%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET918+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 02:15:45 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 109 ( 58 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 129 ( 50 ~; 51 |; 22 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 3 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t59_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( X1 != X2
& in(X2,X3)
& set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).
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(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(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
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(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( X1 != X2
& in(X2,X3)
& set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1) ),
inference(assume_negation,[status(cth)],[t59_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( X1 != X2
& in(X2,X3)
& set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34] :
( ( X34 = set_intersection2(X32,X33)
| in(esk3_3(X32,X33,X34),X34)
| in(esk3_3(X32,X33,X34),X33) )
& ( X34 = set_intersection2(X32,X33)
| in(esk3_3(X32,X33,X34),X34)
| in(esk3_3(X32,X33,X34),X32) )
& ( X34 = set_intersection2(X32,X33)
| ~ in(esk3_3(X32,X33,X34),X33)
| ~ in(esk3_3(X32,X33,X34),X32)
| ~ in(esk3_3(X32,X33,X34),X34) )
& ( X29 != set_intersection2(X27,X28)
| in(X31,X29)
| ~ in(X31,X28)
| ~ in(X31,X27) )
& ( X29 != set_intersection2(X27,X28)
| ~ in(X30,X29)
| in(X30,X28) )
& ( X29 != set_intersection2(X27,X28)
| ~ in(X30,X29)
| in(X30,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)],[d3_xboole_0])])])])])])]) ).
fof(c_0_9,negated_conjecture,
( esk6_0 != esk7_0
& in(esk7_0,esk8_0)
& set_intersection2(unordered_pair(esk6_0,esk7_0),esk8_0) = singleton(esk6_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_10,plain,
! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_11,plain,
! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_12,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( X16 = singleton(X15)
| esk1_2(X15,X16) = X15
| in(esk1_2(X15,X16),X16) )
& ( X16 = singleton(X15)
| esk1_2(X15,X16) != X15
| ~ in(esk1_2(X15,X16),X16) )
& ( X12 != singleton(X11)
| in(X14,X12)
| X14 != X11 )
& ( X12 != singleton(X11)
| X13 = X11
| ~ 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)],[d1_tarski])])])])])])]) ).
cnf(c_0_13,plain,
( X4 != set_intersection2(X2,X3)
| ~ in(X1,X3)
| ~ in(X1,X2)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
set_intersection2(unordered_pair(esk6_0,esk7_0),esk8_0) = singleton(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X18,X19,X20,X21,X22,X23,X24,X25] :
( ( X25 = unordered_pair(X23,X24)
| esk2_3(X23,X24,X25) = X24
| esk2_3(X23,X24,X25) = X23
| in(esk2_3(X23,X24,X25),X25) )
& ( X25 = unordered_pair(X23,X24)
| ~ in(esk2_3(X23,X24,X25),X25)
| esk2_3(X23,X24,X25) != X24 )
& ( X25 = unordered_pair(X23,X24)
| ~ in(esk2_3(X23,X24,X25),X25)
| esk2_3(X23,X24,X25) != X23 )
& ( X20 != unordered_pair(X18,X19)
| in(X22,X20)
| X22 != X19 )
& ( X20 != unordered_pair(X18,X19)
| in(X22,X20)
| X22 != X18 )
& ( X20 != unordered_pair(X18,X19)
| X21 = X19
| X21 = X18
| ~ in(X21,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)],[d2_tarski])])])])])])]) ).
cnf(c_0_18,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
set_intersection2(esk8_0,unordered_pair(esk7_0,esk6_0)) = singleton(esk6_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_21,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(X1,esk8_0)
| ~ in(X1,unordered_pair(esk7_0,esk6_0))
| in(X1,singleton(esk6_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])]) ).
cnf(c_0_25,negated_conjecture,
( ~ in(X1,esk8_0)
| ~ in(X1,unordered_pair(esk7_0,esk6_0))
| X1 = esk6_0 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_27,negated_conjecture,
in(esk7_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
esk6_0 != esk7_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET918+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 05:46:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 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
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2554270 completed with status 0
% 0.11/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.45 % No SInE strategy applied
% 0.11/0.45 % Search class: FGHSS-FFMS32-SFFFFFNN
% 0.11/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 191s (1) cores
% 0.11/0.45 % Starting new_bool_3 with 191s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 191s (1) cores
% 0.11/0.45 % SubtermCWHack with pid 2554274 completed with status 0
% 0.11/0.45 % Result found by SubtermCWHack
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.45 % No SInE strategy applied
% 0.11/0.45 % Search class: FGHSS-FFMS32-SFFFFFNN
% 0.11/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.45 % Preprocessing time : 0.001 s
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Theorem
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 10
% 0.11/0.45 % Removed by relevancy pruning/SinE : 0
% 0.11/0.45 % Initial clauses : 25
% 0.11/0.45 % Removed in clause preprocessing : 0
% 0.11/0.45 % Initial clauses in saturation : 25
% 0.11/0.45 % Processed clauses : 56
% 0.11/0.45 % ...of these trivial : 1
% 0.11/0.45 % ...subsumed : 16
% 0.11/0.45 % ...remaining for further processing : 39
% 0.11/0.45 % Other redundant clauses eliminated : 11
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 0
% 0.11/0.45 % Backward-rewritten : 0
% 0.11/0.45 % Generated clauses : 79
% 0.11/0.45 % ...of the previous two non-redundant : 64
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 0
% 0.11/0.45 % Paramodulations : 71
% 0.11/0.45 % Factorizations : 0
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 11
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 10
% 0.11/0.45 % ...of those cached : 3
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 31
% 0.11/0.45 % Positive orientable unit clauses : 8
% 0.11/0.45 % Positive unorientable unit clauses: 2
% 0.11/0.45 % Negative unit clauses : 7
% 0.11/0.45 % Non-unit-clauses : 14
% 0.11/0.45 % Current number of unprocessed clauses: 32
% 0.11/0.45 % ...number of literals in the above : 92
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 0
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 150
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 137
% 0.11/0.45 % Non-unit clause-clause subsumptions : 11
% 0.11/0.45 % Unit Clause-clause subsumption calls : 7
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 3
% 0.11/0.45 % BW rewrite match successes : 2
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 2112
% 0.11/0.45 % Search garbage collected termcells : 481
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.006 s
% 0.11/0.45 % System time : 0.002 s
% 0.11/0.45 % Total time : 0.008 s
% 0.11/0.45 % Maximum resident set size: 3380 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.015 s
% 0.11/0.45 % System time : 0.009 s
% 0.11/0.45 % Total time : 0.023 s
% 0.11/0.45 % Maximum resident set size: 4608 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------