%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET603+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 : n015.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 02:14:40 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 64 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 63 ( 26 ~; 23 |; 9 &)
% ( 4 <=>; 1 =>; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 3 sgn 26 !; 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(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(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(prove_th74,conjecture,
! [X1] : difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th74) ).
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_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,plain,
! [X19,X20,X21,X22,X23] :
( ( subset(X22,X23)
| ~ member(esk4_2(X22,X23),X23) )
& ( subset(X22,X23)
| member(esk4_2(X22,X23),X22) )
& ( member(X21,X20)
| ~ member(X21,X19)
| ~ subset(X19,X20) ) ),
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,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,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
cnf(c_0_9,plain,
( ~ member(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X8] : ~ member(X8,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
cnf(c_0_12,plain,
( ~ member(esk4_2(X1,difference(X2,X3)),X2)
| member(esk4_2(X1,difference(X2,X3)),X3)
| subset(X1,difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] : difference(X1,empty_set) = X1,
inference(assume_negation,[status(cth)],[prove_th74]) ).
fof(c_0_16,plain,
! [X25,X26] :
( ( X25 = X26
| ~ subset(X26,X25)
| ~ subset(X25,X26) )
& ( X25 != X26
| subset(X26,X25) )
& ( X25 != X26
| subset(X25,X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_17,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( member(esk4_2(X1,difference(X1,X2)),X2)
| subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( member(esk4_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
fof(c_0_20,negated_conjecture,
difference(esk1_0,empty_set) != esk1_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_21,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
subset(X1,difference(X1,empty_set)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
difference(esk1_0,empty_set) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
difference(X1,empty_set) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,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
% 0.00/0.03 % Problem : SET603+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:31:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.44 % Version: 3.5.1
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % sh5l with pid 652654 completed with status 0
% 0.15/0.44 % Result found by sh5l
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.15/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/0.44 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.15/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.44 % SubtermCWHack with pid 652655 completed with status 0
% 0.15/0.44 % Result found by SubtermCWHack
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.15/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/0.44 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.15/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.44 % Preprocessing time : 0.001 s
% 0.15/0.44
% 0.15/0.44 % Proof found!
% 0.15/0.44 % SZS status Theorem
% 0.15/0.44 % SZS output start CNFRefutation
% See solution above
% 0.15/0.44 % Parsed axioms : 9
% 0.15/0.44 % Removed by relevancy pruning/SinE : 1
% 0.15/0.44 % Initial clauses : 18
% 0.15/0.44 % Removed in clause preprocessing : 2
% 0.15/0.44 % Initial clauses in saturation : 16
% 0.15/0.44 % Processed clauses : 65
% 0.15/0.44 % ...of these trivial : 1
% 0.15/0.44 % ...subsumed : 17
% 0.15/0.44 % ...remaining for further processing : 47
% 0.15/0.44 % Other redundant clauses eliminated : 2
% 0.15/0.44 % Clauses deleted for lack of memory : 0
% 0.15/0.44 % Backward-subsumed : 0
% 0.15/0.44 % Backward-rewritten : 5
% 0.15/0.44 % Generated clauses : 196
% 0.15/0.44 % ...of the previous two non-redundant : 113
% 0.15/0.44 % ...aggressively subsumed : 0
% 0.15/0.44 % Contextual simplify-reflections : 0
% 0.15/0.44 % Paramodulations : 190
% 0.15/0.44 % Factorizations : 4
% 0.15/0.44 % NegExts : 0
% 0.15/0.44 % Equation resolutions : 2
% 0.15/0.44 % Disequality decompositions : 0
% 0.15/0.44 % Total rewrite steps : 80
% 0.15/0.44 % ...of those cached : 62
% 0.15/0.44 % Propositional unsat checks : 0
% 0.15/0.44 % Propositional check models : 0
% 0.15/0.44 % Propositional check unsatisfiable : 0
% 0.15/0.44 % Propositional clauses : 0
% 0.15/0.44 % Propositional clauses after purity: 0
% 0.15/0.44 % Propositional unsat core size : 0
% 0.15/0.44 % Propositional preprocessing time : 0.000
% 0.15/0.44 % Propositional encoding time : 0.000
% 0.15/0.44 % Propositional solver time : 0.000
% 0.15/0.44 % Success case prop preproc time : 0.000
% 0.15/0.44 % Success case prop encoding time : 0.000
% 0.15/0.44 % Success case prop solver time : 0.000
% 0.15/0.44 % Current number of processed clauses : 40
% 0.15/0.44 % Positive orientable unit clauses : 8
% 0.15/0.44 % Positive unorientable unit clauses: 0
% 0.15/0.44 % Negative unit clauses : 1
% 0.15/0.44 % Non-unit-clauses : 31
% 0.15/0.44 % Current number of unprocessed clauses: 58
% 0.15/0.44 % ...number of literals in the above : 138
% 0.15/0.44 % Current number of archived formulas : 0
% 0.15/0.44 % Current number of archived clauses : 5
% 0.15/0.44 % Clause-clause subsumption calls (NU) : 91
% 0.15/0.44 % Rec. Clause-clause subsumption calls : 85
% 0.15/0.44 % Non-unit clause-clause subsumptions : 5
% 0.15/0.44 % Unit Clause-clause subsumption calls : 41
% 0.15/0.44 % Rewrite failures with RHS unbound : 0
% 0.15/0.44 % BW rewrite match attempts : 17
% 0.15/0.44 % BW rewrite match successes : 5
% 0.15/0.44 % Condensation attempts : 0
% 0.15/0.44 % Condensation successes : 0
% 0.15/0.44 % Termbank termtop insertions : 3059
% 0.15/0.44 % Search garbage collected termcells : 321
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.007 s
% 0.15/0.44 % System time : 0.002 s
% 0.15/0.44 % Total time : 0.009 s
% 0.15/0.44 % Maximum resident set size: 3636 pages
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.007 s
% 0.15/0.44 % System time : 0.008 s
% 0.15/0.44 % Total time : 0.014 s
% 0.15/0.44 % Maximum resident set size: 4864 pages
% 0.15/0.44 % E exiting
%------------------------------------------------------------------------------