%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET891+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 : n017.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 02:15:42 PM UTC 2026
% Result : Theorem 0.15s 0.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(l52_zfmisc_1,axiom,
! [X1,X2] : union(unordered_pair(X1,X2)) = set_union2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l52_zfmisc_1) ).
fof(t41_enumset1,axiom,
! [X1,X2] : unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).
fof(t32_zfmisc_1,conjecture,
! [X1,X2] : union(unordered_pair(singleton(X1),singleton(X2))) = unordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_zfmisc_1) ).
fof(c_0_4,plain,
! [X11] : set_union2(X11,X11) = X11,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(c_0_5,plain,
! [X12,X13] : union(unordered_pair(X12,X13)) = set_union2(X12,X13),
inference(variable_rename,[status(thm)],[l52_zfmisc_1]) ).
fof(c_0_6,plain,
! [X18,X19] : unordered_pair(X18,X19) = set_union2(singleton(X18),singleton(X19)),
inference(variable_rename,[status(thm)],[t41_enumset1]) ).
cnf(c_0_7,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
union(unordered_pair(X1,X2)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2] : union(unordered_pair(singleton(X1),singleton(X2))) = unordered_pair(X1,X2),
inference(assume_negation,[status(cth)],[t32_zfmisc_1]) ).
cnf(c_0_11,plain,
union(unordered_pair(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
unordered_pair(X1,X2) = union(unordered_pair(singleton(X1),singleton(X2))),
inference(rw,[status(thm)],[c_0_9,c_0_8]) ).
fof(c_0_13,negated_conjecture,
union(unordered_pair(singleton(esk3_0),singleton(esk4_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_10])])])]) ).
cnf(c_0_14,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
union(unordered_pair(singleton(esk3_0),singleton(esk4_0))) != unordered_pair(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
union(unordered_pair(unordered_pair(X1,X1),singleton(X2))) = unordered_pair(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
union(unordered_pair(unordered_pair(esk3_0,esk3_0),unordered_pair(esk4_0,esk4_0))) != unordered_pair(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_14]),c_0_14]) ).
cnf(c_0_18,plain,
union(unordered_pair(unordered_pair(X1,X1),unordered_pair(X2,X2))) = unordered_pair(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET891+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:38:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.43 % Version: 3.5.1
% 0.15/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.43 % Starting sh5l with 300s (1) cores
% 0.15/0.43 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1546276 completed with status 0
% 0.15/0.43 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.15/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.43 % No SInE strategy applied
% 0.15/0.43 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.15/0.43 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/0.43 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.15/0.43 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.15/0.43 % SubtermCWHack with pid 1546280 completed with status 0
% 0.15/0.43 % Result found by SubtermCWHack
% 0.15/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.43 % No SInE strategy applied
% 0.15/0.43 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.15/0.43 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.43 % Preprocessing time : 0.001 s
% 0.15/0.43
% 0.15/0.43 % Proof found!
% 0.15/0.43 % SZS status Theorem
% 0.15/0.43 % SZS output start CNFRefutation
% See solution above
% 0.15/0.43 % Parsed axioms : 10
% 0.15/0.43 % Removed by relevancy pruning/SinE : 0
% 0.15/0.43 % Initial clauses : 10
% 0.15/0.43 % Removed in clause preprocessing : 1
% 0.15/0.43 % Initial clauses in saturation : 9
% 0.15/0.43 % Processed clauses : 49
% 0.15/0.43 % ...of these trivial : 2
% 0.15/0.43 % ...subsumed : 29
% 0.15/0.43 % ...remaining for further processing : 18
% 0.15/0.43 % Other redundant clauses eliminated : 0
% 0.15/0.43 % Clauses deleted for lack of memory : 0
% 0.15/0.43 % Backward-subsumed : 0
% 0.15/0.43 % Backward-rewritten : 1
% 0.15/0.43 % Generated clauses : 66
% 0.15/0.43 % ...of the previous two non-redundant : 41
% 0.15/0.43 % ...aggressively subsumed : 0
% 0.15/0.43 % Contextual simplify-reflections : 0
% 0.15/0.43 % Paramodulations : 66
% 0.15/0.43 % Factorizations : 0
% 0.15/0.43 % NegExts : 0
% 0.15/0.43 % Equation resolutions : 0
% 0.15/0.43 % Disequality decompositions : 0
% 0.15/0.43 % Total rewrite steps : 21
% 0.15/0.43 % ...of those cached : 9
% 0.15/0.43 % Propositional unsat checks : 0
% 0.15/0.43 % Propositional check models : 0
% 0.15/0.43 % Propositional check unsatisfiable : 0
% 0.15/0.43 % Propositional clauses : 0
% 0.15/0.43 % Propositional clauses after purity: 0
% 0.15/0.43 % Propositional unsat core size : 0
% 0.15/0.43 % Propositional preprocessing time : 0.000
% 0.15/0.43 % Propositional encoding time : 0.000
% 0.15/0.43 % Propositional solver time : 0.000
% 0.15/0.43 % Success case prop preproc time : 0.000
% 0.15/0.43 % Success case prop encoding time : 0.000
% 0.15/0.43 % Success case prop solver time : 0.000
% 0.15/0.43 % Current number of processed clauses : 17
% 0.15/0.43 % Positive orientable unit clauses : 7
% 0.15/0.43 % Positive unorientable unit clauses: 2
% 0.15/0.43 % Negative unit clauses : 1
% 0.15/0.43 % Non-unit-clauses : 7
% 0.15/0.43 % Current number of unprocessed clauses: 1
% 0.15/0.43 % ...number of literals in the above : 1
% 0.15/0.43 % Current number of archived formulas : 0
% 0.15/0.43 % Current number of archived clauses : 2
% 0.15/0.43 % Clause-clause subsumption calls (NU) : 28
% 0.15/0.43 % Rec. Clause-clause subsumption calls : 28
% 0.15/0.43 % Non-unit clause-clause subsumptions : 15
% 0.15/0.43 % Unit Clause-clause subsumption calls : 1
% 0.15/0.43 % Rewrite failures with RHS unbound : 0
% 0.15/0.43 % BW rewrite match attempts : 7
% 0.15/0.43 % BW rewrite match successes : 4
% 0.15/0.43 % Condensation attempts : 0
% 0.15/0.43 % Condensation successes : 0
% 0.15/0.43 % Termbank termtop insertions : 929
% 0.15/0.43 % Search garbage collected termcells : 46
% 0.15/0.43
% 0.15/0.43 % -------------------------------------------------
% 0.15/0.43 % User time : 0.006 s
% 0.15/0.43 % System time : 0.001 s
% 0.15/0.43 % Total time : 0.007 s
% 0.15/0.43 % Maximum resident set size: 3584 pages
% 0.15/0.43
% 0.15/0.43 % -------------------------------------------------
% 0.15/0.43 % User time : 0.011 s
% 0.15/0.43 % System time : 0.011 s
% 0.15/0.43 % Total time : 0.022 s
% 0.15/0.43 % Maximum resident set size: 4864 pages
% 0.15/0.43 % E exiting
%------------------------------------------------------------------------------