%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET579+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 : n020.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 02:14:24 PM UTC 2026
% Result : Theorem 0.14s 10.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 5 unt; 0 def)
% Number of atoms : 96 ( 10 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 103 ( 39 ~; 38 |; 15 &)
% ( 7 <=>; 4 =>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 2 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th20,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( ~ member(X4,X3)
& member(X4,X2) ) )
=> X1 = difference(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th20) ).
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(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(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( ~ member(X4,X3)
& member(X4,X2) ) )
=> X1 = difference(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th20]) ).
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,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( ~ member(X4,X3)
& member(X4,X2) ) )
=> X1 = difference(X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_7,plain,
! [X5,X6,X7] :
( ( member(X7,difference(X5,X6))
| member(X7,X6)
| ~ member(X7,X5) )
& ( ~ member(X7,difference(X5,X6))
| ~ member(X7,X6) )
& ( ~ member(X7,difference(X5,X6))
| member(X7,X5) ) ),
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_8,plain,
! [X10,X11,X12,X13,X14] :
( ( subset(X13,X14)
| ~ member(esk1_2(X13,X14),X14) )
& ( subset(X13,X14)
| member(esk1_2(X13,X14),X13) )
& ( member(X12,X11)
| ~ member(X12,X10)
| ~ subset(X10,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)],[subset_defn])])])])])])]) ).
fof(c_0_9,negated_conjecture,
! [X20] :
( esk2_0 != difference(esk3_0,esk4_0)
& ( member(X20,esk2_0)
| member(X20,esk4_0)
| ~ member(X20,esk3_0) )
& ( ~ member(X20,esk2_0)
| ~ member(X20,esk4_0) )
& ( ~ member(X20,esk2_0)
| member(X20,esk3_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])]) ).
cnf(c_0_10,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( ~ member(X1,esk3_0)
| member(X1,esk2_0)
| member(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( ~ member(X1,esk2_0)
| member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( ~ member(esk1_2(difference(X1,X2),X3),X2)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( member(esk1_2(difference(esk3_0,X1),X2),esk4_0)
| member(esk1_2(difference(esk3_0,X1),X2),esk2_0)
| subset(difference(esk3_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X1,esk2_0)
| member(X1,X2)
| member(X1,difference(esk3_0,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_20,plain,
! [X8,X9] :
( ( X8 = X9
| ~ subset(X9,X8)
| ~ subset(X8,X9) )
& ( X8 != X9
| subset(X9,X8) )
& ( X8 != X9
| subset(X8,X9) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_21,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,negated_conjecture,
( member(esk1_2(difference(esk3_0,esk4_0),X1),esk2_0)
| subset(difference(esk3_0,esk4_0),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( member(esk1_2(esk2_0,X1),X2)
| member(esk1_2(esk2_0,X1),difference(esk3_0,X2))
| subset(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_24,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
subset(difference(esk3_0,esk4_0),esk2_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
esk2_0 != difference(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(X1,esk2_0)
| ~ member(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( member(esk1_2(esk2_0,difference(esk3_0,X1)),X1)
| subset(esk2_0,difference(esk3_0,X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
~ subset(esk2_0,difference(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
~ member(esk1_2(esk2_0,difference(esk3_0,esk4_0)),esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_11]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/10.39 % Computer : n020.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Mon Sep 21 05:27:59 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/10.43 Running first-order theorem proving
% 0.14/10.43 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
% 0.14/10.47 % Version: 3.5.1
% 0.14/10.47 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/10.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/10.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/10.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/10.47 % Starting sh5l with 300s (1) cores
% 0.14/10.47 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2090766 completed with status 0
% 0.14/10.47 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.14/10.47 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/10.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/10.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/10.47 % No SInE strategy applied
% 0.14/10.47 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.14/10.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/10.47 % Starting SubtermCWHack with 136s (1) cores
% 0.14/10.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/10.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/10.47 % Starting new_bool_3 with 136s (1) cores
% 0.14/10.47 % Starting new_bool_1 with 136s (1) cores
% 0.14/10.47 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2090772 completed with status 0
% 0.14/10.47 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.14/10.47 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/10.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/10.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/10.47 % No SInE strategy applied
% 0.14/10.47 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.14/10.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/10.47 % Starting SubtermCWHack with 136s (1) cores
% 0.14/10.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/10.47 % Preprocessing time : 0.002 s
% 0.14/10.47
% 0.14/10.47 % Proof found!
