%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:18:50 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 107 ( 36 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 120 ( 46 ~; 52 |; 14 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 76 ( 0 sgn 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(X3,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(l50_zfmisc_1,axiom,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(t31_zfmisc_1,conjecture,
! [X1] : union(singleton(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
fof(c_0_6,plain,
! [X19,X20,X21,X22,X23,X24] :
( ( X24 = singleton(X23)
| esk5_2(X23,X24) = X23
| in(esk5_2(X23,X24),X24) )
& ( X24 = singleton(X23)
| esk5_2(X23,X24) != X23
| ~ in(esk5_2(X23,X24),X24) )
& ( X20 != singleton(X19)
| in(X22,X20)
| X22 != X19 )
& ( X20 != singleton(X19)
| X21 = X19
| ~ in(X21,X20) ) ),
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])])])])])])]) ).
fof(c_0_7,plain,
! [X6,X7,X8,X10,X11,X12,X13,X15] :
( ( X13 = union(X12)
| in(esk3_2(X12,X13),X13)
| in(esk4_2(X12,X13),X12) )
& ( X13 = union(X12)
| in(esk3_2(X12,X13),X13)
| in(esk3_2(X12,X13),esk4_2(X12,X13)) )
& ( X13 = union(X12)
| ~ in(X15,X12)
| ~ in(esk3_2(X12,X13),X15)
| ~ in(esk3_2(X12,X13),X13) )
& ( X7 != union(X6)
| in(X10,X7)
| ~ in(X11,X6)
| ~ in(X10,X11) )
& ( X7 != union(X6)
| ~ in(X8,X7)
| in(esk2_3(X6,X7,X8),X6) )
& ( X7 != union(X6)
| ~ in(X8,X7)
| in(X8,esk2_3(X6,X7,X8)) ) ),
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)],[d4_tarski])])])])])])]) ).
cnf(c_0_8,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( X2 != union(X1)
| ~ in(X3,X2)
| in(esk2_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( X3 != union(X2)
| ~ in(X1,X3)
| in(X1,esk2_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( ~ in(X2,union(X1))
| in(esk2_3(X1,union(X1),X2),X1) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( ~ in(X1,union(X2))
| in(X1,esk2_3(X2,union(X2),X1)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( ~ in(X2,union(singleton(X1)))
| esk2_3(singleton(X1),union(singleton(X1)),X2) = X1 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_15,plain,
! [X28,X29,X30,X31,X32] :
( ( subset(X31,X32)
| ~ in(esk6_2(X31,X32),X32) )
& ( subset(X31,X32)
| in(esk6_2(X31,X32),X31) )
& ( in(X30,X29)
| ~ in(X30,X28)
| ~ subset(X28,X29) ) ),
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)],[d3_tarski])])])])])])]) ).
fof(c_0_16,plain,
! [X34,X35] :
( ( X34 = X35
| ~ subset(X35,X34)
| ~ subset(X34,X35) )
& ( X34 != X35
| subset(X35,X34) )
& ( X34 != X35
| subset(X34,X35) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])]) ).
fof(c_0_17,plain,
! [X17,X18] :
( subset(X17,union(X18))
| ~ in(X17,X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l50_zfmisc_1])])]) ).
cnf(c_0_18,plain,
( ~ in(X1,union(singleton(X2)))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] : union(singleton(X1)) = X1,
inference(assume_negation,[status(cth)],[t31_zfmisc_1]) ).
cnf(c_0_21,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ in(X1,X2)
| subset(X1,union(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( ~ in(esk6_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( in(esk6_2(union(singleton(X1)),X2),X1)
| subset(union(singleton(X1)),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_26,negated_conjecture,
union(singleton(esk1_0)) != esk1_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_27,plain,
( ~ in(X2,X1)
| ~ subset(union(X1),X2)
| union(X1) = X2 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
subset(union(singleton(X1)),X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_25])]) ).
cnf(c_0_30,negated_conjecture,
union(singleton(esk1_0)) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
union(singleton(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:42:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.44 % Version: 3.5.1
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % sh5l with pid 2363859 completed with status 0
% 0.12/0.44 % Result found by sh5l
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.44 % Search class: FGHSF-FFMF31-SFFFFFNN
% 0.12/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.44 % SubtermCWHack with pid 2363860 completed with status 0
% 0.12/0.44 % Result found by SubtermCWHack
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.44 % Search class: FGHSF-FFMF31-SFFFFFNN
% 0.12/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.44 % Preprocessing time : 0.001 s
% 0.12/0.44
% 0.12/0.44 % Proof found!
