%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET906+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 : n007.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 02:15:43 PM UTC 2026
% Result : Theorem 0.16s 0.58s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 91 ( 33 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 99 ( 35 ~; 43 |; 13 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 70 ( 5 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t47_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(set_union2(unordered_pair(X1,X2),X3),X3)
=> in(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
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(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/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(set_union2(unordered_pair(X1,X2),X3),X3)
=> in(X1,X3) ),
inference(assume_negation,[status(cth)],[t47_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
( ~ in(esk1_0,esk3_0)
& subset(set_union2(unordered_pair(esk1_0,esk2_0),esk3_0),esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_8,plain,
! [X26,X27] : set_union2(X26,X27) = set_union2(X27,X26),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_9,plain,
! [X19,X20,X21,X22,X23] :
( ( subset(X22,X23)
| ~ in(esk5_2(X22,X23),X23) )
& ( subset(X22,X23)
| in(esk5_2(X22,X23),X22) )
& ( in(X21,X20)
| ~ in(X21,X19)
| ~ subset(X19,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)],[d3_tarski])])])])])])]) ).
cnf(c_0_10,negated_conjecture,
subset(set_union2(unordered_pair(esk1_0,esk2_0),esk3_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X10,X11,X12,X13,X14,X15,X16,X17] :
( ( X17 = set_union2(X15,X16)
| in(esk4_3(X15,X16,X17),X16)
| in(esk4_3(X15,X16,X17),X15)
| in(esk4_3(X15,X16,X17),X17) )
& ( X17 = set_union2(X15,X16)
| ~ in(esk4_3(X15,X16,X17),X17)
| ~ in(esk4_3(X15,X16,X17),X16) )
& ( X17 = set_union2(X15,X16)
| ~ in(esk4_3(X15,X16,X17),X17)
| ~ in(esk4_3(X15,X16,X17),X15) )
& ( X12 != set_union2(X10,X11)
| in(X14,X12)
| ~ in(X14,X11) )
& ( X12 != set_union2(X10,X11)
| in(X14,X12)
| ~ in(X14,X10) )
& ( X12 != set_union2(X10,X11)
| in(X13,X11)
| in(X13,X10)
| ~ in(X13,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)],[d2_xboole_0])])])])])])]) ).
fof(c_0_13,plain,
! [X35,X36,X37,X38,X39,X40,X41,X42] :
( ( X42 = unordered_pair(X40,X41)
| esk6_3(X40,X41,X42) = X41
| esk6_3(X40,X41,X42) = X40
| in(esk6_3(X40,X41,X42),X42) )
& ( X42 = unordered_pair(X40,X41)
| ~ in(esk6_3(X40,X41,X42),X42)
| esk6_3(X40,X41,X42) != X41 )
& ( X42 = unordered_pair(X40,X41)
| ~ in(esk6_3(X40,X41,X42),X42)
| esk6_3(X40,X41,X42) != X40 )
& ( X37 != unordered_pair(X35,X36)
| in(X39,X37)
| X39 != X36 )
& ( X37 != unordered_pair(X35,X36)
| in(X39,X37)
| X39 != X35 )
& ( X37 != unordered_pair(X35,X36)
| X38 = X36
| X38 = X35
| ~ in(X38,X37) ) ),
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_14,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
subset(set_union2(esk3_0,unordered_pair(esk1_0,esk2_0)),esk3_0),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( X3 != set_union2(X4,X2)
| ~ in(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X33,X34] : unordered_pair(X33,X34) = unordered_pair(X34,X33),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_19,negated_conjecture,
( ~ in(X1,set_union2(esk3_0,unordered_pair(esk1_0,esk2_0)))
| in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( ~ in(X1,X3)
| in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_17])]) ).
cnf(c_0_22,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(X1,unordered_pair(esk1_0,esk2_0))
| in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
~ in(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
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
% 0.00/0.02 % Problem : SET906+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.51 % Computer : n007.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Mon Sep 21 05:41:05 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.56 Running first-order theorem proving
% 0.09/0.56 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
% 0.16/0.58 % Version: 3.5.1
% 0.16/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.58 % Starting sh5l with 300s (1) cores
% 0.16/0.58 % new_bool_3 with pid 294052 completed with status 0
% 0.16/0.58 % Result found by new_bool_3
% 0.16/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.58 % Search class: FGHSM-FFMF32-SFFFFFNN
% 0.16/0.58 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.58 % Starting SubtermCWHack with 28s (1) cores
% 0.16/0.58 % SubtermCWHack with pid 294055 completed with status 0
% 0.16/0.58 % Result found by SubtermCWHack
% 0.16/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.58 % Search class: FGHSM-FFMF32-SFFFFFNN
% 0.16/0.58 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.58 % Starting SubtermCWHack with 28s (1) cores
% 0.16/0.58 % Preprocessing time : 0.001 s
% 0.16/0.58
% 0.16/0.58 % Proof found!
