%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET603+4 : 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 02:14:40 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 29 ~; 24 |; 9 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 3 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(thI30,conjecture,
! [X4] : equal_set(difference(X4,empty_set),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI30) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(c_0_5,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(c_0_6,negated_conjecture,
~ ! [X4] : equal_set(difference(X4,empty_set),X4),
inference(assume_negation,[status(cth)],[thI30]) ).
fof(c_0_7,plain,
! [X9,X10,X11] :
( ( member(X9,difference(X11,X10))
| member(X9,X10)
| ~ member(X9,X11) )
& ( ~ member(X9,difference(X11,X10))
| ~ member(X9,X10) )
& ( ~ member(X9,difference(X11,X10))
| member(X9,X11) ) ),
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,
! [X13,X14,X15,X16,X17] :
( ( subset(X16,X17)
| ~ member(esk2_2(X16,X17),X17) )
& ( subset(X16,X17)
| member(esk2_2(X16,X17),X16) )
& ( member(X15,X14)
| ~ member(X15,X13)
| ~ subset(X13,X14) ) ),
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])])])])])])]) ).
fof(c_0_9,negated_conjecture,
~ equal_set(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_6])])])]) ).
fof(c_0_10,plain,
! [X7,X8] :
( ( equal_set(X7,X8)
| ~ subset(X8,X7)
| ~ subset(X7,X8) )
& ( ~ equal_set(X7,X8)
| subset(X8,X7) )
& ( ~ equal_set(X7,X8)
| subset(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
cnf(c_0_11,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
cnf(c_0_14,plain,
( ~ member(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
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,
~ equal_set(difference(esk1_0,empty_set),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( subset(difference(X1,X2),X3)
| member(esk2_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_19,plain,
! [X12] : ~ member(X12,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_13])]) ).
cnf(c_0_20,plain,
( ~ member(esk2_2(X1,difference(X2,X3)),X2)
| subset(X1,difference(X2,X3))
| member(esk2_2(X1,difference(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( ~ subset(difference(esk1_0,empty_set),esk1_0)
| ~ subset(esk1_0,difference(esk1_0,empty_set)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_23,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( subset(X1,difference(X1,X2))
| member(esk2_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_25,negated_conjecture,
~ subset(esk1_0,difference(esk1_0,empty_set)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_26,plain,
subset(X1,difference(X1,empty_set)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET603+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:29:17 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.42 % Version: 3.5.1
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % sh5l with pid 2095121 completed with status 0
% 0.13/0.42 % Result found by sh5l
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.13/0.42 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.13/0.42 % Search class: FGHNF-FFSF21-SFFFFFNN
% 0.13/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.42 % SubtermCWHack with pid 2095122 completed with status 0
% 0.13/0.42 % Result found by SubtermCWHack
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.13/0.42 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.13/0.42 % Search class: FGHNF-FFSF21-SFFFFFNN
% 0.13/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.42 % Preprocessing time : 0.001 s
% 0.13/0.42
% 0.13/0.42 % Proof found!
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start CNFRefutation
% See solution above
% 0.13/0.42 % Parsed axioms : 12
% 0.13/0.42 % Removed by relevancy pruning/SinE : 6
% 0.13/0.42 % Initial clauses : 13
% 0.13/0.42 % Removed in clause preprocessing : 0
% 0.13/0.42 % Initial clauses in saturation : 13
% 0.13/0.42 % Processed clauses : 35
% 0.13/0.42 % ...of these trivial : 0
% 0.13/0.42 % ...subsumed : 3
% 0.13/0.42 % ...remaining for further processing : 32
% 0.13/0.42 % Other redundant clauses eliminated : 0
% 0.13/0.42 % Clauses deleted for lack of memory : 0
% 0.13/0.42 % Backward-subsumed : 0
% 0.13/0.42 % Backward-rewritten : 2
% 0.13/0.42 % Generated clauses : 53
% 0.13/0.42 % ...of the previous two non-redundant : 41
% 0.13/0.42 % ...aggressively subsumed : 0
% 0.13/0.42 % Contextual simplify-reflections : 0
% 0.13/0.42 % Paramodulations : 53
% 0.13/0.42 % Factorizations : 0
% 0.13/0.42 % NegExts : 0
% 0.13/0.42 % Equation resolutions : 0
% 0.13/0.42 % Disequality decompositions : 0
% 0.13/0.42 % Total rewrite steps : 7
% 0.13/0.42 % ...of those cached : 0
% 0.13/0.42 % Propositional unsat checks : 0
% 0.13/0.42 % Propositional check models : 0
% 0.13/0.42 % Propositional check unsatisfiable : 0
% 0.13/0.42 % Propositional clauses : 0
% 0.13/0.42 % Propositional clauses after purity: 0
% 0.13/0.42 % Propositional unsat core size : 0
% 0.13/0.42 % Propositional preprocessing time : 0.000
% 0.13/0.42 % Propositional encoding time : 0.000
% 0.13/0.42 % Propositional solver time : 0.000
% 0.13/0.42 % Success case prop preproc time : 0.000
% 0.13/0.42 % Success case prop encoding time : 0.000
% 0.13/0.42 % Success case prop solver time : 0.000
% 0.13/0.42 % Current number of processed clauses : 30
% 0.13/0.42 % Positive orientable unit clauses : 6
% 0.13/0.42 % Positive unorientable unit clauses: 0
% 0.13/0.42 % Negative unit clauses : 2
% 0.13/0.42 % Non-unit-clauses : 22
% 0.13/0.42 % Current number of unprocessed clauses: 19
% 0.13/0.42 % ...number of literals in the above : 45
% 0.13/0.42 % Current number of archived formulas : 0
% 0.13/0.42 % Current number of archived clauses : 2
% 0.13/0.42 % Clause-clause subsumption calls (NU) : 50
% 0.13/0.42 % Rec. Clause-clause subsumption calls : 47
% 0.13/0.42 % Non-unit clause-clause subsumptions : 1
% 0.13/0.42 % Unit Clause-clause subsumption calls : 20
% 0.13/0.42 % Rewrite failures with RHS unbound : 0
% 0.13/0.42 % BW rewrite match attempts : 10
% 0.13/0.42 % BW rewrite match successes : 2
% 0.13/0.42 % Condensation attempts : 0
% 0.13/0.42 % Condensation successes : 0
% 0.13/0.42 % Termbank termtop insertions : 1506
% 0.13/0.42 % Search garbage collected termcells : 230
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.005 s
% 0.13/0.42 % System time : 0.001 s
% 0.13/0.42 % Total time : 0.007 s
% 0.13/0.42 % Maximum resident set size: 3648 pages
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.008 s
% 0.13/0.42 % System time : 0.005 s
% 0.13/0.42 % Total time : 0.013 s
% 0.13/0.42 % Maximum resident set size: 4608 pages
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------