%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 02:14:26 PM UTC 2026
% Result : Theorem 0.10s 5.58s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 83 ( 14 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 81 ( 32 ~; 33 |; 8 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 5 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(prove_difference_empty_set,conjecture,
! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(member_equal,axiom,
! [X1,X2] :
( ! [X3] :
( member(X3,X1)
<=> member(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[prove_difference_empty_set]) ).
fof(c_0_7,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_8,plain,
! [X16,X17,X18] :
( ( member(X18,difference(X16,X17))
| member(X18,X17)
| ~ member(X18,X16) )
& ( ~ member(X18,difference(X16,X17))
| ~ member(X18,X17) )
& ( ~ member(X18,difference(X16,X17))
| member(X18,X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_9,negated_conjecture,
( ( subset(esk1_0,esk2_0)
| difference(esk1_0,esk2_0) = empty_set )
& ( ~ subset(esk1_0,esk2_0)
| difference(esk1_0,esk2_0) != empty_set ) ),
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,
! [X15] : ~ member(X15,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_11,plain,
! [X6,X7,X8,X9,X10] :
( ( subset(X9,X10)
| ~ member(esk3_2(X9,X10),X10) )
& ( subset(X9,X10)
| member(esk3_2(X9,X10),X9) )
& ( member(X8,X7)
| ~ member(X8,X6)
| ~ subset(X6,X7) ) ),
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])])])])])])]) ).
cnf(c_0_12,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( subset(esk1_0,esk2_0)
| difference(esk1_0,esk2_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_20,plain,
! [X19,X20] :
( ( X19 = X20
| member(esk4_2(X19,X20),X20)
| member(esk4_2(X19,X20),X19) )
& ( X19 = X20
| ~ member(esk4_2(X19,X20),X20)
| ~ member(esk4_2(X19,X20),X19) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_equal])])])])]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(esk3_2(X1,esk2_0),esk1_0)
| subset(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( member(esk3_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( X1 = X2
| member(esk4_2(X1,X2),X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
subset(difference(esk1_0,X1),esk2_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,plain,
( member(esk4_2(empty_set,X1),X1)
| empty_set = X1 ),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(X1,difference(esk1_0,X2))
| member(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( ~ subset(esk1_0,esk2_0)
| difference(esk1_0,esk2_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,negated_conjecture,
subset(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_30,plain,
( ~ member(esk4_2(empty_set,difference(X1,X2)),X2)
| difference(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( member(esk4_2(empty_set,difference(esk1_0,X1)),esk2_0)
| difference(esk1_0,X1) = empty_set ),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
difference(esk1_0,esk2_0) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.52 % Computer : n014.cluster.edu
% 0.10/5.52 % Model : x86_64 x86_64
% 0.10/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.52 % Memory : 8046.5625MB
% 0.10/5.52 % OS : Linux 6.8.0-71-generic
% 0.10/5.52 % CPULimit : 300
% 0.10/5.52 % WCLimit : 300
% 0.10/5.52 % DateTime : Mon Sep 21 05:27:41 UTC 2026
% 0.10/5.52 % CPUTime :
% 0.10/5.52 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.56 Running first-order theorem proving
% 0.10/5.56 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.10/5.58 % Version: 3.5.1
% 0.10/5.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/5.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/5.58 % Starting new_bool_3 with 300s (1) cores
% 0.10/5.58 % Starting new_bool_1 with 300s (1) cores
% 0.10/5.58 % Starting sh5l with 300s (1) cores
% 0.10/5.58 % new_bool_3 with pid 3223216 completed with status 0
% 0.10/5.58 % Result found by new_bool_3
% 0.10/5.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/5.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/5.58 % Starting new_bool_3 with 300s (1) cores
% 0.10/5.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/5.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/5.58 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.10/5.58 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/5.58 % Starting SubtermCWHack with 31s (1) cores
% 0.10/5.58 % SubtermCWHack with pid 3223220 completed with status 0
% 0.10/5.58 % Result found by SubtermCWHack
% 0.10/5.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/5.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/5.58 % Starting new_bool_3 with 300s (1) cores
% 0.10/5.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/5.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/5.58 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.10/5.58 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/5.58 % Starting SubtermCWHack with 31s (1) cores
% 0.10/5.58 % Preprocessing time : 0.001 s
% 0.10/5.58
% 0.10/5.58 % Proof found!
