%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET887+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 02:15:41 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 13 unt; 0 def)
% Number of atoms : 136 ( 101 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 149 ( 58 ~; 60 |; 24 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 81 ( 8 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t28_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
~ ( X1 != X4
& X1 != X3
& subset(unordered_pair(X1,X2),unordered_pair(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
fof(l46_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(t8_zfmisc_1,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_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(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( X1 != X4
& X1 != X3
& subset(unordered_pair(X1,X2),unordered_pair(X3,X4)) ),
inference(assume_negation,[status(cth)],[t28_zfmisc_1]) ).
fof(c_0_7,plain,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
inference(fof_simplification,[status(thm)],[l46_zfmisc_1]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( X1 != X4
& X1 != X3
& subset(unordered_pair(X1,X2),unordered_pair(X3,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X9,X10,X11] :
( ( subset(X9,unordered_pair(X10,X11))
| X9 != unordered_pair(X10,X11) )
& ( subset(X9,unordered_pair(X10,X11))
| X9 != singleton(X11) )
& ( subset(X9,unordered_pair(X10,X11))
| X9 != singleton(X10) )
& ( subset(X9,unordered_pair(X10,X11))
| X9 != empty_set )
& ( X9 = unordered_pair(X10,X11)
| X9 = singleton(X11)
| X9 = singleton(X10)
| X9 = empty_set
| ~ subset(X9,unordered_pair(X10,X11)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_10,negated_conjecture,
( esk1_0 != esk4_0
& esk1_0 != esk3_0
& subset(unordered_pair(esk1_0,esk2_0),unordered_pair(esk3_0,esk4_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_11,plain,
! [X19,X20,X21] :
( X19 = X20
| singleton(X19) != unordered_pair(X20,X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])])]) ).
cnf(c_0_12,plain,
( ~ subset(X1,unordered_pair(X2,X3))
| X1 = unordered_pair(X2,X3)
| X1 = singleton(X3)
| X1 = singleton(X2)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
subset(unordered_pair(esk1_0,esk2_0),unordered_pair(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( singleton(X1) != unordered_pair(X2,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( unordered_pair(esk1_0,esk2_0) = empty_set
| singleton(esk3_0) = unordered_pair(esk1_0,esk2_0)
| singleton(esk4_0) = unordered_pair(esk1_0,esk2_0)
| unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
! [X28,X29,X30,X31,X32,X33,X34,X35] :
( ( X35 = unordered_pair(X33,X34)
| esk6_3(X33,X34,X35) = X34
| esk6_3(X33,X34,X35) = X33
| in(esk6_3(X33,X34,X35),X35) )
& ( X35 = unordered_pair(X33,X34)
| ~ in(esk6_3(X33,X34,X35),X35)
| esk6_3(X33,X34,X35) != X34 )
& ( X35 = unordered_pair(X33,X34)
| ~ in(esk6_3(X33,X34,X35),X35)
| esk6_3(X33,X34,X35) != X33 )
& ( X30 != unordered_pair(X28,X29)
| in(X32,X30)
| X32 != X29 )
& ( X30 != unordered_pair(X28,X29)
| in(X32,X30)
| X32 != X28 )
& ( X30 != unordered_pair(X28,X29)
| X31 = X29
| X31 = X28
| ~ in(X31,X30) ) ),
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_17,negated_conjecture,
( unordered_pair(esk1_0,esk2_0) != unordered_pair(X1,X2)
| esk4_0 = X1
| unordered_pair(esk1_0,esk2_0) = empty_set
| singleton(esk3_0) = unordered_pair(esk1_0,esk2_0)
| unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
esk1_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X13,X14] : unordered_pair(X13,X14) = unordered_pair(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_21,negated_conjecture,
( unordered_pair(esk1_0,esk2_0) = empty_set
| singleton(esk3_0) = unordered_pair(esk1_0,esk2_0)
| unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_18]) ).
cnf(c_0_22,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_19])]) ).
cnf(c_0_23,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( unordered_pair(esk1_0,esk2_0) != unordered_pair(X1,X2)
| esk3_0 = X1
| unordered_pair(esk1_0,esk2_0) = empty_set
| unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
esk1_0 != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_26,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_27,plain,
( X2 != unordered_pair(X3,X4)
| ~ in(X1,X2)
| X1 = X4
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( unordered_pair(esk1_0,esk2_0) = empty_set
| unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).
fof(c_0_30,plain,
! [X22,X23,X24] :
( ( X24 = empty_set
| in(esk5_1(X24),X24) )
& ( ~ in(X23,X22)
| X22 != 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_26])])])])])]) ).
cnf(c_0_31,plain,
( ~ in(X1,unordered_pair(X3,X2))
| X1 = X3
| X1 = X2 ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( in(esk3_0,unordered_pair(esk1_0,esk2_0))
| unordered_pair(esk1_0,esk2_0) = empty_set ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( esk2_0 = esk3_0
| unordered_pair(esk1_0,esk2_0) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_25]) ).
cnf(c_0_35,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_36,negated_conjecture,
esk2_0 = esk3_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_34]),c_0_35]) ).
cnf(c_0_37,negated_conjecture,
( unordered_pair(esk1_0,esk3_0) = empty_set
| unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_36]),c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( in(esk4_0,unordered_pair(esk1_0,esk3_0))
| unordered_pair(esk1_0,esk3_0) = empty_set ),
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( esk4_0 = esk3_0
| unordered_pair(esk1_0,esk3_0) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_38]),c_0_18]) ).
