%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET914+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 : n002.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 02:15:44 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 101 ( 40 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 113 ( 44 ~; 45 |; 16 &)
% ( 7 <=>; 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 74 ( 5 sgn 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t55_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( in(X1,X3)
& disjoint(unordered_pair(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_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_7,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( in(X1,X3)
& disjoint(unordered_pair(X1,X2),X3) ),
inference(assume_negation,[status(cth)],[t55_zfmisc_1]) ).
fof(c_0_8,plain,
! [X21,X22] :
( disjoint(X22,X21)
| ~ disjoint(X21,X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])]) ).
fof(c_0_9,negated_conjecture,
( in(esk1_0,esk3_0)
& disjoint(unordered_pair(esk1_0,esk2_0),esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_11,plain,
! [X10,X11,X12,X13,X14,X15,X16,X17] :
( ( X17 = set_intersection2(X15,X16)
| in(esk4_3(X15,X16,X17),X17)
| in(esk4_3(X15,X16,X17),X16) )
& ( X17 = set_intersection2(X15,X16)
| in(esk4_3(X15,X16,X17),X17)
| in(esk4_3(X15,X16,X17),X15) )
& ( X17 = set_intersection2(X15,X16)
| ~ in(esk4_3(X15,X16,X17),X16)
| ~ in(esk4_3(X15,X16,X17),X15)
| ~ in(esk4_3(X15,X16,X17),X17) )
& ( X12 != set_intersection2(X10,X11)
| in(X14,X12)
| ~ in(X14,X11)
| ~ in(X14,X10) )
& ( X12 != set_intersection2(X10,X11)
| ~ in(X13,X12)
| in(X13,X11) )
& ( X12 != set_intersection2(X10,X11)
| ~ in(X13,X12)
| in(X13,X10) ) ),
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_xboole_0])])])])])])]) ).
fof(c_0_12,plain,
! [X19,X20] :
( ( disjoint(X19,X20)
| set_intersection2(X19,X20) != empty_set )
& ( set_intersection2(X19,X20) = empty_set
| ~ disjoint(X19,X20) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])]) ).
cnf(c_0_13,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
disjoint(unordered_pair(esk1_0,esk2_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X37,X38,X39] :
( ( X39 = empty_set
| in(esk6_1(X39),X39) )
& ( ~ in(X38,X37)
| X37 != 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_10])])])])])]) ).
fof(c_0_16,plain,
! [X25,X26,X27,X28,X29,X30,X31,X32] :
( ( X32 = unordered_pair(X30,X31)
| esk5_3(X30,X31,X32) = X31
| esk5_3(X30,X31,X32) = X30
| in(esk5_3(X30,X31,X32),X32) )
& ( X32 = unordered_pair(X30,X31)
| ~ in(esk5_3(X30,X31,X32),X32)
| esk5_3(X30,X31,X32) != X31 )
& ( X32 = unordered_pair(X30,X31)
| ~ in(esk5_3(X30,X31,X32),X32)
| esk5_3(X30,X31,X32) != X30 )
& ( X27 != unordered_pair(X25,X26)
| in(X29,X27)
| X29 != X26 )
& ( X27 != unordered_pair(X25,X26)
| in(X29,X27)
| X29 != X25 )
& ( X27 != unordered_pair(X25,X26)
| X28 = X26
| X28 = X25
| ~ in(X28,X27) ) ),
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,plain,
( X4 != set_intersection2(X2,X3)
| ~ in(X1,X3)
| ~ in(X1,X2)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
disjoint(esk3_0,unordered_pair(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X23,X24] : unordered_pair(X23,X24) = unordered_pair(X24,X23),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_23,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
set_intersection2(esk3_0,unordered_pair(esk1_0,esk2_0)) = empty_set,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])]) ).
cnf(c_0_27,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( ~ in(X1,esk3_0)
| ~ in(X1,unordered_pair(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
in(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET914+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.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 05:46:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.44 % Version: 3.5.1
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % new_bool_1 with pid 2553466 completed with status 0
% 0.11/0.44 % Result found by new_bool_1
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.44 % Search class: FGHSS-FFMS32-SFFFFFNN
% 0.11/0.44 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % SubtermCWHack with pid 2553468 completed with status 0
% 0.11/0.44 % Result found by SubtermCWHack
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.44 % Search class: FGHSS-FFMS32-SFFFFFNN
% 0.11/0.44 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % Preprocessing time : 0.001 s
% 0.11/0.44
% 0.11/0.44 % Proof found!
