%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET956+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 : n003.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 02:15:51 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 72 ( 11 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 75 ( 30 ~; 27 |; 12 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 72 ( 2 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t109_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ( ! [X5,X6] :
( in(ordered_pair(X5,X6),X1)
=> in(ordered_pair(X5,X6),X4) )
& subset(X1,cartesian_product2(X2,X3)) )
=> subset(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t103_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
~ ( ! [X5,X6] :
~ ( X4 = ordered_pair(X5,X6)
& in(X6,X3)
& in(X5,X2) )
& in(X4,X1)
& subset(X1,cartesian_product2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_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(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(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( ! [X5,X6] :
( in(ordered_pair(X5,X6),X1)
=> in(ordered_pair(X5,X6),X4) )
& subset(X1,cartesian_product2(X2,X3)) )
=> subset(X1,X4) ),
inference(assume_negation,[status(cth)],[t109_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
! [X34,X35] :
( ~ subset(esk6_0,esk9_0)
& ( in(ordered_pair(X34,X35),esk9_0)
| ~ in(ordered_pair(X34,X35),esk6_0) )
& subset(esk6_0,cartesian_product2(esk7_0,esk8_0)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
fof(c_0_7,plain,
! [X17,X18] : ordered_pair(X17,X18) = unordered_pair(unordered_pair(X17,X18),singleton(X17)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,plain,
! [X24,X25,X26,X27] :
( ( ~ in(X27,X24)
| ~ subset(X24,cartesian_product2(X25,X26))
| X27 = ordered_pair(esk4_4(X24,X25,X26,X27),esk5_4(X24,X25,X26,X27)) )
& ( ~ in(X27,X24)
| ~ subset(X24,cartesian_product2(X25,X26))
| in(esk5_4(X24,X25,X26,X27),X26) )
& ( ~ in(X27,X24)
| ~ subset(X24,cartesian_product2(X25,X26))
| in(esk4_4(X24,X25,X26,X27),X25) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t103_zfmisc_1])])])])]) ).
cnf(c_0_9,negated_conjecture,
( ~ in(ordered_pair(X1,X2),esk6_0)
| in(ordered_pair(X1,X2),esk9_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( ~ in(X1,X2)
| ~ subset(X2,cartesian_product2(X3,X4))
| X1 = ordered_pair(esk4_4(X2,X3,X4,X1),esk5_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk6_0)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk9_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_14,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ subset(X2,cartesian_product2(X3,X4))
| ~ in(X1,X2)
| X1 = unordered_pair(unordered_pair(esk4_4(X2,X3,X4,X1),esk5_4(X2,X3,X4,X1)),singleton(esk4_4(X2,X3,X4,X1))) ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk6_0)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk9_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( ~ in(X4,X1)
| ~ subset(X1,cartesian_product2(X2,X3))
| unordered_pair(singleton(esk4_4(X1,X2,X3,X4)),unordered_pair(esk4_4(X1,X2,X3,X4),esk5_4(X1,X2,X3,X4))) = X4 ),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
fof(c_0_18,plain,
! [X11,X12,X13,X14,X15] :
( ( subset(X14,X15)
| ~ in(esk1_2(X14,X15),X15) )
& ( subset(X14,X15)
| in(esk1_2(X14,X15),X14) )
& ( in(X13,X12)
| ~ in(X13,X11)
| ~ subset(X11,X12) ) ),
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])])])])])])]) ).
cnf(c_0_19,negated_conjecture,
( ~ in(X1,X2)
| ~ in(X1,esk6_0)
| ~ subset(X2,cartesian_product2(X3,X4))
| in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
subset(esk6_0,cartesian_product2(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,plain,
( ~ in(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(X1,esk6_0)
| in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(esk1_2(X1,esk9_0),esk6_0)
| subset(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
( subset(X1,X2)
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
~ subset(esk6_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 05:46:15 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.15/0.44 % Version: 3.5.1
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3534410 completed with status 0
% 0.15/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.44 % No SInE strategy applied
% 0.15/0.44 % Search class: FGHSS-FFSF32-MFFFFFNN
% 0.15/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.44 % SubtermCWHack with pid 3534415 completed with status 0
% 0.15/0.44 % Result found by SubtermCWHack
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.44 % No SInE strategy applied
% 0.15/0.44 % Search class: FGHSS-FFSF32-MFFFFFNN
% 0.15/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.44 % Preprocessing time : 0.001 s
% 0.15/0.44
% 0.15/0.44 % Proof found!
