%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET872+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 : 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 02:15:39 PM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 76 ( 36 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 82 ( 30 ~; 36 |; 10 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 60 ( 3 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t12_zfmisc_1,conjecture,
! [X1,X2] : subset(singleton(X1),unordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_zfmisc_1) ).
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(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,plain,
! [X25,X26,X27,X28,X29,X30] :
( ( X30 = singleton(X29)
| esk5_2(X29,X30) = X29
| in(esk5_2(X29,X30),X30) )
& ( X30 = singleton(X29)
| esk5_2(X29,X30) != X29
| ~ in(esk5_2(X29,X30),X30) )
& ( X26 != singleton(X25)
| in(X28,X26)
| X28 != X25 )
& ( X26 != singleton(X25)
| X27 = X25
| ~ in(X27,X26) ) ),
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_6,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X7,X8,X9,X10,X11] :
( ( subset(X10,X11)
| ~ in(esk3_2(X10,X11),X11) )
& ( subset(X10,X11)
| in(esk3_2(X10,X11),X10) )
& ( in(X9,X8)
| ~ in(X9,X7)
| ~ subset(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)],[d3_tarski])])])])])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] : subset(singleton(X1),unordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[t12_zfmisc_1]) ).
cnf(c_0_9,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| in(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X16,X17,X18,X19,X20,X21,X22,X23] :
( ( X23 = unordered_pair(X21,X22)
| esk4_3(X21,X22,X23) = X22
| esk4_3(X21,X22,X23) = X21
| in(esk4_3(X21,X22,X23),X23) )
& ( X23 = unordered_pair(X21,X22)
| ~ in(esk4_3(X21,X22,X23),X23)
| esk4_3(X21,X22,X23) != X22 )
& ( X23 = unordered_pair(X21,X22)
| ~ in(esk4_3(X21,X22,X23),X23)
| esk4_3(X21,X22,X23) != X21 )
& ( X18 != unordered_pair(X16,X17)
| in(X20,X18)
| X20 != X17 )
& ( X18 != unordered_pair(X16,X17)
| in(X20,X18)
| X20 != X16 )
& ( X18 != unordered_pair(X16,X17)
| X19 = X17
| X19 = X16
| ~ in(X19,X18) ) ),
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])])])])])])]) ).
fof(c_0_12,negated_conjecture,
~ subset(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_13,plain,
( ~ in(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( subset(singleton(X1),X2)
| esk3_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X14,X15] : unordered_pair(X14,X15) = unordered_pair(X15,X14),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_17,negated_conjecture,
~ subset(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ in(X1,X2)
| subset(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_15])]) ).
cnf(c_0_20,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
~ in(esk1_0,unordered_pair(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET872+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:42:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43 % Version: 3.5.1
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % sh5l with pid 50030 completed with status 0
% 0.10/0.43 % Result found by sh5l
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.43 % Search class: FGHSS-FFSF32-SFFFFFNN
% 0.10/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.43 % SubtermCWHack with pid 50032 completed with status 0
% 0.10/0.43 % Result found by SubtermCWHack
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.43 % Search class: FGHSS-FFSF32-SFFFFFNN
% 0.10/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.43 % Preprocessing time : 0.001 s
% 0.10/0.43
% 0.10/0.43 % Proof found!
% 0.10/0.43 % SZS status Theorem
% 0.10/0.43 % SZS output start CNFRefutation
% See solution above
% 0.10/0.43 % Parsed axioms : 9
% 0.10/0.43 % Removed by relevancy pruning/SinE : 2
% 0.10/0.43 % Initial clauses : 17
% 0.10/0.43 % Removed in clause preprocessing : 0
% 0.10/0.43 % Initial clauses in saturation : 17
% 0.10/0.43 % Processed clauses : 23
% 0.10/0.43 % ...of these trivial : 0
% 0.10/0.43 % ...subsumed : 1
% 0.10/0.43 % ...remaining for further processing : 22
% 0.10/0.43 % Other redundant clauses eliminated : 7
% 0.10/0.43 % Clauses deleted for lack of memory : 0
% 0.10/0.43 % Backward-subsumed : 0
% 0.10/0.43 % Backward-rewritten : 1
% 0.10/0.43 % Generated clauses : 24
% 0.10/0.43 % ...of the previous two non-redundant : 17
% 0.10/0.43 % ...aggressively subsumed : 0
% 0.10/0.43 % Contextual simplify-reflections : 0
% 0.10/0.43 % Paramodulations : 20
% 0.10/0.43 % Factorizations : 0
% 0.10/0.43 % NegExts : 0
% 0.10/0.43 % Equation resolutions : 7
% 0.10/0.43 % Disequality decompositions : 0
% 0.10/0.43 % Total rewrite steps : 3
% 0.10/0.43 % ...of those cached : 0
% 0.10/0.43 % Propositional unsat checks : 0
% 0.10/0.43 % Propositional check models : 0
% 0.10/0.43 % Propositional check unsatisfiable : 0
% 0.10/0.43 % Propositional clauses : 0
% 0.10/0.43 % Propositional clauses after purity: 0
% 0.10/0.43 % Propositional unsat core size : 0
% 0.10/0.43 % Propositional preprocessing time : 0.000
% 0.10/0.43 % Propositional encoding time : 0.000
% 0.10/0.43 % Propositional solver time : 0.000
% 0.10/0.43 % Success case prop preproc time : 0.000
% 0.10/0.43 % Success case prop encoding time : 0.000
% 0.10/0.43 % Success case prop solver time : 0.000
% 0.10/0.43 % Current number of processed clauses : 17
% 0.10/0.43 % Positive orientable unit clauses : 4
% 0.10/0.43 % Positive unorientable unit clauses: 1
% 0.10/0.43 % Negative unit clauses : 3
% 0.10/0.43 % Non-unit-clauses : 9
% 0.10/0.43 % Current number of unprocessed clauses: 11
% 0.10/0.43 % ...number of literals in the above : 27
% 0.10/0.43 % Current number of archived formulas : 0
% 0.10/0.43 % Current number of archived clauses : 1
% 0.10/0.43 % Clause-clause subsumption calls (NU) : 15
% 0.10/0.43 % Rec. Clause-clause subsumption calls : 12
% 0.10/0.43 % Non-unit clause-clause subsumptions : 0
% 0.10/0.43 % Unit Clause-clause subsumption calls : 1
% 0.10/0.43 % Rewrite failures with RHS unbound : 0
% 0.10/0.43 % BW rewrite match attempts : 5
% 0.10/0.43 % BW rewrite match successes : 3
% 0.10/0.43 % Condensation attempts : 0
% 0.10/0.43 % Condensation successes : 0
% 0.10/0.43 % Termbank termtop insertions : 1241
% 0.10/0.43 % Search garbage collected termcells : 378
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.003 s
% 0.10/0.43 % System time : 0.003 s
% 0.10/0.43 % Total time : 0.006 s
% 0.10/0.43 % Maximum resident set size: 3636 pages
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.005 s
% 0.10/0.43 % System time : 0.007 s
% 0.10/0.43 % Total time : 0.012 s
% 0.10/0.43 % Maximum resident set size: 4864 pages
% 0.10/0.43 % E exiting
%------------------------------------------------------------------------------