%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:24:31 PM UTC 2026
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 4 unt; 0 def)
% Number of atoms : 52 ( 51 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 62 ( 26 ~; 24 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 10 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_mcart_1,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_second(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).
fof(t7_mcart_1,conjecture,
! [X1,X2] :
( pair_second(ordered_pair(X1,X2)) = X2
& pair_first(ordered_pair(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(d1_mcart_1,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_first(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mcart_1) ).
fof(c_0_3,plain,
! [X9,X10,X11,X12,X13,X14,X15] :
( ( X9 != ordered_pair(X10,X11)
| X15 = pair_second(X9)
| X15 != esk4_2(X9,X15) )
& ( X9 != ordered_pair(X10,X11)
| X15 = pair_second(X9)
| X9 = ordered_pair(esk3_2(X9,X15),esk4_2(X9,X15)) )
& ( X9 != ordered_pair(X10,X11)
| X12 = X14
| X9 != ordered_pair(X13,X14)
| X12 != pair_second(X9) ) ),
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_mcart_1])])])])])])]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( pair_second(ordered_pair(X1,X2)) = X2
& pair_first(ordered_pair(X1,X2)) = X1 ),
inference(assume_negation,[status(cth)],[t7_mcart_1]) ).
cnf(c_0_5,plain,
( X2 != ordered_pair(X5,X6)
| X2 != ordered_pair(X3,X4)
| X1 != pair_second(X2)
| X1 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_6,plain,
! [X72,X73,X74,X75,X76,X77,X78] :
( ( X72 != ordered_pair(X73,X74)
| X78 = pair_first(X72)
| X78 != esk20_2(X72,X78) )
& ( X72 != ordered_pair(X73,X74)
| X78 = pair_first(X72)
| X72 = ordered_pair(esk20_2(X72,X78),esk21_2(X72,X78)) )
& ( X72 != ordered_pair(X73,X74)
| X75 = X76
| X72 != ordered_pair(X76,X77)
| X75 != pair_first(X72) ) ),
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)],[d1_mcart_1])])])])])])]) ).
fof(c_0_7,negated_conjecture,
( pair_second(ordered_pair(esk1_0,esk2_0)) != esk2_0
| pair_first(ordered_pair(esk1_0,esk2_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])])])]) ).
cnf(c_0_8,plain,
( ordered_pair(X1,X2) != ordered_pair(X4,X3)
| pair_second(ordered_pair(X1,X2)) = X3 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_5])]) ).
cnf(c_0_9,plain,
( X2 != ordered_pair(X5,X6)
| X2 != ordered_pair(X3,X4)
| X1 != pair_first(X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( pair_second(ordered_pair(esk1_0,esk2_0)) != esk2_0
| pair_first(ordered_pair(esk1_0,esk2_0)) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
pair_second(ordered_pair(X1,X2)) = X2,
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( ordered_pair(X1,X2) != ordered_pair(X3,X4)
| pair_first(ordered_pair(X1,X2)) = X3 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_13,negated_conjecture,
pair_first(ordered_pair(esk1_0,esk2_0)) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]) ).
cnf(c_0_14,plain,
pair_first(ordered_pair(X1,X2)) = X1,
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:05:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 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
% 0.19/0.51 % Version: 3.5.1
% 0.19/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.51 % Starting sh5l with 300s (1) cores
% 0.19/0.51 % new_bool_3 with pid 92654 completed with status 0
% 0.19/0.51 % Result found by new_bool_3
% 0.19/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.51 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.19/0.51 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.51 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.51 % SubtermCWHack with pid 92658 completed with status 0
% 0.19/0.51 % Result found by SubtermCWHack
% 0.19/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.51 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.19/0.51 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.51 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.51 % Preprocessing time : 0.002 s
% 0.19/0.51
% 0.19/0.51 % Proof found!
