%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 02:13:47 PM UTC 2026
% Result : Theorem 0.14s 5.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 61 ( 20 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 57 ( 22 ~; 27 |; 5 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(prove_union_empty_set,conjecture,
! [X1] : union(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_empty_set) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_5,plain,
! [X5,X6,X7] :
( ( member(X7,union(X5,X6))
| ~ member(X7,X6) )
& ( member(X7,union(X5,X6))
| ~ member(X7,X5) )
& ( member(X7,X6)
| member(X7,X5)
| ~ member(X7,union(X5,X6)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( X15 = X16
| member(esk2_2(X15,X16),X16)
| member(esk2_2(X15,X16),X15) )
& ( X15 = X16
| ~ member(esk2_2(X15,X16),X16)
| ~ member(esk2_2(X15,X16),X15) )
& ( X11 != X12
| member(X14,X11)
| ~ member(X14,X12) )
& ( X11 != X12
| member(X13,X12)
| ~ member(X13,X11) ) ),
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)],[equal_member_defn])])])])])])]) ).
fof(c_0_7,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
cnf(c_0_8,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( X1 = X2
| member(esk2_2(X1,X2),X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X10] : ~ member(X10,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
cnf(c_0_11,plain,
( member(esk2_2(union(X1,X2),X3),X1)
| member(esk2_2(union(X1,X2),X3),X2)
| member(esk2_2(union(X1,X2),X3),X3)
| union(X1,X2) = X3 ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] : union(X1,empty_set) = X1,
inference(assume_negation,[status(cth)],[prove_union_empty_set]) ).
cnf(c_0_13,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( member(esk2_2(union(X1,X2),X2),X2)
| member(esk2_2(union(X1,X2),X2),X1)
| union(X1,X2) = X2 ),
inference(ef,[status(thm)],[c_0_11]) ).
fof(c_0_15,negated_conjecture,
union(esk1_0,empty_set) != esk1_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_16,plain,
! [X8,X9] : union(X8,X9) = union(X9,X8),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_17,plain,
( ~ member(esk2_2(X1,X2),X2)
| ~ member(esk2_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,plain,
( member(esk2_2(union(empty_set,X1),X1),X1)
| union(empty_set,X1) = X1 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
union(esk1_0,empty_set) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( ~ member(esk2_2(union(empty_set,X1),X1),union(empty_set,X1))
| union(empty_set,X1) = X1 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,negated_conjecture,
union(empty_set,esk1_0) != esk1_0,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
union(empty_set,X1) = X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_18]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n001.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 05:03:04 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.45 % Version: 3.5.1
% 0.14/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.45 % Starting sh5l with 300s (1) cores
% 0.14/5.45 % new_bool_3 with pid 2243751 completed with status 0
% 0.14/5.45 % Result found by new_bool_3
% 0.14/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.45 % Search class: FGUSF-FFSF22-SFFFFFNN
% 0.14/5.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.45 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.45 % SubtermCWHack with pid 2243754 completed with status 0
% 0.14/5.45 % Result found by SubtermCWHack
% 0.14/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.45 % Search class: FGUSF-FFSF22-SFFFFFNN
% 0.14/5.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.45 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.45 % Preprocessing time : 0.001 s
% 0.14/5.45
% 0.14/5.45 % Proof found!
% 0.14/5.45 % SZS status Theorem
% 0.14/5.45 % SZS output start CNFRefutation
% See solution above
% 0.14/5.45 % Parsed axioms : 9
% 0.14/5.45 % Removed by relevancy pruning/SinE : 4
% 0.14/5.45 % Initial clauses : 10
% 0.14/5.45 % Removed in clause preprocessing : 2
% 0.14/5.45 % Initial clauses in saturation : 8
% 0.14/5.45 % Processed clauses : 83
% 0.14/5.45 % ...of these trivial : 0
% 0.14/5.45 % ...subsumed : 48
% 0.14/5.45 % ...remaining for further processing : 35
% 0.14/5.45 % Other redundant clauses eliminated : 0
% 0.14/5.45 % Clauses deleted for lack of memory : 0
% 0.14/5.45 % Backward-subsumed : 0
% 0.14/5.45 % Backward-rewritten : 11
% 0.14/5.45 % Generated clauses : 300
% 0.14/5.45 % ...of the previous two non-redundant : 248
% 0.14/5.45 % ...aggressively subsumed : 0
% 0.14/5.45 % Contextual simplify-reflections : 2
% 0.14/5.45 % Paramodulations : 262
% 0.14/5.45 % Factorizations : 38
% 0.14/5.45 % NegExts : 0
% 0.14/5.45 % Equation resolutions : 0
% 0.14/5.45 % Disequality decompositions : 0
% 0.14/5.45 % Total rewrite steps : 62
% 0.14/5.45 % ...of those cached : 53
% 0.14/5.45 % Propositional unsat checks : 0
% 0.14/5.45 % Propositional check models : 0
% 0.14/5.45 % Propositional check unsatisfiable : 0
% 0.14/5.45 % Propositional clauses : 0
% 0.14/5.45 % Propositional clauses after purity: 0
% 0.14/5.45 % Propositional unsat core size : 0
% 0.14/5.45 % Propositional preprocessing time : 0.000
% 0.14/5.45 % Propositional encoding time : 0.000
% 0.14/5.45 % Propositional solver time : 0.000
% 0.14/5.45 % Success case prop preproc time : 0.000
% 0.14/5.45 % Success case prop encoding time : 0.000
% 0.14/5.45 % Success case prop solver time : 0.000
% 0.14/5.45 % Current number of processed clauses : 24
% 0.14/5.45 % Positive orientable unit clauses : 2
% 0.14/5.45 % Positive unorientable unit clauses: 1
% 0.14/5.45 % Negative unit clauses : 1
% 0.14/5.45 % Non-unit-clauses : 20
% 0.14/5.45 % Current number of unprocessed clauses: 168
% 0.14/5.45 % ...number of literals in the above : 589
% 0.14/5.45 % Current number of archived formulas : 0
% 0.14/5.45 % Current number of archived clauses : 11
% 0.14/5.45 % Clause-clause subsumption calls (NU) : 860
% 0.14/5.45 % Rec. Clause-clause subsumption calls : 318
% 0.14/5.45 % Non-unit clause-clause subsumptions : 47
% 0.14/5.45 % Unit Clause-clause subsumption calls : 36
% 0.14/5.45 % Rewrite failures with RHS unbound : 0
% 0.14/5.45 % BW rewrite match attempts : 14
% 0.14/5.45 % BW rewrite match successes : 6
% 0.14/5.45 % Condensation attempts : 0
% 0.14/5.45 % Condensation successes : 0
% 0.14/5.45 % Termbank termtop insertions : 4940
% 0.14/5.45 % Search garbage collected termcells : 185
% 0.14/5.45
% 0.14/5.45 % -------------------------------------------------
% 0.14/5.45 % User time : 0.007 s
% 0.14/5.45 % System time : 0.001 s
% 0.14/5.45 % Total time : 0.008 s
% 0.14/5.45 % Maximum resident set size: 3592 pages
% 0.14/5.45
% 0.14/5.45 % -------------------------------------------------
% 0.14/5.45 % User time : 0.008 s
% 0.14/5.45 % System time : 0.006 s
% 0.14/5.45 % Total time : 0.014 s
% 0.14/5.45 % Maximum resident set size: 4608 pages
% 0.14/5.45 % E exiting
%------------------------------------------------------------------------------