% 0.14/10.47 % SZS status Theorem
% 0.14/10.47 % SZS output start CNFRefutation
% See solution above
% 0.14/10.47 % Parsed axioms : 5
% 0.14/10.47 % Removed by relevancy pruning/SinE : 0
% 0.14/10.47 % Initial clauses : 14
% 0.14/10.47 % Removed in clause preprocessing : 0
% 0.14/10.47 % Initial clauses in saturation : 14
% 0.14/10.47 % Processed clauses : 121
% 0.14/10.47 % ...of these trivial : 2
% 0.14/10.47 % ...subsumed : 46
% 0.14/10.47 % ...remaining for further processing : 73
% 0.14/10.47 % Other redundant clauses eliminated : 2
% 0.14/10.47 % Clauses deleted for lack of memory : 0
% 0.14/10.47 % Backward-subsumed : 5
% 0.14/10.47 % Backward-rewritten : 3
% 0.14/10.47 % Generated clauses : 439
% 0.14/10.47 % ...of the previous two non-redundant : 305
% 0.14/10.47 % ...aggressively subsumed : 0
% 0.14/10.47 % Contextual simplify-reflections : 1
% 0.14/10.47 % Paramodulations : 435
% 0.14/10.47 % Factorizations : 2
% 0.14/10.47 % NegExts : 0
% 0.14/10.47 % Equation resolutions : 2
% 0.14/10.47 % Disequality decompositions : 0
% 0.14/10.47 % Total rewrite steps : 241
% 0.14/10.47 % ...of those cached : 193
% 0.14/10.47 % Propositional unsat checks : 0
% 0.14/10.47 % Propositional check models : 0
% 0.14/10.47 % Propositional check unsatisfiable : 0
% 0.14/10.47 % Propositional clauses : 0
% 0.14/10.47 % Propositional clauses after purity: 0
% 0.14/10.47 % Propositional unsat core size : 0
% 0.14/10.47 % Propositional preprocessing time : 0.000
% 0.14/10.47 % Propositional encoding time : 0.000
% 0.14/10.47 % Propositional solver time : 0.000
% 0.14/10.47 % Success case prop preproc time : 0.000
% 0.14/10.47 % Success case prop encoding time : 0.000
% 0.14/10.47 % Success case prop solver time : 0.000
% 0.14/10.47 % Current number of processed clauses : 63
% 0.14/10.47 % Positive orientable unit clauses : 13
% 0.14/10.47 % Positive unorientable unit clauses: 2
% 0.14/10.47 % Negative unit clauses : 4
% 0.14/10.47 % Non-unit-clauses : 44
% 0.14/10.47 % Current number of unprocessed clauses: 179
% 0.14/10.47 % ...number of literals in the above : 447
% 0.14/10.47 % Current number of archived formulas : 0
% 0.14/10.47 % Current number of archived clauses : 8
% 0.14/10.47 % Clause-clause subsumption calls (NU) : 286
% 0.14/10.47 % Rec. Clause-clause subsumption calls : 236
% 0.14/10.47 % Non-unit clause-clause subsumptions : 25
% 0.14/10.47 % Unit Clause-clause subsumption calls : 60
% 0.14/10.47 % Rewrite failures with RHS unbound : 0
% 0.14/10.47 % BW rewrite match attempts : 45
% 0.14/10.47 % BW rewrite match successes : 5
% 0.14/10.47 % Condensation attempts : 0
% 0.14/10.47 % Condensation successes : 0
% 0.14/10.47 % Termbank termtop insertions : 5644
% 0.14/10.47 % Search garbage collected termcells : 239
% 0.14/10.47
% 0.14/10.47 % -------------------------------------------------
% 0.14/10.47 % User time : 0.014 s
% 0.14/10.47 % System time : 0.004 s
% 0.14/10.47 % Total time : 0.018 s
% 0.14/10.47 % Maximum resident set size: 3324 pages
% 0.14/10.47
% 0.14/10.47 % -------------------------------------------------
% 0.14/10.47 % User time : 0.058 s
% 0.14/10.47 % System time : 0.020 s
% 0.14/10.47 % Total time : 0.079 s
% 0.14/10.47 % Maximum resident set size: 4608 pages
% 0.14/10.47 % E exiting
%------------------------------------------------------------------------------