% 0.16/0.58 % SZS status Theorem
% 0.16/0.58 % SZS output start CNFRefutation
% See solution above
% 0.16/0.58 % Parsed axioms : 13
% 0.16/0.58 % Removed by relevancy pruning/SinE : 0
% 0.16/0.58 % Initial clauses : 26
% 0.16/0.58 % Removed in clause preprocessing : 0
% 0.16/0.58 % Initial clauses in saturation : 26
% 0.16/0.58 % Processed clauses : 63
% 0.16/0.58 % ...of these trivial : 1
% 0.16/0.58 % ...subsumed : 29
% 0.16/0.58 % ...remaining for further processing : 33
% 0.16/0.58 % Other redundant clauses eliminated : 8
% 0.16/0.58 % Clauses deleted for lack of memory : 0
% 0.16/0.58 % Backward-subsumed : 0
% 0.16/0.58 % Backward-rewritten : 0
% 0.16/0.58 % Generated clauses : 70
% 0.16/0.58 % ...of the previous two non-redundant : 59
% 0.16/0.58 % ...aggressively subsumed : 0
% 0.16/0.58 % Contextual simplify-reflections : 0
% 0.16/0.58 % Paramodulations : 64
% 0.16/0.58 % Factorizations : 0
% 0.16/0.58 % NegExts : 0
% 0.16/0.58 % Equation resolutions : 8
% 0.16/0.58 % Disequality decompositions : 0
% 0.16/0.58 % Total rewrite steps : 8
% 0.16/0.58 % ...of those cached : 3
% 0.16/0.58 % Propositional unsat checks : 0
% 0.16/0.58 % Propositional check models : 0
% 0.16/0.58 % Propositional check unsatisfiable : 0
% 0.16/0.58 % Propositional clauses : 0
% 0.16/0.58 % Propositional clauses after purity: 0
% 0.16/0.58 % Propositional unsat core size : 0
% 0.16/0.58 % Propositional preprocessing time : 0.000
% 0.16/0.58 % Propositional encoding time : 0.000
% 0.16/0.58 % Propositional solver time : 0.000
% 0.16/0.58 % Success case prop preproc time : 0.000
% 0.16/0.58 % Success case prop encoding time : 0.000
% 0.16/0.58 % Success case prop solver time : 0.000
% 0.16/0.58 % Current number of processed clauses : 27
% 0.16/0.58 % Positive orientable unit clauses : 6
% 0.16/0.58 % Positive unorientable unit clauses: 2
% 0.16/0.58 % Negative unit clauses : 8
% 0.16/0.58 % Non-unit-clauses : 11
% 0.16/0.58 % Current number of unprocessed clauses: 20
% 0.16/0.58 % ...number of literals in the above : 46
% 0.16/0.58 % Current number of archived formulas : 0
% 0.16/0.58 % Current number of archived clauses : 0
% 0.16/0.58 % Clause-clause subsumption calls (NU) : 31
% 0.16/0.58 % Rec. Clause-clause subsumption calls : 28
% 0.16/0.58 % Non-unit clause-clause subsumptions : 5
% 0.16/0.58 % Unit Clause-clause subsumption calls : 11
% 0.16/0.58 % Rewrite failures with RHS unbound : 0
% 0.16/0.58 % BW rewrite match attempts : 7
% 0.16/0.58 % BW rewrite match successes : 6
% 0.16/0.58 % Condensation attempts : 0
% 0.16/0.58 % Condensation successes : 0
% 0.16/0.58 % Termbank termtop insertions : 1949
% 0.16/0.58 % Search garbage collected termcells : 463
% 0.16/0.58
% 0.16/0.58 % -------------------------------------------------
% 0.16/0.58 % User time : 0.006 s
% 0.16/0.58 % System time : 0.001 s
% 0.16/0.58 % Total time : 0.007 s
% 0.16/0.58 % Maximum resident set size: 3640 pages
% 0.16/0.58
% 0.16/0.58 % -------------------------------------------------
% 0.16/0.58 % User time : 0.007 s
% 0.16/0.58 % System time : 0.006 s
% 0.16/0.58 % Total time : 0.013 s
% 0.16/0.58 % Maximum resident set size: 4608 pages
% 0.16/0.58 % E exiting
%------------------------------------------------------------------------------