%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET920+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 : n010.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 02:15:45 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 78 ( 38 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 84 ( 30 ~; 36 |; 12 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 61 ( 6 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t63_zfmisc_1,conjecture,
! [X1,X2,X3] :
( set_intersection2(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
=> in(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_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/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,
! [X19,X20,X21,X22,X23,X24,X25,X26] :
( ( X26 = set_intersection2(X24,X25)
| in(esk5_3(X24,X25,X26),X26)
| in(esk5_3(X24,X25,X26),X25) )
& ( X26 = set_intersection2(X24,X25)
| in(esk5_3(X24,X25,X26),X26)
| in(esk5_3(X24,X25,X26),X24) )
& ( X26 = set_intersection2(X24,X25)
| ~ in(esk5_3(X24,X25,X26),X25)
| ~ in(esk5_3(X24,X25,X26),X24)
| ~ in(esk5_3(X24,X25,X26),X26) )
& ( X21 != set_intersection2(X19,X20)
| in(X23,X21)
| ~ in(X23,X20)
| ~ in(X23,X19) )
& ( X21 != set_intersection2(X19,X20)
| ~ in(X22,X21)
| in(X22,X20) )
& ( X21 != set_intersection2(X19,X20)
| ~ in(X22,X21)
| in(X22,X19) ) ),
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_6,negated_conjecture,
~ ! [X1,X2,X3] :
( set_intersection2(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
=> in(X1,X3) ),
inference(assume_negation,[status(cth)],[t63_zfmisc_1]) ).
cnf(c_0_7,plain,
( X3 != set_intersection2(X4,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X30,X31] : set_intersection2(X30,X31) = set_intersection2(X31,X30),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_9,negated_conjecture,
( ~ in(esk1_0,esk3_0)
& set_intersection2(unordered_pair(esk1_0,esk2_0),esk3_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_6])])])]) ).
fof(c_0_10,plain,
! [X10,X11,X12,X13,X14,X15,X16,X17] :
( ( X17 = unordered_pair(X15,X16)
| esk4_3(X15,X16,X17) = X16
| esk4_3(X15,X16,X17) = X15
| in(esk4_3(X15,X16,X17),X17) )
& ( X17 = unordered_pair(X15,X16)
| ~ in(esk4_3(X15,X16,X17),X17)
| esk4_3(X15,X16,X17) != X16 )
& ( X17 = unordered_pair(X15,X16)
| ~ in(esk4_3(X15,X16,X17),X17)
| esk4_3(X15,X16,X17) != X15 )
& ( X12 != unordered_pair(X10,X11)
| in(X14,X12)
| X14 != X11 )
& ( X12 != unordered_pair(X10,X11)
| in(X14,X12)
| X14 != X10 )
& ( X12 != unordered_pair(X10,X11)
| X13 = X11
| 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_tarski])])])])])])]) ).
cnf(c_0_11,plain,
( ~ in(X1,set_intersection2(X3,X2))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
set_intersection2(unordered_pair(esk1_0,esk2_0),esk3_0) = unordered_pair(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X28,X29] : unordered_pair(X28,X29) = unordered_pair(X29,X28),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_16,plain,
( ~ in(X1,set_intersection2(X2,X3))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
set_intersection2(esk3_0,unordered_pair(esk1_0,esk2_0)) = unordered_pair(esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).
cnf(c_0_19,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( ~ in(X1,unordered_pair(esk1_0,esk2_0))
| in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
~ in(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET920+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 : n010.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 05:44:11 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.44 % Version: 3.5.1
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % sh5l with pid 142849 completed with status 0
% 0.12/0.44 % Result found by sh5l
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.44 % Search class: FGHSS-FFMF32-SFFFFFNN
% 0.12/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.44 % SubtermCWHack with pid 142850 completed with status 0
% 0.12/0.44 % Result found by SubtermCWHack
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.44 % Search class: FGHSS-FFMF32-SFFFFFNN
% 0.12/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.44 % Preprocessing time : 0.001 s
% 0.12/0.44
% 0.12/0.44 % Proof found!
