%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET185+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 : 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 02:13:51 PM UTC 2026
% Result : Theorem 0.23s 0.61s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 84 ( 14 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 72 ( 26 ~; 32 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 6 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subset_union,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_union) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
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(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
inference(assume_negation,[status(cth)],[prove_subset_union]) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14,X15] :
( ( subset(X14,X15)
| ~ member(esk3_2(X14,X15),X15) )
& ( subset(X14,X15)
| member(esk3_2(X14,X15),X14) )
& ( member(X13,X12)
| ~ member(X13,X11)
| ~ subset(X11,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)],[subset_defn])])])])])])]) ).
fof(c_0_7,negated_conjecture,
( union(esk1_0,esk2_0) != esk2_0
& subset(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_5])])])]) ).
fof(c_0_8,plain,
! [X6,X7,X8] :
( ( member(X8,union(X6,X7))
| ~ member(X8,X7) )
& ( member(X8,union(X6,X7))
| ~ member(X8,X6) )
& ( member(X8,X7)
| member(X8,X6)
| ~ member(X8,union(X6,X7)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
cnf(c_0_9,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( ~ member(esk3_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( member(esk3_2(esk1_0,X1),esk2_0)
| subset(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_17,plain,
! [X9,X10] : union(X9,X10) = union(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_18,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
subset(esk1_0,union(X1,esk2_0)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( member(esk3_2(union(X1,X2),X3),X1)
| member(esk3_2(union(X1,X2),X3),X2)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_22,negated_conjecture,
subset(esk1_0,union(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_23,plain,
! [X17,X18] :
( ( X17 = X18
| ~ subset(X18,X17)
| ~ subset(X17,X18) )
& ( X17 != X18
| subset(X18,X17) )
& ( X17 != X18
| subset(X17,X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_24,plain,
( member(esk3_2(union(X1,X1),X2),X1)
| subset(union(X1,X1),X2) ),
inference(ef,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,union(esk2_0,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_22]) ).
cnf(c_0_27,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
subset(union(X1,X1),X1),
inference(spm,[status(thm)],[c_0_11,c_0_24]) ).
cnf(c_0_29,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( ~ member(esk3_2(X1,union(esk2_0,X2)),esk1_0)
| subset(X1,union(esk2_0,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_26]) ).
cnf(c_0_31,plain,
union(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
( ~ member(esk3_2(X1,esk2_0),esk1_0)
| subset(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,plain,
( member(esk3_2(union(X1,X2),X1),X2)
| subset(union(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_34,negated_conjecture,
union(esk1_0,esk2_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_35,negated_conjecture,
subset(union(esk2_0,esk1_0),esk2_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
union(esk2_0,esk1_0) != esk2_0,
inference(rw,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_35]),c_0_29])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET185+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.48 % Computer : n010.cluster.edu
% 0.18/0.48 % Model : x86_64 x86_64
% 0.18/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.48 % Memory : 8046.5625MB
% 0.18/0.48 % OS : Linux 6.8.0-71-generic
% 0.18/0.48 % CPULimit : 300
% 0.18/0.48 % WCLimit : 300
% 0.18/0.48 % DateTime : Mon Sep 21 04:59:55 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.57 Running first-order theorem proving
% 0.23/0.57 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
% 0.23/0.61 % Version: 3.5.1
% 0.23/0.61 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.23/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.61 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.23/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.61 % Starting sh5l with 300s (1) cores
% 0.23/0.61 % new_bool_3 with pid 72761 completed with status 0
% 0.23/0.61 % Result found by new_bool_3
% 0.23/0.61 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.23/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.61 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.23/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.61 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.23/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.61 % SubtermCWHack with pid 72764 completed with status 0
% 0.23/0.61 % Result found by SubtermCWHack
% 0.23/0.61 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.23/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.61 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.23/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.61 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.23/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.61 % Preprocessing time : 0.002 s
% 0.23/0.61
% 0.23/0.61 % Proof found!
