%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET908+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 02:15:44 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 70 ( 34 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 80 ( 34 ~; 31 |; 9 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 55 ( 5 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t49_zfmisc_1,conjecture,
! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
inference(assume_negation,[status(cth)],[t49_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_8,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ( X20 = set_union2(X18,X19)
| in(esk4_3(X18,X19,X20),X19)
| in(esk4_3(X18,X19,X20),X18)
| in(esk4_3(X18,X19,X20),X20) )
& ( X20 = set_union2(X18,X19)
| ~ in(esk4_3(X18,X19,X20),X20)
| ~ in(esk4_3(X18,X19,X20),X19) )
& ( X20 = set_union2(X18,X19)
| ~ in(esk4_3(X18,X19,X20),X20)
| ~ in(esk4_3(X18,X19,X20),X18) )
& ( X15 != set_union2(X13,X14)
| in(X17,X15)
| ~ in(X17,X14) )
& ( X15 != set_union2(X13,X14)
| in(X17,X15)
| ~ in(X17,X13) )
& ( X15 != set_union2(X13,X14)
| in(X16,X14)
| in(X16,X13)
| ~ in(X16,X15) ) ),
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_9,negated_conjecture,
set_union2(singleton(esk1_0),esk2_0) = empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X11,X12] : set_union2(X11,X12) = set_union2(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_11,plain,
! [X7,X8,X9] :
( ( X9 = empty_set
| in(esk3_1(X9),X9) )
& ( ~ in(X8,X7)
| X7 != empty_set ) ),
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_7])])])])])]) ).
cnf(c_0_12,plain,
( X3 != set_union2(X4,X2)
| ~ in(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
set_union2(singleton(esk1_0),esk2_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X27,X28,X29,X30,X31,X32] :
( ( X32 = singleton(X31)
| esk5_2(X31,X32) = X31
| in(esk5_2(X31,X32),X32) )
& ( X32 = singleton(X31)
| esk5_2(X31,X32) != X31
| ~ in(esk5_2(X31,X32),X32) )
& ( X28 != singleton(X27)
| in(X30,X28)
| X30 != X27 )
& ( X28 != singleton(X27)
| X29 = X27
| ~ in(X29,X28) ) ),
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_tarski])])])])])])]) ).
cnf(c_0_17,plain,
( ~ in(X1,X3)
| in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
set_union2(esk2_0,singleton(esk1_0)) = empty_set,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
~ in(X1,singleton(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_20])]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_21,c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET908+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n015.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:46:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % sh5l with pid 684475 completed with status 0
% 0.14/0.43 % Result found by sh5l
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.43 % Search class: FGHSS-FFSS31-SFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % SubtermCWHack with pid 684476 completed with status 0
% 0.14/0.43 % Result found by SubtermCWHack
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.43 % Search class: FGHSS-FFSS31-SFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % Preprocessing time : 0.001 s
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Theorem
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 12
% 0.14/0.43 % Removed by relevancy pruning/SinE : 0
% 0.14/0.43 % Initial clauses : 21
% 0.14/0.43 % Removed in clause preprocessing : 0
% 0.14/0.43 % Initial clauses in saturation : 21
% 0.14/0.43 % Processed clauses : 30
% 0.14/0.43 % ...of these trivial : 0
% 0.14/0.43 % ...subsumed : 5
% 0.14/0.43 % ...remaining for further processing : 25
% 0.14/0.43 % Other redundant clauses eliminated : 5
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 0
% 0.14/0.43 % Backward-rewritten : 1
% 0.14/0.43 % Generated clauses : 29
% 0.14/0.43 % ...of the previous two non-redundant : 21
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 0
% 0.14/0.43 % Paramodulations : 25
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 5
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 10
% 0.14/0.43 % ...of those cached : 3
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 20
% 0.14/0.43 % Positive orientable unit clauses : 7
% 0.14/0.43 % Positive unorientable unit clauses: 1
% 0.14/0.43 % Negative unit clauses : 4
% 0.14/0.43 % Non-unit-clauses : 8
% 0.14/0.43 % Current number of unprocessed clauses: 11
% 0.14/0.43 % ...number of literals in the above : 30
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 1
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 11
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 11
% 0.14/0.43 % Non-unit clause-clause subsumptions : 4
% 0.14/0.43 % Unit Clause-clause subsumption calls : 3
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 8
% 0.14/0.43 % BW rewrite match successes : 8
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 1402
% 0.14/0.43 % Search garbage collected termcells : 367
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.003 s
% 0.14/0.43 % System time : 0.003 s
% 0.14/0.43 % Total time : 0.006 s
% 0.14/0.43 % Maximum resident set size: 3636 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.006 s
% 0.14/0.43 % System time : 0.006 s
% 0.14/0.43 % Total time : 0.012 s
% 0.14/0.43 % Maximum resident set size: 4608 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------