% 0.12/0.44 % SZS status Theorem
% 0.12/0.44 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44 % Parsed axioms : 9
% 0.12/0.44 % Removed by relevancy pruning/SinE : 2
% 0.12/0.44 % Initial clauses : 18
% 0.12/0.44 % Removed in clause preprocessing : 0
% 0.12/0.44 % Initial clauses in saturation : 18
% 0.12/0.44 % Processed clauses : 23
% 0.12/0.44 % ...of these trivial : 1
% 0.12/0.44 % ...subsumed : 5
% 0.12/0.44 % ...remaining for further processing : 17
% 0.12/0.44 % Other redundant clauses eliminated : 6
% 0.12/0.44 % Clauses deleted for lack of memory : 0
% 0.12/0.44 % Backward-subsumed : 0
% 0.12/0.44 % Backward-rewritten : 0
% 0.12/0.44 % Generated clauses : 26
% 0.12/0.44 % ...of the previous two non-redundant : 16
% 0.12/0.44 % ...aggressively subsumed : 0
% 0.12/0.44 % Contextual simplify-reflections : 0
% 0.12/0.44 % Paramodulations : 22
% 0.12/0.44 % Factorizations : 0
% 0.12/0.44 % NegExts : 0
% 0.12/0.44 % Equation resolutions : 6
% 0.12/0.44 % Disequality decompositions : 0
% 0.12/0.44 % Total rewrite steps : 7
% 0.12/0.44 % ...of those cached : 3
% 0.12/0.44 % Propositional unsat checks : 0
% 0.12/0.44 % Propositional check models : 0
% 0.12/0.44 % Propositional check unsatisfiable : 0
% 0.12/0.44 % Propositional clauses : 0
% 0.12/0.44 % Propositional clauses after purity: 0
% 0.12/0.44 % Propositional unsat core size : 0
% 0.12/0.44 % Propositional preprocessing time : 0.000
% 0.12/0.44 % Propositional encoding time : 0.000
% 0.12/0.44 % Propositional solver time : 0.000
% 0.12/0.44 % Success case prop preproc time : 0.000
% 0.12/0.44 % Success case prop encoding time : 0.000
% 0.12/0.44 % Success case prop solver time : 0.000
% 0.12/0.44 % Current number of processed clauses : 13
% 0.12/0.44 % Positive orientable unit clauses : 4
% 0.12/0.44 % Positive unorientable unit clauses: 2
% 0.12/0.44 % Negative unit clauses : 3
% 0.12/0.44 % Non-unit-clauses : 4
% 0.12/0.44 % Current number of unprocessed clauses: 11
% 0.12/0.44 % ...number of literals in the above : 34
% 0.12/0.44 % Current number of archived formulas : 0
% 0.12/0.44 % Current number of archived clauses : 0
% 0.12/0.44 % Clause-clause subsumption calls (NU) : 7
% 0.12/0.44 % Rec. Clause-clause subsumption calls : 7
% 0.12/0.44 % Non-unit clause-clause subsumptions : 1
% 0.12/0.44 % Unit Clause-clause subsumption calls : 1
% 0.12/0.44 % Rewrite failures with RHS unbound : 0
% 0.12/0.44 % BW rewrite match attempts : 3
% 0.12/0.44 % BW rewrite match successes : 2
% 0.12/0.44 % Condensation attempts : 0
% 0.12/0.44 % Condensation successes : 0
% 0.12/0.44 % Termbank termtop insertions : 1239
% 0.12/0.44 % Search garbage collected termcells : 364
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.006 s
% 0.12/0.44 % System time : 0.000 s
% 0.12/0.44 % Total time : 0.006 s
% 0.12/0.44 % Maximum resident set size: 3636 pages
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.007 s
% 0.12/0.44 % System time : 0.004 s
% 0.12/0.44 % Total time : 0.011 s
% 0.12/0.44 % Maximum resident set size: 4608 pages
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------