%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET878+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 02:15:40 PM UTC 2026
% Result : Theorem 0.27s 0.59s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 48 ( 33 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 46 ( 19 ~; 19 |; 5 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 42 ( 3 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t19_zfmisc_1,conjecture,
! [X1,X2] : set_intersection2(singleton(X1),unordered_pair(X1,X2)) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(l32_zfmisc_1,axiom,
! [X1,X2] :
( in(X1,X2)
=> set_intersection2(X2,singleton(X1)) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] : set_intersection2(singleton(X1),unordered_pair(X1,X2)) = singleton(X1),
inference(assume_negation,[status(cth)],[t19_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
set_intersection2(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)) != singleton(esk1_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_7,plain,
! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_8,plain,
! [X14,X15,X16,X17,X18,X19,X20,X21] :
( ( X21 = unordered_pair(X19,X20)
| esk3_3(X19,X20,X21) = X20
| esk3_3(X19,X20,X21) = X19
| in(esk3_3(X19,X20,X21),X21) )
& ( X21 = unordered_pair(X19,X20)
| ~ in(esk3_3(X19,X20,X21),X21)
| esk3_3(X19,X20,X21) != X20 )
& ( X21 = unordered_pair(X19,X20)
| ~ in(esk3_3(X19,X20,X21),X21)
| esk3_3(X19,X20,X21) != X19 )
& ( X16 != unordered_pair(X14,X15)
| in(X18,X16)
| X18 != X15 )
& ( X16 != unordered_pair(X14,X15)
| in(X18,X16)
| X18 != X14 )
& ( X16 != unordered_pair(X14,X15)
| X17 = X15
| X17 = X14
| ~ in(X17,X16) ) ),
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_tarski])])])])])])]) ).
cnf(c_0_9,negated_conjecture,
set_intersection2(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)) != singleton(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X7,X8] :
( set_intersection2(X8,singleton(X7)) = singleton(X7)
| ~ in(X7,X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_zfmisc_1])])]) ).
cnf(c_0_12,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X12,X13] : unordered_pair(X12,X13) = unordered_pair(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_14,negated_conjecture,
set_intersection2(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)) != singleton(esk1_0),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( ~ in(X1,X2)
| set_intersection2(X2,singleton(X1)) = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_12])]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
~ in(esk1_0,unordered_pair(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET878+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n015.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 05:45:36 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.54 Running first-order theorem proving
% 0.27/0.54 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
% 0.27/0.59 % Version: 3.5.1
% 0.27/0.59 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.59 % Starting sh5l with 300s (1) cores
% 0.27/0.59 % sh5l with pid 682436 completed with status 0
% 0.27/0.59 % Result found by sh5l
% 0.27/0.59 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.59 % Starting sh5l with 300s (1) cores
% 0.27/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.27/0.59 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.27/0.59 % Search class: FGHSS-FFSF32-SFFFFFNN
% 0.27/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.59 % SubtermCWHack with pid 682442 completed with status 0
% 0.27/0.59 % Result found by SubtermCWHack
% 0.27/0.59 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.59 % Starting sh5l with 300s (1) cores
% 0.27/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.27/0.59 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.27/0.59 % Search class: FGHSS-FFSF32-SFFFFFNN
% 0.27/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.59 % Preprocessing time : 0.002 s
% 0.27/0.59
% 0.27/0.59 % Proof found!
% 0.27/0.59 % SZS status Theorem
% 0.27/0.59 % SZS output start CNFRefutation
% See solution above
% 0.27/0.59 % Parsed axioms : 9
% 0.27/0.59 % Removed by relevancy pruning/SinE : 2
% 0.27/0.59 % Initial clauses : 12
% 0.27/0.59 % Removed in clause preprocessing : 0
% 0.27/0.59 % Initial clauses in saturation : 12
% 0.27/0.59 % Processed clauses : 14
% 0.27/0.59 % ...of these trivial : 0
% 0.27/0.59 % ...subsumed : 2
% 0.27/0.59 % ...remaining for further processing : 12
% 0.27/0.59 % Other redundant clauses eliminated : 2
% 0.27/0.59 % Clauses deleted for lack of memory : 0
% 0.27/0.59 % Backward-subsumed : 0
% 0.27/0.59 % Backward-rewritten : 1
% 0.27/0.59 % Generated clauses : 17
% 0.27/0.59 % ...of the previous two non-redundant : 12
% 0.27/0.59 % ...aggressively subsumed : 0
% 0.27/0.59 % Contextual simplify-reflections : 0
% 0.27/0.59 % Paramodulations : 16
% 0.27/0.59 % Factorizations : 0
% 0.27/0.59 % NegExts : 0
% 0.27/0.59 % Equation resolutions : 2
% 0.27/0.59 % Disequality decompositions : 0
% 0.27/0.59 % Total rewrite steps : 4
% 0.27/0.59 % ...of those cached : 1
% 0.27/0.59 % Propositional unsat checks : 0
% 0.27/0.59 % Propositional check models : 0
% 0.27/0.59 % Propositional check unsatisfiable : 0
% 0.27/0.59 % Propositional clauses : 0
% 0.27/0.59 % Propositional clauses after purity: 0
% 0.27/0.59 % Propositional unsat core size : 0
% 0.27/0.59 % Propositional preprocessing time : 0.000
% 0.27/0.59 % Propositional encoding time : 0.000
% 0.27/0.59 % Propositional solver time : 0.000
% 0.27/0.59 % Success case prop preproc time : 0.000
% 0.27/0.59 % Success case prop encoding time : 0.000
% 0.27/0.59 % Success case prop solver time : 0.000
% 0.27/0.59 % Current number of processed clauses : 10
% 0.27/0.59 % Positive orientable unit clauses : 3
% 0.27/0.59 % Positive unorientable unit clauses: 2
% 0.27/0.59 % Negative unit clauses : 2
% 0.27/0.59 % Non-unit-clauses : 3
% 0.27/0.59 % Current number of unprocessed clauses: 10
% 0.27/0.59 % ...number of literals in the above : 25
% 0.27/0.59 % Current number of archived formulas : 0
% 0.27/0.59 % Current number of archived clauses : 1
% 0.27/0.59 % Clause-clause subsumption calls (NU) : 5
% 0.27/0.59 % Rec. Clause-clause subsumption calls : 5
% 0.27/0.59 % Non-unit clause-clause subsumptions : 2
% 0.27/0.59 % Unit Clause-clause subsumption calls : 1
% 0.27/0.59 % Rewrite failures with RHS unbound : 0
% 0.27/0.59 % BW rewrite match attempts : 5
% 0.27/0.59 % BW rewrite match successes : 3
% 0.27/0.59 % Condensation attempts : 0
% 0.27/0.59 % Condensation successes : 0
% 0.27/0.59 % Termbank termtop insertions : 775
% 0.27/0.59 % Search garbage collected termcells : 201
% 0.27/0.59
% 0.27/0.59 % -------------------------------------------------
% 0.27/0.59 % User time : 0.008 s
% 0.27/0.59 % System time : 0.003 s
% 0.27/0.59 % Total time : 0.011 s
% 0.27/0.59 % Maximum resident set size: 3632 pages
% 0.27/0.59
% 0.27/0.59 % -------------------------------------------------
% 0.27/0.59 % User time : 0.010 s
% 0.27/0.59 % System time : 0.009 s
% 0.27/0.59 % Total time : 0.019 s
% 0.27/0.59 % Maximum resident set size: 4608 pages
% 0.27/0.59 % E exiting
%------------------------------------------------------------------------------