% 0.10/5.58 % SZS status Theorem
% 0.10/5.58 % SZS output start CNFRefutation
% See solution above
% 0.10/5.58 % Parsed axioms : 9
% 0.10/5.58 % Removed by relevancy pruning/SinE : 1
% 0.10/5.58 % Initial clauses : 19
% 0.10/5.58 % Removed in clause preprocessing : 2
% 0.10/5.58 % Initial clauses in saturation : 17
% 0.10/5.58 % Processed clauses : 59
% 0.10/5.58 % ...of these trivial : 1
% 0.10/5.58 % ...subsumed : 14
% 0.10/5.58 % ...remaining for further processing : 44
% 0.10/5.58 % Other redundant clauses eliminated : 2
% 0.10/5.58 % Clauses deleted for lack of memory : 0
% 0.10/5.58 % Backward-subsumed : 0
% 0.10/5.58 % Backward-rewritten : 4
% 0.10/5.58 % Generated clauses : 117
% 0.10/5.58 % ...of the previous two non-redundant : 87
% 0.10/5.58 % ...aggressively subsumed : 0
% 0.10/5.58 % Contextual simplify-reflections : 1
% 0.10/5.58 % Paramodulations : 111
% 0.10/5.58 % Factorizations : 4
% 0.10/5.58 % NegExts : 0
% 0.10/5.58 % Equation resolutions : 2
% 0.10/5.58 % Disequality decompositions : 0
% 0.10/5.58 % Total rewrite steps : 26
% 0.10/5.58 % ...of those cached : 18
% 0.10/5.58 % Propositional unsat checks : 0
% 0.10/5.58 % Propositional check models : 0
% 0.10/5.58 % Propositional check unsatisfiable : 0
% 0.10/5.58 % Propositional clauses : 0
% 0.10/5.58 % Propositional clauses after purity: 0
% 0.10/5.58 % Propositional unsat core size : 0
% 0.10/5.58 % Propositional preprocessing time : 0.000
% 0.10/5.58 % Propositional encoding time : 0.000
% 0.10/5.58 % Propositional solver time : 0.000
% 0.10/5.58 % Success case prop preproc time : 0.000
% 0.10/5.58 % Success case prop encoding time : 0.000
% 0.10/5.58 % Success case prop solver time : 0.000
% 0.10/5.58 % Current number of processed clauses : 38
% 0.10/5.58 % Positive orientable unit clauses : 7
% 0.10/5.58 % Positive unorientable unit clauses: 0
% 0.10/5.58 % Negative unit clauses : 2
% 0.10/5.58 % Non-unit-clauses : 29
% 0.10/5.58 % Current number of unprocessed clauses: 40
% 0.10/5.58 % ...number of literals in the above : 102
% 0.10/5.58 % Current number of archived formulas : 0
% 0.10/5.58 % Current number of archived clauses : 4
% 0.10/5.58 % Clause-clause subsumption calls (NU) : 83
% 0.10/5.58 % Rec. Clause-clause subsumption calls : 69
% 0.10/5.58 % Non-unit clause-clause subsumptions : 6
% 0.10/5.58 % Unit Clause-clause subsumption calls : 51
% 0.10/5.58 % Rewrite failures with RHS unbound : 0
% 0.10/5.58 % BW rewrite match attempts : 15
% 0.10/5.58 % BW rewrite match successes : 3
% 0.10/5.58 % Condensation attempts : 0
% 0.10/5.58 % Condensation successes : 0
% 0.10/5.58 % Termbank termtop insertions : 2407
% 0.10/5.58 % Search garbage collected termcells : 327
% 0.10/5.58
% 0.10/5.58 % -------------------------------------------------
% 0.10/5.58 % User time : 0.007 s
% 0.10/5.58 % System time : 0.003 s
% 0.10/5.58 % Total time : 0.011 s
% 0.10/5.58 % Maximum resident set size: 3636 pages
% 0.10/5.58
% 0.10/5.58 % -------------------------------------------------
% 0.10/5.58 % User time : 0.009 s
% 0.10/5.58 % System time : 0.008 s
% 0.10/5.58 % Total time : 0.017 s
% 0.10/5.58 % Maximum resident set size: 4864 pages
% 0.10/5.58 % E exiting
%------------------------------------------------------------------------------