : 29
% 0.04/0.46 % Removed by relevancy pruning/SinE : 10
% 0.04/0.46 % Initial clauses : 32
% 0.04/0.46 % Removed in clause preprocessing : 0
% 0.04/0.46 % Initial clauses in saturation : 32
% 0.04/0.46 % Processed clauses : 72
% 0.04/0.46 % ...of these trivial : 0
% 0.04/0.46 % ...subsumed : 8
% 0.04/0.46 % ...remaining for further processing : 64
% 0.04/0.46 % Other redundant clauses eliminated : 3
% 0.04/0.46 % Clauses deleted for lack of memory : 0
% 0.04/0.46 % Backward-subsumed : 0
% 0.04/0.46 % Backward-rewritten : 4
% 0.04/0.46 % Generated clauses : 74
% 0.04/0.46 % ...of the previous two non-redundant : 68
% 0.04/0.46 % ...aggressively subsumed : 0
% 0.04/0.46 % Contextual simplify-reflections : 0
% 0.04/0.46 % Paramodulations : 69
% 0.04/0.46 % Factorizations : 2
% 0.04/0.46 % NegExts : 0
% 0.04/0.46 % Equation resolutions : 3
% 0.04/0.46 % Disequality decompositions : 0
% 0.04/0.46 % Total rewrite steps : 8
% 0.04/0.46 % ...of those cached : 4
% 0.04/0.46 % Propositional unsat checks : 0
% 0.04/0.46 % Propositional check models : 0
% 0.04/0.46 % Propositional check unsatisfiable : 0
% 0.04/0.46 % Propositional clauses : 0
% 0.04/0.46 % Propositional clauses after purity: 0
% 0.04/0.46 % Propositional unsat core size : 0
% 0.04/0.46 % Propositional preprocessing time : 0.000
% 0.04/0.46 % Propositional encoding time : 0.000
% 0.04/0.46 % Propositional solver time : 0.000
% 0.04/0.46 % Success case prop preproc time : 0.000
% 0.04/0.46 % Success case prop encoding time : 0.000
% 0.04/0.46 % Success case prop solver time : 0.000
% 0.04/0.46 % Current number of processed clauses : 57
% 0.04/0.46 % Positive orientable unit clauses : 16
% 0.04/0.46 % Positive unorientable unit clauses: 0
% 0.04/0.46 % Negative unit clauses : 6
% 0.04/0.46 % Non-unit-clauses : 35
% 0.04/0.46 % Current number of unprocessed clauses: 28
% 0.04/0.46 % ...number of literals in the above : 149
% 0.04/0.46 % Current number of archived formulas : 0
% 0.04/0.46 % Current number of archived clauses : 4
% 0.04/0.46 % Clause-clause subsumption calls (NU) : 217
% 0.04/0.46 % Rec. Clause-clause subsumption calls : 151
% 0.04/0.46 % Non-unit clause-clause subsumptions : 7
% 0.04/0.46 % Unit Clause-clause subsumption calls : 19
% 0.04/0.46 % Rewrite failures with RHS unbound : 0
% 0.04/0.46 % BW rewrite match attempts : 2
% 0.04/0.46 % BW rewrite match successes : 2
% 0.04/0.46 % Condensation attempts : 0
% 0.04/0.46 % Condensation successes : 0
% 0.04/0.46 % Termbank termtop insertions : 2896
% 0.04/0.46 % Search garbage collected termcells : 423
% 0.04/0.46
% 0.04/0.46 % -------------------------------------------------
% 0.04/0.46 % User time : 0.007 s
% 0.04/0.46 % System time : 0.005 s
% 0.04/0.46 % Total time : 0.012 s
% 0.04/0.46 % Maximum resident set size: 3652 pages
% 0.04/0.46
% 0.04/0.46 % -------------------------------------------------
% 0.04/0.46 % User time : 0.008 s
% 0.04/0.46 % System time : 0.011 s
% 0.04/0.46 % Total time : 0.018 s
% 0.04/0.46 % Maximum resident set size: 4608 pages
% 0.04/0.46 % E exiting
%------------------------------------------------------------------------------