%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU406+3 : 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 : 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 02:25:00 PM UTC 2026
% Result : Theorem 10.51s 8.02s
% Output : CNFRefutation 10.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 126 ( 20 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 159 ( 66 ~; 52 |; 35 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( ~ r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d4_xboole_0) ).
fof(t1_latsum_1,conjecture,
! [X1,X2,X3,X4] :
~ ( ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& r2_hidden(X2,k2_xboole_0(X3,X4))
& r2_hidden(X1,k2_xboole_0(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k2_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X2)
| r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d2_xboole_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k2_xboole_0) ).
fof(c_0_4,plain,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( ~ r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& r2_hidden(X2,k2_xboole_0(X3,X4))
& r2_hidden(X1,k2_xboole_0(X3,X4)) ),
inference(assume_negation,[status(cth)],[t1_latsum_1]) ).
fof(c_0_6,plain,
! [X71,X72,X73,X74,X75,X76,X77,X78] :
( ( X78 = k4_xboole_0(X76,X77)
| r2_hidden(esk10_3(X76,X77,X78),X78)
| ~ r2_hidden(esk10_3(X76,X77,X78),X77) )
& ( X78 = k4_xboole_0(X76,X77)
| r2_hidden(esk10_3(X76,X77,X78),X78)
| r2_hidden(esk10_3(X76,X77,X78),X76) )
& ( X78 = k4_xboole_0(X76,X77)
| r2_hidden(esk10_3(X76,X77,X78),X77)
| ~ r2_hidden(esk10_3(X76,X77,X78),X76)
| ~ r2_hidden(esk10_3(X76,X77,X78),X78) )
& ( X73 != k4_xboole_0(X71,X72)
| r2_hidden(X75,X73)
| r2_hidden(X75,X72)
| ~ r2_hidden(X75,X71) )
& ( X73 != k4_xboole_0(X71,X72)
| ~ r2_hidden(X74,X73)
| ~ r2_hidden(X74,X72) )
& ( X73 != k4_xboole_0(X71,X72)
| ~ r2_hidden(X74,X73)
| r2_hidden(X74,X71) ) ),
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_4])])])])])])]) ).
fof(c_0_7,plain,
! [X262,X263,X264,X265,X266,X267,X268,X269] :
( ( X269 = k2_xboole_0(X267,X268)
| r2_hidden(esk13_3(X267,X268,X269),X268)
| r2_hidden(esk13_3(X267,X268,X269),X267)
| r2_hidden(esk13_3(X267,X268,X269),X269) )
& ( X269 = k2_xboole_0(X267,X268)
| ~ r2_hidden(esk13_3(X267,X268,X269),X269)
| ~ r2_hidden(esk13_3(X267,X268,X269),X268) )
& ( X269 = k2_xboole_0(X267,X268)
| ~ r2_hidden(esk13_3(X267,X268,X269),X269)
| ~ r2_hidden(esk13_3(X267,X268,X269),X267) )
& ( X264 != k2_xboole_0(X262,X263)
| r2_hidden(X266,X264)
| ~ r2_hidden(X266,X263) )
& ( X264 != k2_xboole_0(X262,X263)
| r2_hidden(X266,X264)
| ~ r2_hidden(X266,X262) )
& ( X264 != k2_xboole_0(X262,X263)
| r2_hidden(X265,X263)
| r2_hidden(X265,X262)
| ~ r2_hidden(X265,X264) ) ),
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)],[d2_xboole_0])])])])])])]) ).
fof(c_0_8,negated_conjecture,
( ( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,esk4_0) )
& ( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) )
& ( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0) )
& ( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) )
& r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0))
& r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_9,plain,
! [X274,X275] : k2_xboole_0(X274,X275) = k2_xboole_0(X275,X274),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_10,plain,
( X4 != k4_xboole_0(X2,X3)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4)
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( X2 != k2_xboole_0(X3,X4)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4)
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( ~ r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| r2_hidden(X1,k4_xboole_0(X2,X3)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( ~ r2_hidden(X1,k2_xboole_0(X3,X2))
| r2_hidden(X1,X3)
| r2_hidden(X1,X2) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,negated_conjecture,
( ~ r2_hidden(esk2_0,esk3_0)
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( r2_hidden(esk2_0,esk4_0)
| r2_hidden(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( ~ r2_hidden(esk2_0,esk3_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_20]) ).
cnf(c_0_25,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_26,negated_conjecture,
~ r2_hidden(esk1_0,esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_16]) ).
cnf(c_0_27,negated_conjecture,
( ~ r2_hidden(esk1_0,esk3_0)
| ~ r2_hidden(esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_15]),c_0_22]) ).
cnf(c_0_28,negated_conjecture,
r2_hidden(esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_25]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( ~ r2_hidden(esk1_0,esk3_0)
| ~ r2_hidden(esk2_0,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_15]),c_0_16]) ).
cnf(c_0_30,negated_conjecture,
~ r2_hidden(esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
~ r2_hidden(esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_23,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU406+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.59 % Computer : n018.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Mon Sep 21 06:23:11 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.62 Running first-order theorem proving
% 0.16/5.62 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
% 10.51/8.02 % Version: 3.5.1
% 10.51/8.02 % Preprocessing class: FMLLSMLLSSSNFFN.
% 10.51/8.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.51/8.02 % Starting new_bool_3 with 900s (3) cores
% 10.51/8.02 % Starting new_bool_1 with 900s (3) cores
% 10.51/8.02 % Starting sh5l with 300s (1) cores
% 10.51/8.02 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 10.51/8.02 % new_bool_3 with pid 1161938 completed with status 0
% 10.51/8.02 % Result found by new_bool_3
% 10.51/8.02 % Preprocessing class: FMLLSMLLSSSNFFN.
