%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET588+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 : n008.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 0.24s 0.55s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 62 ( 24 ~; 25 |; 7 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 4 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_difference_subset1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X1,X3),difference(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_subset1) ).
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(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(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X1,X3),difference(X2,X3)) ),
inference(assume_negation,[status(cth)],[prove_difference_subset1]) ).
fof(c_0_4,plain,
! [X7,X8,X9,X10,X11] :
( ( subset(X10,X11)
| ~ member(esk1_2(X10,X11),X11) )
& ( subset(X10,X11)
| member(esk1_2(X10,X11),X10) )
& ( member(X9,X8)
| ~ member(X9,X7)
| ~ subset(X7,X8) ) ),
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_5,negated_conjecture,
( ~ subset(difference(esk2_0,esk4_0),difference(esk3_0,esk4_0))
& subset(esk2_0,esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
cnf(c_0_7,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X4,X5,X6] :
( ( member(X6,difference(X4,X5))
| member(X6,X5)
| ~ member(X6,X4) )
& ( ~ member(X6,difference(X4,X5))
| ~ member(X6,X5) )
& ( ~ member(X6,difference(X4,X5))
| member(X6,X4) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_10,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
( ~ member(X1,esk2_0)
| member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
( ~ member(esk1_2(X1,esk3_0),esk2_0)
| subset(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
subset(difference(esk2_0,X1),esk3_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( ~ member(X1,difference(esk2_0,X2))
| member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_19,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
( ~ member(esk1_2(X1,difference(X2,X3)),X2)
| member(esk1_2(X1,difference(X2,X3)),X3)
| subset(X1,difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( member(esk1_2(difference(esk2_0,X1),X2),esk3_0)
| subset(difference(esk2_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_22,plain,
( ~ member(esk1_2(difference(X1,X2),X3),X2)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_23,negated_conjecture,
( member(esk1_2(difference(esk2_0,X1),difference(esk3_0,X2)),X2)
| subset(difference(esk2_0,X1),difference(esk3_0,X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
~ subset(difference(esk2_0,esk4_0),difference(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_25,negated_conjecture,
subset(difference(esk2_0,X1),difference(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET588+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n008.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 05:28:25 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.55 % Version: 3.5.1
% 0.24/0.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.55 % Starting sh5l with 300s (1) cores
% 0.24/0.55 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 228266 completed with status 0
% 0.24/0.55 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.24/0.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.55 % No SInE strategy applied
% 0.24/0.55 % Search class: FGHNF-FFSF22-SFFFFFNN
% 0.24/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.24/0.55 % Starting new_bool_3 with 136s (1) cores
% 0.24/0.55 % Starting new_bool_1 with 136s (1) cores
% 0.24/0.55 % SubtermCWHack with pid 228270 completed with status 0
% 0.24/0.55 % Result found by SubtermCWHack
% 0.24/0.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.55 % No SInE strategy applied
% 0.24/0.55 % Search class: FGHNF-FFSF22-SFFFFFNN
% 0.24/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.55 % Preprocessing time : 0.001 s
% 0.24/0.55
% 0.24/0.55 % Proof found!
% 0.24/0.55 % SZS status Theorem
% 0.24/0.55 % SZS output start CNFRefutation
% See solution above
% 0.24/0.55 % Parsed axioms : 4
% 0.24/0.55 % Removed by relevancy pruning/SinE : 0
% 0.24/0.55 % Initial clauses : 9
% 0.24/0.55 % Removed in clause preprocessing : 0
% 0.24/0.55 % Initial clauses in saturation : 9
% 0.24/0.55 % Processed clauses : 74
% 0.24/0.55 % ...of these trivial : 1
% 0.24/0.55 % ...subsumed : 25
% 0.24/0.55 % ...remaining for further processing : 48
% 0.24/0.55 % Other redundant clauses eliminated : 0
% 0.24/0.55 % Clauses deleted for lack of memory : 0
% 0.24/0.55 % Backward-subsumed : 0
% 0.24/0.55 % Backward-rewritten : 1
% 0.24/0.55 % Generated clauses : 158
% 0.24/0.55 % ...of the previous two non-redundant : 138
% 0.24/0.55 % ...aggressively subsumed : 0
% 0.24/0.55 % Contextual simplify-reflections : 0
% 0.24/0.55 % Paramodulations : 158
% 0.24/0.55 % Factorizations : 0
% 0.24/0.55 % NegExts : 0
% 0.24/0.55 % Equation resolutions : 0
% 0.24/0.56 % Disequality decompositions : 0
% 0.24/0.56 % Total rewrite steps : 15
% 0.24/0.56 % ...of those cached : 3
% 0.24/0.56 % Propositional unsat checks : 0
% 0.24/0.56 % Propositional check models : 0
% 0.24/0.56 % Propositional check unsatisfiable : 0
% 0.24/0.56 % Propositional clauses : 0
% 0.24/0.56 % Propositional clauses after purity: 0
% 0.24/0.56 % Propositional unsat core size : 0
% 0.24/0.56 % Propositional preprocessing time : 0.000
% 0.24/0.56 % Propositional encoding time : 0.000
% 0.24/0.56 % Propositional solver time : 0.000
% 0.24/0.56 % Success case prop preproc time : 0.000
% 0.24/0.56 % Success case prop encoding time : 0.000
% 0.24/0.56 % Success case prop solver time : 0.000
% 0.24/0.56 % Current number of processed clauses : 47
% 0.24/0.56 % Positive orientable unit clauses : 16
% 0.24/0.56 % Positive unorientable unit clauses: 0
% 0.24/0.56 % Negative unit clauses : 0
% 0.24/0.56 % Non-unit-clauses : 31
% 0.24/0.56 % Current number of unprocessed clauses: 73
% 0.24/0.56 % ...number of literals in the above : 157
% 0.24/0.56 % Current number of archived formulas : 0
% 0.24/0.56 % Current number of archived clauses : 1
% 0.24/0.56 % Clause-clause subsumption calls (NU) : 219
% 0.24/0.56 % Rec. Clause-clause subsumption calls : 213
% 0.24/0.56 % Non-unit clause-clause subsumptions : 25
% 0.24/0.56 % Unit Clause-clause subsumption calls : 27
% 0.24/0.56 % Rewrite failures with RHS unbound : 0
% 0.24/0.56 % BW rewrite match attempts : 30
% 0.24/0.56 % BW rewrite match successes : 1
% 0.24/0.56 % Condensation attempts : 0
% 0.24/0.56 % Condensation successes : 0
% 0.24/0.56 % Termbank termtop insertions : 2825
% 0.24/0.56 % Search garbage collected termcells : 140
% 0.24/0.56
% 0.24/0.56 % -------------------------------------------------
% 0.24/0.56 % User time : 0.009 s
% 0.24/0.56 % System time : 0.003 s
% 0.24/0.56 % Total time : 0.012 s
% 0.24/0.56 % Maximum resident set size: 3320 pages
% 0.24/0.56
% 0.24/0.56 % -------------------------------------------------
% 0.24/0.56 % User time : 0.035 s
% 0.24/0.56 % System time : 0.010 s
% 0.24/0.56 % Total time : 0.045 s
% 0.24/0.56 % Maximum resident set size: 4608 pages
% 0.24/0.56 % E exiting
%------------------------------------------------------------------------------