cnf(c_0_40,negated_conjecture,
esk4_0 = esk3_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_39]),c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( unordered_pair(esk1_0,esk3_0) = empty_set
| unordered_pair(esk3_0,esk3_0) = unordered_pair(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
( ~ in(X1,unordered_pair(esk1_0,esk3_0))
| X1 = esk3_0
| unordered_pair(esk1_0,esk3_0) = empty_set ),
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
unordered_pair(esk1_0,esk3_0) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_28]),c_0_25]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_43]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:46:05 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 0.15/0.45 % Version: 3.5.1
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % Starting sh5l with 300s (1) cores
% 0.15/0.45 % new_bool_1 with pid 683671 completed with status 0
% 0.15/0.45 % Result found by new_bool_1
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.45 % Search class: FGHSS-FFMS31-SFFFFFNN
% 0.15/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.45 % SubtermCWHack with pid 683674 completed with status 0
% 0.15/0.45 % Result found by SubtermCWHack
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.45 % Search class: FGHSS-FFMS31-SFFFFFNN
% 0.15/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.45 % Preprocessing time : 0.001 s
% 0.15/0.45
% 0.15/0.45 % Proof found!
% 0.15/0.45 % SZS status Theorem
% 0.15/0.45 % SZS output start CNFRefutation
% See solution above
% 0.15/0.45 % Parsed axioms : 12
% 0.15/0.45 % Removed by relevancy pruning/SinE : 0
% 0.15/0.45 % Initial clauses : 24
% 0.15/0.45 % Removed in clause preprocessing : 0
% 0.15/0.45 % Initial clauses in saturation : 24
% 0.15/0.45 % Processed clauses : 126
% 0.15/0.45 % ...of these trivial : 3
% 0.15/0.45 % ...subsumed : 55
% 0.15/0.45 % ...remaining for further processing : 68
% 0.15/0.45 % Other redundant clauses eliminated : 34
% 0.15/0.45 % Clauses deleted for lack of memory : 0
% 0.15/0.45 % Backward-subsumed : 8
% 0.15/0.45 % Backward-rewritten : 15
% 0.15/0.45 % Generated clauses : 273
% 0.15/0.45 % ...of the previous two non-redundant : 205
% 0.15/0.45 % ...aggressively subsumed : 0
% 0.15/0.45 % Contextual simplify-reflections : 0
% 0.15/0.45 % Paramodulations : 221
% 0.15/0.45 % Factorizations : 16
% 0.15/0.45 % NegExts : 0
% 0.15/0.45 % Equation resolutions : 38
% 0.15/0.45 % Disequality decompositions : 0
% 0.15/0.45 % Total rewrite steps : 72
% 0.15/0.45 % ...of those cached : 49
% 0.15/0.45 % Propositional unsat checks : 0
% 0.15/0.45 % Propositional check models : 0
% 0.15/0.45 % Propositional check unsatisfiable : 0
% 0.15/0.45 % Propositional clauses : 0
% 0.15/0.45 % Propositional clauses after purity: 0
% 0.15/0.45 % Propositional unsat core size : 0
% 0.15/0.45 % Propositional preprocessing time : 0.000
% 0.15/0.45 % Propositional encoding time : 0.000
% 0.15/0.45 % Propositional solver time : 0.000
% 0.15/0.45 % Success case prop preproc time : 0.000
% 0.15/0.45 % Success case prop encoding time : 0.000
% 0.15/0.45 % Success case prop solver time : 0.000
% 0.15/0.45 % Current number of processed clauses : 37
% 0.15/0.45 % Positive orientable unit clauses : 12
% 0.15/0.45 % Positive unorientable unit clauses: 1
% 0.15/0.45 % Negative unit clauses : 5
% 0.15/0.45 % Non-unit-clauses : 19
% 0.15/0.45 % Current number of unprocessed clauses: 76
% 0.15/0.45 % ...number of literals in the above : 334
% 0.15/0.45 % Current number of archived formulas : 0
% 0.15/0.45 % Current number of archived clauses : 23
% 0.15/0.45 % Clause-clause subsumption calls (NU) : 269
% 0.15/0.45 % Rec. Clause-clause subsumption calls : 160
% 0.15/0.45 % Non-unit clause-clause subsumptions : 41
% 0.15/0.45 % Unit Clause-clause subsumption calls : 41
% 0.15/0.45 % Rewrite failures with RHS unbound : 0
% 0.15/0.45 % BW rewrite match attempts : 5
% 0.15/0.45 % BW rewrite match successes : 3
% 0.15/0.45 % Condensation attempts : 0
% 0.15/0.45 % Condensation successes : 0
% 0.15/0.45 % Termbank termtop insertions : 3844
% 0.15/0.45 % Search garbage collected termcells : 370
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.008 s
% 0.15/0.45 % System time : 0.004 s
% 0.15/0.45 % Total time : 0.012 s
% 0.15/0.45 % Maximum resident set size: 3640 pages
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.010 s
% 0.15/0.45 % System time : 0.008 s
% 0.15/0.45 % Total time : 0.018 s
% 0.15/0.45 % Maximum resident set size: 4608 pages
% 0.15/0.45 % E exiting
%------------------------------------------------------------------------------