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 % SZS output start CNFRefutation
% See solution above
% 0.19/0.51 % Parsed axioms : 342
% 0.19/0.51 % Removed by relevancy pruning/SinE : 285
% 0.19/0.51 % Initial clauses : 105
% 0.19/0.51 % Removed in clause preprocessing : 2
% 0.19/0.51 % Initial clauses in saturation : 103
% 0.19/0.51 % Processed clauses : 782
% 0.19/0.51 % ...of these trivial : 4
% 0.19/0.51 % ...subsumed : 472
% 0.19/0.51 % ...remaining for further processing : 306
% 0.19/0.51 % Other redundant clauses eliminated : 31
% 0.19/0.51 % Clauses deleted for lack of memory : 0
% 0.19/0.51 % Backward-subsumed : 5
% 0.19/0.51 % Backward-rewritten : 14
% 0.19/0.51 % Generated clauses : 2940
% 0.19/0.51 % ...of the previous two non-redundant : 2364
% 0.19/0.51 % ...aggressively subsumed : 0
% 0.19/0.51 % Contextual simplify-reflections : 0
% 0.19/0.51 % Paramodulations : 2902
% 0.19/0.51 % Factorizations : 2
% 0.19/0.51 % NegExts : 0
% 0.19/0.51 % Equation resolutions : 35
% 0.19/0.51 % Disequality decompositions : 0
% 0.19/0.51 % Total rewrite steps : 875
% 0.19/0.51 % ...of those cached : 824
% 0.19/0.51 % Propositional unsat checks : 0
% 0.19/0.51 % Propositional check models : 0
% 0.19/0.51 % Propositional check unsatisfiable : 0
% 0.19/0.51 % Propositional clauses : 0
% 0.19/0.51 % Propositional clauses after purity: 0
% 0.19/0.51 % Propositional unsat core size : 0
% 0.19/0.51 % Propositional preprocessing time : 0.000
% 0.19/0.51 % Propositional encoding time : 0.000
% 0.19/0.51 % Propositional solver time : 0.000
% 0.19/0.51 % Success case prop preproc time : 0.000
% 0.19/0.51 % Success case prop encoding time : 0.000
% 0.19/0.51 % Success case prop solver time : 0.000
% 0.19/0.51 % Current number of processed clauses : 269
% 0.19/0.51 % Positive orientable unit clauses : 37
% 0.19/0.51 % Positive unorientable unit clauses: 0
% 0.19/0.51 % Negative unit clauses : 13
% 0.19/0.51 % Non-unit-clauses : 219
% 0.19/0.51 % Current number of unprocessed clauses: 1667
% 0.19/0.51 % ...number of literals in the above : 5332
% 0.19/0.51 % Current number of archived formulas : 0
% 0.19/0.51 % Current number of archived clauses : 22
% 0.19/0.51 % Clause-clause subsumption calls (NU) : 5842
% 0.19/0.51 % Rec. Clause-clause subsumption calls : 4651
% 0.19/0.51 % Non-unit clause-clause subsumptions : 337
% 0.19/0.51 % Unit Clause-clause subsumption calls : 325
% 0.19/0.51 % Rewrite failures with RHS unbound : 0
% 0.19/0.51 % BW rewrite match attempts : 88
% 0.19/0.51 % BW rewrite match successes : 10
% 0.19/0.51 % Condensation attempts : 0
% 0.19/0.51 % Condensation successes : 0
% 0.19/0.51 % Termbank termtop insertions : 40835
% 0.19/0.51 % Search garbage collected termcells : 3762
% 0.19/0.51
% 0.19/0.51 % -------------------------------------------------
% 0.19/0.51 % User time : 0.051 s
% 0.19/0.51 % System time : 0.008 s
% 0.19/0.51 % Total time : 0.059 s
% 0.19/0.51 % Maximum resident set size: 4268 pages
% 0.19/0.51
% 0.19/0.51 % -------------------------------------------------
% 0.19/0.51 % User time : 0.066 s
% 0.19/0.51 % System time : 0.016 s
% 0.19/0.51 % Total time : 0.082 s
% 0.19/0.51 % Maximum resident set size: 5120 pages
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------