% 0.23/0.61 % SZS status Theorem
% 0.23/0.61 % SZS output start CNFRefutation
% See solution above
% 0.23/0.61 % Parsed axioms : 7
% 0.23/0.61 % Removed by relevancy pruning/SinE : 0
% 0.23/0.61 % Initial clauses : 17
% 0.23/0.61 % Removed in clause preprocessing : 2
% 0.23/0.61 % Initial clauses in saturation : 15
% 0.23/0.61 % Processed clauses : 81
% 0.23/0.61 % ...of these trivial : 2
% 0.23/0.61 % ...subsumed : 36
% 0.23/0.61 % ...remaining for further processing : 43
% 0.23/0.61 % Other redundant clauses eliminated : 2
% 0.23/0.61 % Clauses deleted for lack of memory : 0
% 0.23/0.61 % Backward-subsumed : 0
% 0.23/0.61 % Backward-rewritten : 3
% 0.23/0.61 % Generated clauses : 175
% 0.23/0.61 % ...of the previous two non-redundant : 142
% 0.23/0.61 % ...aggressively subsumed : 0
% 0.23/0.61 % Contextual simplify-reflections : 0
% 0.23/0.61 % Paramodulations : 161
% 0.23/0.61 % Factorizations : 12
% 0.23/0.61 % NegExts : 0
% 0.23/0.61 % Equation resolutions : 2
% 0.23/0.61 % Disequality decompositions : 0
% 0.23/0.61 % Total rewrite steps : 41
% 0.23/0.61 % ...of those cached : 26
% 0.23/0.61 % Propositional unsat checks : 0
% 0.23/0.61 % Propositional check models : 0
% 0.23/0.61 % Propositional check unsatisfiable : 0
% 0.23/0.61 % Propositional clauses : 0
% 0.23/0.61 % Propositional clauses after purity: 0
% 0.23/0.61 % Propositional unsat core size : 0
% 0.23/0.61 % Propositional preprocessing time : 0.000
% 0.23/0.61 % Propositional encoding time : 0.000
% 0.23/0.61 % Propositional solver time : 0.000
% 0.23/0.61 % Success case prop preproc time : 0.000
% 0.23/0.61 % Success case prop encoding time : 0.000
% 0.23/0.61 % Success case prop solver time : 0.000
% 0.23/0.61 % Current number of processed clauses : 38
% 0.23/0.61 % Positive orientable unit clauses : 8
% 0.23/0.61 % Positive unorientable unit clauses: 1
% 0.23/0.61 % Negative unit clauses : 1
% 0.23/0.61 % Non-unit-clauses : 28
% 0.23/0.61 % Current number of unprocessed clauses: 69
% 0.23/0.61 % ...number of literals in the above : 189
% 0.23/0.61 % Current number of archived formulas : 0
% 0.23/0.61 % Current number of archived clauses : 3
% 0.23/0.61 % Clause-clause subsumption calls (NU) : 165
% 0.23/0.61 % Rec. Clause-clause subsumption calls : 147
% 0.23/0.61 % Non-unit clause-clause subsumptions : 36
% 0.23/0.61 % Unit Clause-clause subsumption calls : 21
% 0.23/0.61 % Rewrite failures with RHS unbound : 0
% 0.23/0.61 % BW rewrite match attempts : 24
% 0.23/0.61 % BW rewrite match successes : 3
% 0.23/0.61 % Condensation attempts : 0
% 0.23/0.61 % Condensation successes : 0
% 0.23/0.61 % Termbank termtop insertions : 2748
% 0.23/0.61 % Search garbage collected termcells : 280
% 0.23/0.61
% 0.23/0.61 % -------------------------------------------------
% 0.23/0.61 % User time : 0.014 s
% 0.23/0.61 % System time : 0.002 s
% 0.23/0.61 % Total time : 0.016 s
% 0.23/0.61 % Maximum resident set size: 3632 pages
% 0.23/0.61
% 0.23/0.61 % -------------------------------------------------
% 0.23/0.61 % User time : 0.017 s
% 0.23/0.61 % System time : 0.009 s
% 0.23/0.61 % Total time : 0.025 s
% 0.23/0.61 % Maximum resident set size: 4864 pages
% 0.23/0.61 % E exiting
%------------------------------------------------------------------------------