% 0.11/0.44 % SZS status Theorem
% 0.11/0.44 % SZS output start CNFRefutation
% See solution above
% 0.11/0.44 % Parsed axioms : 13
% 0.11/0.44 % Removed by relevancy pruning/SinE : 0
% 0.11/0.44 % Initial clauses : 26
% 0.11/0.44 % Removed in clause preprocessing : 0
% 0.11/0.44 % Initial clauses in saturation : 26
% 0.11/0.44 % Processed clauses : 68
% 0.11/0.44 % ...of these trivial : 4
% 0.11/0.44 % ...subsumed : 21
% 0.11/0.44 % ...remaining for further processing : 43
% 0.11/0.44 % Other redundant clauses eliminated : 9
% 0.11/0.44 % Clauses deleted for lack of memory : 0
% 0.11/0.44 % Backward-subsumed : 0
% 0.11/0.44 % Backward-rewritten : 0
% 0.11/0.44 % Generated clauses : 100
% 0.11/0.44 % ...of the previous two non-redundant : 75
% 0.11/0.44 % ...aggressively subsumed : 0
% 0.11/0.44 % Contextual simplify-reflections : 0
% 0.11/0.44 % Paramodulations : 93
% 0.11/0.44 % Factorizations : 0
% 0.11/0.44 % NegExts : 0
% 0.11/0.44 % Equation resolutions : 9
% 0.11/0.44 % Disequality decompositions : 0
% 0.11/0.44 % Total rewrite steps : 19
% 0.11/0.44 % ...of those cached : 10
% 0.11/0.44 % Propositional unsat checks : 0
% 0.11/0.44 % Propositional check models : 0
% 0.11/0.44 % Propositional check unsatisfiable : 0
% 0.11/0.44 % Propositional clauses : 0
% 0.11/0.44 % Propositional clauses after purity: 0
% 0.11/0.44 % Propositional unsat core size : 0
% 0.11/0.44 % Propositional preprocessing time : 0.000
% 0.11/0.44 % Propositional encoding time : 0.000
% 0.11/0.44 % Propositional solver time : 0.000
% 0.11/0.44 % Success case prop preproc time : 0.000
% 0.11/0.44 % Success case prop encoding time : 0.000
% 0.11/0.44 % Success case prop solver time : 0.000
% 0.11/0.44 % Current number of processed clauses : 36
% 0.11/0.44 % Positive orientable unit clauses : 11
% 0.11/0.44 % Positive unorientable unit clauses: 2
% 0.11/0.44 % Negative unit clauses : 5
% 0.11/0.44 % Non-unit-clauses : 18
% 0.11/0.44 % Current number of unprocessed clauses: 28
% 0.11/0.44 % ...number of literals in the above : 80
% 0.11/0.44 % Current number of archived formulas : 0
% 0.11/0.44 % Current number of archived clauses : 0
% 0.11/0.44 % Clause-clause subsumption calls (NU) : 69
% 0.11/0.44 % Rec. Clause-clause subsumption calls : 67
% 0.11/0.44 % Non-unit clause-clause subsumptions : 13
% 0.11/0.44 % Unit Clause-clause subsumption calls : 3
% 0.11/0.44 % Rewrite failures with RHS unbound : 0
% 0.11/0.44 % BW rewrite match attempts : 5
% 0.11/0.44 % BW rewrite match successes : 4
% 0.11/0.44 % Condensation attempts : 0
% 0.11/0.44 % Condensation successes : 0
% 0.11/0.44 % Termbank termtop insertions : 2204
% 0.11/0.44 % Search garbage collected termcells : 422
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.007 s
% 0.11/0.44 % System time : 0.000 s
% 0.11/0.44 % Total time : 0.007 s
% 0.11/0.44 % Maximum resident set size: 3640 pages
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.010 s
% 0.11/0.44 % System time : 0.002 s
% 0.11/0.44 % Total time : 0.013 s
% 0.11/0.44 % Maximum resident set size: 4864 pages
% 0.11/0.44 % E exiting
%------------------------------------------------------------------------------