%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET596+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 : n019.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 02:14:28 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 59 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 53 ( 22 ~; 16 |; 9 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th55,conjecture,
! [X1,X2,X3] :
( ( intersection(X2,X3) = empty_set
& subset(X1,X2) )
=> intersection(X1,X3) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th55) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(intersection_of_subset,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(intersection(X1,X3),intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subset) ).
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(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( ( intersection(X2,X3) = empty_set
& subset(X1,X2) )
=> intersection(X1,X3) = empty_set ),
inference(assume_negation,[status(cth)],[prove_th55]) ).
fof(c_0_7,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_8,plain,
! [X9,X10,X11] :
( subset(intersection(X9,X11),intersection(X10,X11))
| ~ subset(X9,X10) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_of_subset])])]) ).
fof(c_0_9,negated_conjecture,
( intersection(esk1_0,esk3_0) != empty_set
& intersection(esk2_0,esk3_0) = empty_set
& 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_6])])])]) ).
fof(c_0_10,plain,
! [X8] : ~ member(X8,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_11,plain,
! [X17,X18,X19,X20,X21] :
( ( subset(X20,X21)
| ~ member(esk4_2(X20,X21),X21) )
& ( subset(X20,X21)
| member(esk4_2(X20,X21),X20) )
& ( member(X19,X18)
| ~ member(X19,X17)
| ~ subset(X17,X18) ) ),
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_12,plain,
! [X23,X24] :
( ( X23 = X24
| ~ subset(X24,X23)
| ~ subset(X23,X24) )
& ( X23 != X24
| subset(X24,X23) )
& ( X23 != X24
| subset(X23,X24) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_13,plain,
( ~ subset(X1,X2)
| subset(intersection(X1,X3),intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
intersection(esk2_0,esk3_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X15,X16] : intersection(X15,X16) = intersection(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_18,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( ~ subset(X1,esk2_0)
| subset(intersection(X1,esk3_0),empty_set) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
intersection(esk1_0,esk3_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ~ subset(X1,esk2_0)
| intersection(X1,esk3_0) = empty_set ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,negated_conjecture,
intersection(esk3_0,esk1_0) != empty_set,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( ~ subset(X1,esk2_0)
| intersection(esk3_0,X1) = empty_set ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET596+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:28:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % new_bool_3 with pid 1770706 completed with status 0
% 0.14/0.44 % Result found by new_bool_3
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.14/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.44 % SubtermCWHack with pid 1770711 completed with status 0
% 0.14/0.44 % Result found by SubtermCWHack
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.14/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 11
% 0.14/0.44 % Removed by relevancy pruning/SinE : 1
% 0.14/0.44 % Initial clauses : 21
% 0.14/0.44 % Removed in clause preprocessing : 2
% 0.14/0.44 % Initial clauses in saturation : 19
% 0.14/0.44 % Processed clauses : 39
% 0.14/0.44 % ...of these trivial : 0
% 0.14/0.44 % ...subsumed : 12
% 0.14/0.44 % ...remaining for further processing : 27
% 0.14/0.44 % Other redundant clauses eliminated : 2
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 0
% 0.14/0.44 % Backward-rewritten : 1
% 0.14/0.44 % Generated clauses : 73
% 0.14/0.44 % ...of the previous two non-redundant : 58
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 0
% 0.14/0.44 % Paramodulations : 69
% 0.14/0.44 % Factorizations : 2
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 2
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 17
% 0.14/0.44 % ...of those cached : 7
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 24
% 0.14/0.44 % Positive orientable unit clauses : 4
% 0.14/0.44 % Positive unorientable unit clauses: 1
% 0.14/0.44 % Negative unit clauses : 2
% 0.14/0.44 % Non-unit-clauses : 17
% 0.14/0.44 % Current number of unprocessed clauses: 32
% 0.14/0.44 % ...number of literals in the above : 79
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 1
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 27
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 27
% 0.14/0.44 % Non-unit clause-clause subsumptions : 7
% 0.14/0.44 % Unit Clause-clause subsumption calls : 0
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 5
% 0.14/0.44 % BW rewrite match successes : 4
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 1791
% 0.14/0.44 % Search garbage collected termcells : 328
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.006 s
% 0.14/0.44 % System time : 0.003 s
% 0.14/0.44 % Total time : 0.009 s
% 0.14/0.44 % Maximum resident set size: 3636 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.007 s
% 0.14/0.44 % System time : 0.008 s
% 0.14/0.44 % Total time : 0.016 s
% 0.14/0.44 % Maximum resident set size: 4864 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------