% 0.15/0.44 % SZS status Theorem
% 0.15/0.44 % SZS output start CNFRefutation
% See solution above
% 0.15/0.44 % Parsed axioms : 10
% 0.15/0.44 % Removed by relevancy pruning/SinE : 0
% 0.15/0.44 % Initial clauses : 16
% 0.15/0.44 % Removed in clause preprocessing : 1
% 0.15/0.44 % Initial clauses in saturation : 15
% 0.15/0.44 % Processed clauses : 56
% 0.15/0.44 % ...of these trivial : 0
% 0.15/0.44 % ...subsumed : 16
% 0.15/0.44 % ...remaining for further processing : 40
% 0.15/0.44 % Other redundant clauses eliminated : 0
% 0.15/0.44 % Clauses deleted for lack of memory : 0
% 0.15/0.44 % Backward-subsumed : 6
% 0.15/0.44 % Backward-rewritten : 0
% 0.15/0.44 % Generated clauses : 75
% 0.15/0.44 % ...of the previous two non-redundant : 71
% 0.15/0.44 % ...aggressively subsumed : 0
% 0.15/0.44 % Contextual simplify-reflections : 0
% 0.15/0.44 % Paramodulations : 75
% 0.15/0.44 % Factorizations : 0
% 0.15/0.44 % NegExts : 0
% 0.15/0.44 % Equation resolutions : 0
% 0.15/0.44 % Disequality decompositions : 0
% 0.15/0.44 % Total rewrite steps : 3
% 0.15/0.44 % ...of those cached : 0
% 0.15/0.44 % Propositional unsat checks : 0
% 0.15/0.44 % Propositional check models : 0
% 0.15/0.44 % Propositional check unsatisfiable : 0
% 0.15/0.44 % Propositional clauses : 0
% 0.15/0.44 % Propositional clauses after purity: 0
% 0.15/0.44 % Propositional unsat core size : 0
% 0.15/0.44 % Propositional preprocessing time : 0.000
% 0.15/0.44 % Propositional encoding time : 0.000
% 0.15/0.44 % Propositional solver time : 0.000
% 0.15/0.44 % Success case prop preproc time : 0.000
% 0.15/0.44 % Success case prop encoding time : 0.000
% 0.15/0.44 % Success case prop solver time : 0.000
% 0.15/0.44 % Current number of processed clauses : 34
% 0.15/0.44 % Positive orientable unit clauses : 3
% 0.15/0.44 % Positive unorientable unit clauses: 1
% 0.15/0.44 % Negative unit clauses : 9
% 0.15/0.44 % Non-unit-clauses : 21
% 0.15/0.44 % Current number of unprocessed clauses: 13
% 0.15/0.44 % ...number of literals in the above : 42
% 0.15/0.44 % Current number of archived formulas : 0
% 0.15/0.44 % Current number of archived clauses : 7
% 0.15/0.44 % Clause-clause subsumption calls (NU) : 110
% 0.15/0.44 % Rec. Clause-clause subsumption calls : 92
% 0.15/0.44 % Non-unit clause-clause subsumptions : 9
% 0.15/0.44 % Unit Clause-clause subsumption calls : 42
% 0.15/0.44 % Rewrite failures with RHS unbound : 0
% 0.15/0.44 % BW rewrite match attempts : 0
% 0.15/0.44 % BW rewrite match successes : 0
% 0.15/0.44 % Condensation attempts : 0
% 0.15/0.44 % Condensation successes : 0
% 0.15/0.44 % Termbank termtop insertions : 1940
% 0.15/0.44 % Search garbage collected termcells : 240
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.006 s
% 0.15/0.44 % System time : 0.002 s
% 0.15/0.44 % Total time : 0.008 s
% 0.15/0.44 % Maximum resident set size: 3640 pages
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.018 s
% 0.15/0.44 % System time : 0.009 s
% 0.15/0.44 % Total time : 0.026 s
% 0.15/0.44 % Maximum resident set size: 4608 pages
% 0.15/0.44 % E exiting
%------------------------------------------------------------------------------