% 0.12/0.44 % SZS status Theorem
% 0.12/0.44 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44 % Parsed axioms : 10
% 0.12/0.44 % Removed by relevancy pruning/SinE : 2
% 0.12/0.44 % Initial clauses : 20
% 0.12/0.44 % Removed in clause preprocessing : 0
% 0.12/0.44 % Initial clauses in saturation : 20
% 0.12/0.44 % Processed clauses : 155
% 0.12/0.44 % ...of these trivial : 0
% 0.12/0.44 % ...subsumed : 23
% 0.12/0.44 % ...remaining for further processing : 132
% 0.12/0.44 % Other redundant clauses eliminated : 11
% 0.12/0.44 % Clauses deleted for lack of memory : 0
% 0.12/0.44 % Backward-subsumed : 0
% 0.12/0.44 % Backward-rewritten : 30
% 0.12/0.44 % Generated clauses : 971
% 0.12/0.44 % ...of the previous two non-redundant : 827
% 0.12/0.44 % ...aggressively subsumed : 0
% 0.12/0.44 % Contextual simplify-reflections : 0
% 0.12/0.44 % Paramodulations : 959
% 0.12/0.44 % Factorizations : 2
% 0.12/0.44 % NegExts : 0
% 0.12/0.44 % Equation resolutions : 11
% 0.12/0.44 % Disequality decompositions : 0
% 0.12/0.44 % Total rewrite steps : 116
% 0.12/0.44 % ...of those cached : 85
% 0.12/0.44 % Propositional unsat checks : 0
% 0.12/0.44 % Propositional check models : 0
% 0.12/0.44 % Propositional check unsatisfiable : 0
% 0.12/0.44 % Propositional clauses : 0
% 0.12/0.44 % Propositional clauses after purity: 0
% 0.12/0.44 % Propositional unsat core size : 0
% 0.12/0.44 % Propositional preprocessing time : 0.000
% 0.12/0.44 % Propositional encoding time : 0.000
% 0.12/0.44 % Propositional solver time : 0.000
% 0.12/0.44 % Success case prop preproc time : 0.000
% 0.12/0.44 % Success case prop encoding time : 0.000
% 0.12/0.44 % Success case prop solver time : 0.000
% 0.12/0.44 % Current number of processed clauses : 95
% 0.12/0.44 % Positive orientable unit clauses : 36
% 0.12/0.44 % Positive unorientable unit clauses: 0
% 0.12/0.44 % Negative unit clauses : 15
% 0.12/0.44 % Non-unit-clauses : 44
% 0.12/0.44 % Current number of unprocessed clauses: 675
% 0.12/0.44 % ...number of literals in the above : 1204
% 0.12/0.44 % Current number of archived formulas : 0
% 0.12/0.44 % Current number of archived clauses : 30
% 0.12/0.44 % Clause-clause subsumption calls (NU) : 369
% 0.12/0.44 % Rec. Clause-clause subsumption calls : 326
% 0.12/0.44 % Non-unit clause-clause subsumptions : 6
% 0.12/0.44 % Unit Clause-clause subsumption calls : 131
% 0.12/0.44 % Rewrite failures with RHS unbound : 0
% 0.12/0.44 % BW rewrite match attempts : 578
% 0.12/0.44 % BW rewrite match successes : 13
% 0.12/0.44 % Condensation attempts : 0
% 0.12/0.44 % Condensation successes : 0
% 0.12/0.44 % Termbank termtop insertions : 19498
% 0.12/0.44 % Search garbage collected termcells : 438
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.019 s
% 0.12/0.44 % System time : 0.005 s
% 0.12/0.44 % Total time : 0.024 s
% 0.12/0.44 % Maximum resident set size: 3636 pages
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.021 s
% 0.12/0.44 % System time : 0.008 s
% 0.12/0.44 % Total time : 0.030 s
% 0.12/0.44 % Maximum resident set size: 4608 pages
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------