% 10.51/8.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.51/8.02 % Starting new_bool_3 with 900s (3) cores
% 10.51/8.02 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 10.51/8.02 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 10.51/8.02 % Search class: FGHSM-SMLM32-MFFFFFNN
% 10.51/8.02 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 10.51/8.02 % Starting SubtermCWHack with 82s (1) cores
% 10.51/8.02 % Starting new_bool_3 with 91s (1) cores
% 10.51/8.02 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 10.51/8.02 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 1161945 completed with status 0
% 10.51/8.02 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 10.51/8.02 % Preprocessing class: FMLLSMLLSSSNFFN.
% 10.51/8.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.51/8.02 % Starting new_bool_3 with 900s (3) cores
% 10.51/8.02 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 10.51/8.02 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 10.51/8.02 % Search class: FGHSM-SMLM32-MFFFFFNN
% 10.51/8.02 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 10.51/8.02 % Starting SubtermCWHack with 82s (1) cores
% 10.51/8.02 % Starting new_bool_3 with 91s (1) cores
% 10.51/8.02 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 10.51/8.02 % Preprocessing time : 0.062 s
% 10.51/8.02 % Presaturation interreduction done
% 10.51/8.02
% 10.51/8.02 % Proof found!
% 10.51/8.02 % SZS status Theorem
% 10.51/8.02 % SZS output start CNFRefutation
% See solution above
% 10.51/8.02 % Parsed axioms : 19023
% 10.51/8.02 % Removed by relevancy pruning/SinE : 18156
% 10.51/8.02 % Initial clauses : 1716
% 10.51/8.02 % Removed in clause preprocessing : 33
% 10.51/8.02 % Initial clauses in saturation : 1683
% 10.51/8.02 % Processed clauses : 7790
% 10.51/8.02 % ...of these trivial : 75
% 10.51/8.02 % ...subsumed : 4393
% 10.51/8.02 % ...remaining for further processing : 3321
% 10.51/8.02 % Other redundant clauses eliminated : 330
% 10.51/8.02 % Clauses deleted for lack of memory : 0
% 10.51/8.02 % Backward-subsumed : 78
% 10.51/8.02 % Backward-rewritten : 50
% 10.51/8.02 % Generated clauses : 19714
% 10.51/8.02 % ...of the previous two non-redundant : 17158
% 10.51/8.02 % ...aggressively subsumed : 0
% 10.51/8.02 % Contextual simplify-reflections : 96
% 10.51/8.02 % Paramodulations : 19383
% 10.51/8.02 % Factorizations : 1
% 10.51/8.02 % NegExts : 0
% 10.51/8.02 % Equation resolutions : 336
% 10.51/8.02 % Disequality decompositions : 0
% 10.51/8.02 % Total rewrite steps : 4820
% 10.51/8.02 % ...of those cached : 3800
% 10.51/8.02 % Propositional unsat checks : 0
% 10.51/8.02 % Propositional check models : 0
% 10.51/8.02 % Propositional check unsatisfiable : 0
% 10.51/8.02 % Propositional clauses : 0
% 10.51/8.02 % Propositional clauses after purity: 0
% 10.51/8.02 % Propositional unsat core size : 0
% 10.51/8.02 % Propositional preprocessing time : 0.000
% 10.51/8.02 % Propositional encoding time : 0.000
% 10.51/8.02 % Propositional solver time : 0.000
% 10.51/8.02 % Success case prop preproc time : 0.000
% 10.51/8.02 % Success case prop encoding time : 0.000
% 10.51/8.02 % Success case prop solver time : 0.000
% 10.51/8.02 % Current number of processed clauses : 1518
% 10.51/8.02 % Positive orientable unit clauses : 297
% 10.51/8.02 % Positive unorientable unit clauses: 3
% 10.51/8.02 % Negative unit clauses : 328
% 10.51/8.02 % Non-unit-clauses : 890
% 10.51/8.02 % Current number of unprocessed clauses: 12514
% 10.51/8.02 % ...number of literals in the above : 34322
% 10.51/8.02 % Current number of archived formulas : 0
% 10.51/8.02 % Current number of archived clauses : 1657
% 10.51/8.02 % Clause-clause subsumption calls (NU) : 1238903
% 10.51/8.02 % Rec. Clause-clause subsumption calls : 302334
% 10.51/8.02 % Non-unit clause-clause subsumptions : 1387
% 10.51/8.02 % Unit Clause-clause subsumption calls : 37854
% 10.51/8.02 % Rewrite failures with RHS unbound : 0
% 10.51/8.02 % BW rewrite match attempts : 267
% 10.51/8.02 % BW rewrite match successes : 171
% 10.51/8.02 % Condensation attempts : 0
% 10.51/8.02 % Condensation successes : 0
% 10.51/8.02 % Termbank termtop insertions : 858821
% 10.51/8.02 % Search garbage collected termcells : 204799
% 10.51/8.02
% 10.51/8.02 % -------------------------------------------------
% 10.51/8.02 % User time : 1.291 s
% 10.51/8.02 % System time : 0.117 s
% 10.51/8.02 % Total time : 1.408 s
% 10.51/8.02 % Maximum resident set size: 40972 pages
% 10.51/8.02
% 10.51/8.02 % -------------------------------------------------
% 10.51/8.02 % User time : 4.262 s
% 10.51/8.02 % System time : 0.308 s
% 10.51/8.02 % Total time : 4.570 s
% 10.51/8.02 % Maximum resident set size: 32768 pages
% 10.51/8.02 % E exiting
%------------------------------------------------------------------------------