%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU418+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 02:25:04 PM UTC 2026
% Result : Theorem 9.87s 2.78s
% Output : CNFRefutation 9.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 64 ( 3 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 62 ( 25 ~; 20 |; 4 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_relset_2,conjecture,
! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> r1_tarski(k5_relat_1(k3_xboole_0(X1,X2),X3),k3_xboole_0(k5_relat_1(X1,X3),k5_relat_1(X2,X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_relset_2) ).
fof(t19_xboole_1,axiom,
! [X1,X2,X3] :
( ( r1_tarski(X1,X3)
& r1_tarski(X1,X2) )
=> r1_tarski(X1,k3_xboole_0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t19_xboole_1) ).
fof(t49_relat_1,axiom,
! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> ( r1_tarski(X1,X2)
=> r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',t49_relat_1) ).
fof(t3_relat_1,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X1,X2)
=> v1_relat_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',t3_relat_1) ).
fof(t17_xboole_1,axiom,
! [X1,X2] : r1_tarski(k3_xboole_0(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t17_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k3_xboole_0) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> r1_tarski(k5_relat_1(k3_xboole_0(X1,X2),X3),k3_xboole_0(k5_relat_1(X1,X3),k5_relat_1(X2,X3))) ) ) ),
inference(assume_negation,[status(cth)],[t8_relset_2]) ).
fof(c_0_7,negated_conjecture,
( ~ r1_tarski(k5_relat_1(k3_xboole_0(esk1_0,esk2_0),esk3_0),k3_xboole_0(k5_relat_1(esk1_0,esk3_0),k5_relat_1(esk2_0,esk3_0)))
& v1_relat_1(esk3_0)
& v1_relat_1(esk2_0)
& v1_relat_1(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_8,plain,
! [X122,X123,X124] :
( r1_tarski(X122,k3_xboole_0(X123,X124))
| ~ r1_tarski(X122,X124)
| ~ r1_tarski(X122,X123) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])])]) ).
fof(c_0_9,plain,
! [X313,X314,X315] :
( r1_tarski(k5_relat_1(X313,X315),k5_relat_1(X314,X315))
| ~ r1_tarski(X313,X314)
| ~ v1_relat_1(X315)
| ~ v1_relat_1(X314)
| ~ v1_relat_1(X313) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t49_relat_1])])])]) ).
fof(c_0_10,plain,
! [X51,X52] :
( v1_relat_1(X51)
| ~ r1_tarski(X51,X52)
| ~ v1_relat_1(X52) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_relat_1])])]) ).
fof(c_0_11,plain,
! [X117,X118] : r1_tarski(k3_xboole_0(X117,X118),X117),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(c_0_12,plain,
! [X110,X111] : k3_xboole_0(X110,X111) = k3_xboole_0(X111,X110),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_13,negated_conjecture,
~ r1_tarski(k5_relat_1(k3_xboole_0(esk1_0,esk2_0),esk3_0),k3_xboole_0(k5_relat_1(esk1_0,esk3_0),k5_relat_1(esk2_0,esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( ~ r1_tarski(X1,X3)
| ~ r1_tarski(X1,X2)
| r1_tarski(X1,k3_xboole_0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( ~ r1_tarski(X1,X2)
| ~ v1_relat_1(X3)
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ r1_tarski(X2,X1)
| ~ v1_relat_1(X1)
| v1_relat_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
r1_tarski(k3_xboole_0(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( ~ r1_tarski(k5_relat_1(k3_xboole_0(esk1_0,esk2_0),esk3_0),k5_relat_1(esk1_0,esk3_0))
| ~ r1_tarski(k5_relat_1(k3_xboole_0(esk1_0,esk2_0),esk3_0),k5_relat_1(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( ~ r1_tarski(X1,X3)
| ~ v1_relat_1(X3)
| ~ v1_relat_1(X2)
| r1_tarski(k5_relat_1(X1,X2),k5_relat_1(X3,X2)) ),
inference(csr,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
v1_relat_1(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
v1_relat_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,plain,
r1_tarski(k3_xboole_0(X1,X2),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
~ r1_tarski(k5_relat_1(k3_xboole_0(esk1_0,esk2_0),esk3_0),k5_relat_1(esk1_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_25,negated_conjecture,
v1_relat_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_20]),c_0_21]),c_0_25]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU418+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 06:25:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 9.87/2.78 % Version: 3.5.1
% 9.87/2.78 % Preprocessing class: FMLLMMLLSSSNFFN.
% 9.87/2.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.87/2.78 % Starting new_bool_3 with 900s (3) cores
% 9.87/2.78 % Starting new_bool_1 with 900s (3) cores
% 9.87/2.78 % Starting sh5l with 300s (1) cores
% 9.87/2.78 % Starting G-E--_211_C18_F1_AE_CS_SP_S0Y with 300s (1) cores
% 9.87/2.78 % new_bool_3 with pid 1884649 completed with status 0
% 9.87/2.78 % Result found by new_bool_3
% 9.87/2.78 % Preprocessing class: FMLLMMLLSSSNFFN.
% 9.87/2.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.87/2.78 % Starting new_bool_3 with 900s (3) cores
% 9.87/2.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.87/2.78 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.87/2.78 % Search class: FGHSM-SMLM32-MFFFFFNN
% 9.87/2.78 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 9.87/2.78 % Starting SubtermCWHack with 82s (1) cores
% 9.87/2.78 % Starting new_bool_3 with 91s (1) cores
% 9.87/2.78 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 9.87/2.78 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 1884813 completed with status 0
% 9.87/2.78 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 9.87/2.78 % Preprocessing class: FMLLMMLLSSSNFFN.
% 9.87/2.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.87/2.78 % Starting new_bool_3 with 900s (3) cores
% 9.87/2.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.87/2.78 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.87/2.78 % Search class: FGHSM-SMLM32-MFFFFFNN
% 9.87/2.78 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 9.87/2.78 % Starting SubtermCWHack with 82s (1) cores
% 9.87/2.78 % Starting new_bool_3 with 91s (1) cores
% 9.87/2.78 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 9.87/2.78 % Preprocessing time : 0.059 s
% 9.87/2.78 % Presaturation interreduction done
% 9.87/2.78
% 9.87/2.78 % Proof found!
% 9.87/2.78 % SZS status Theorem
% 9.87/2.78 % SZS output start CNFRefutation
% See solution above
% 9.87/2.78 % Parsed axioms : 19075
% 9.87/2.78 % Removed by relevancy pruning/SinE : 18194
% 9.87/2.78 % Initial clauses : 1749
% 9.87/2.78 % Removed in clause preprocessing : 31
% 9.87/2.78 % Initial clauses in saturation : 1718
% 9.87/2.78 % Processed clauses : 6855
% 9.87/2.78 % ...of these trivial : 68
% 9.87/2.78 % ...subsumed : 3555
% 9.87/2.78 % ...remaining for further processing : 3232
% 9.87/2.78 % Other redundant clauses eliminated : 277
% 9.87/2.78 % Clauses deleted for lack of memory : 0
% 9.87/2.78 % Backward-subsumed : 61
% 9.87/2.78 % Backward-rewritten : 53
% 9.87/2.78 % Generated clauses : 17154
% 9.87/2.78 % ...of the previous two non-redundant : 14396
% 9.87/2.78 % ...aggressively subsumed : 0
% 9.87/2.78 % Contextual simplify-reflections : 85
% 9.87/2.78 % Paramodulations : 16877
% 9.87/2.78 % Factorizations : 0
% 9.87/2.78 % NegExts : 0
% 9.87/2.78 % Equation resolutions : 284
% 9.87/2.78 % Disequality decompositions : 0
% 9.87/2.78 % Total rewrite steps : 5756
% 9.87/2.78 % ...of those cached : 4776
% 9.87/2.78 % Propositional unsat checks : 0
% 9.87/2.78 % Propositional check models : 0
% 9.87/2.78 % Propositional check unsatisfiable : 0
% 9.87/2.78 % Propositional clauses : 0
% 9.87/2.78 % Propositional clauses after purity: 0
% 9.87/2.78 % Propositional unsat core size : 0
% 9.87/2.78 % Propositional preprocessing time : 0.000
% 9.87/2.78 % Propositional encoding time : 0.000
% 9.87/2.78 % Propositional solver time : 0.000
% 9.87/2.78 % Success case prop preproc time : 0.000
% 9.87/2.78 % Success case prop encoding time : 0.000
% 9.87/2.78 % Success case prop solver time : 0.000
% 9.87/2.78 % Current number of processed clauses : 1415
% 9.87/2.78 % Positive orientable unit clauses : 345
% 9.87/2.78 % Positive unorientable unit clauses: 3
% 9.87/2.78 % Negative unit clauses : 266
% 9.87/2.78 % Non-unit-clauses : 801
% 9.87/2.78 % Current number of unprocessed clauses: 10660
% 9.87/2.78 % ...number of literals in the above : 27245
% 9.87/2.78 % Current number of archived formulas : 0
% 9.87/2.78 % Current number of archived clauses : 1667
% 9.87/2.78 % Clause-clause subsumption calls (NU) : 1319878
% 9.87/2.78 % Rec. Clause-clause subsumption calls : 334838
% 9.87/2.78 % Non-unit clause-clause subsumptions : 1542
% 9.87/2.78 % Unit Clause-clause subsumption calls : 58300
% 9.87/2.78 % Rewrite failures with RHS unbound : 12
% 9.87/2.78 % BW rewrite match attempts : 303
% 9.87/2.78 % BW rewrite match successes : 196
% 9.87/2.78 % Condensation attempts : 0
% 9.87/2.78 % Condensation successes : 0
% 9.87/2.78 % Termbank termtop insertions : 834073
% 9.87/2.78 % Search garbage collected termcells : 205477
% 9.87/2.78
% 9.87/2.78 % -------------------------------------------------
% 9.87/2.78 % User time : 1.228 s
% 9.87/2.78 % System time : 0.120 s
% 9.87/2.78 % Total time : 1.348 s
% 9.87/2.78 % Maximum resident set size: 41312 pages
% 9.87/2.78
% 9.87/2.78 % -------------------------------------------------
% 9.87/2.78 % User time : 4.139 s
% 9.87/2.78 % System time : 0.319 s
% 9.87/2.78 % Total time : 4.458 s
% 9.87/2.78 % Maximum resident set size: 32768 pages
% 9.87/2.78 % E exiting
%------------------------------------------------------------------------------