%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET697+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 : n019.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 02:15:01 PM UTC 2026
% Result : Theorem 0.45s 0.57s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 10 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 121 ( 48 ~; 46 |; 17 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 8 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI31,conjecture,
! [X1,X2,X4] :
( ( subset(X2,X4)
& subset(X1,X4) )
=> ( subset(X1,X2)
<=> equal_set(intersection(X1,difference(X4,X2)),empty_set) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI31) ).
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(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(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
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(c_0_6,negated_conjecture,
~ ! [X1,X2,X4] :
( ( subset(X2,X4)
& subset(X1,X4) )
=> ( subset(X1,X2)
<=> equal_set(intersection(X1,difference(X4,X2)),empty_set) ) ),
inference(assume_negation,[status(cth)],[thI31]) ).
fof(c_0_7,plain,
! [X9,X10] :
( ( equal_set(X9,X10)
| ~ subset(X10,X9)
| ~ subset(X9,X10) )
& ( ~ equal_set(X9,X10)
| subset(X10,X9) )
& ( ~ equal_set(X9,X10)
| subset(X9,X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
fof(c_0_8,negated_conjecture,
( ( equal_set(intersection(esk1_0,difference(esk3_0,esk2_0)),empty_set)
| subset(esk1_0,esk2_0) )
& ( ~ equal_set(intersection(esk1_0,difference(esk3_0,esk2_0)),empty_set)
| ~ subset(esk1_0,esk2_0) )
& subset(esk2_0,esk3_0)
& subset(esk1_0,esk3_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_9,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(c_0_10,plain,
! [X18,X19,X20,X21,X22] :
( ( subset(X21,X22)
| ~ member(esk4_2(X21,X22),X22) )
& ( subset(X21,X22)
| member(esk4_2(X21,X22),X21) )
& ( member(X20,X19)
| ~ member(X20,X18)
| ~ subset(X18,X19) ) ),
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])])])])])])]) ).
cnf(c_0_11,plain,
( ~ equal_set(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( equal_set(intersection(esk1_0,difference(esk3_0,esk2_0)),empty_set)
| subset(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X11] : ~ member(X11,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])]) ).
cnf(c_0_14,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( subset(esk1_0,esk2_0)
| subset(intersection(esk1_0,difference(esk3_0,esk2_0)),empty_set) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X12,X13,X14] :
( ( member(X12,intersection(X13,X14))
| ~ member(X12,X14)
| ~ member(X12,X13) )
& ( ~ member(X12,intersection(X13,X14))
| member(X12,X14) )
& ( ~ member(X12,intersection(X13,X14))
| member(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])])]) ).
fof(c_0_18,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X1,intersection(esk1_0,difference(esk3_0,esk2_0)))
| subset(esk1_0,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_20,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X15,X16,X17] :
( ( member(X15,difference(X17,X16))
| member(X15,X16)
| ~ member(X15,X17) )
& ( ~ member(X15,difference(X17,X16))
| ~ member(X15,X16) )
& ( ~ member(X15,difference(X17,X16))
| member(X15,X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
cnf(c_0_22,negated_conjecture,
subset(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
( ~ member(X1,esk1_0)
| ~ member(X1,difference(esk3_0,esk2_0))
| subset(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
cnf(c_0_26,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_14]) ).
cnf(c_0_28,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,negated_conjecture,
( ~ equal_set(intersection(esk1_0,difference(esk3_0,esk2_0)),empty_set)
| ~ subset(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_32,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_33,plain,
( ~ member(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_34,negated_conjecture,
( subset(esk1_0,X1)
| member(esk4_2(esk1_0,X1),esk2_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_35,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_36,plain,
( subset(intersection(X1,X2),X3)
| member(esk4_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_37,plain,
( subset(intersection(X1,X2),X3)
| member(esk4_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_38,negated_conjecture,
( ~ subset(esk1_0,esk2_0)
| ~ subset(intersection(esk1_0,difference(esk3_0,esk2_0)),empty_set) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_39,negated_conjecture,
subset(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,plain,
( ~ member(esk4_2(intersection(X1,difference(X2,X3)),X4),X3)
| subset(intersection(X1,difference(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( subset(intersection(esk1_0,X1),X2)
| member(esk4_2(intersection(esk1_0,X1),X2),esk2_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
~ subset(intersection(esk1_0,difference(esk3_0,esk2_0)),empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_43,negated_conjecture,
subset(intersection(esk1_0,difference(X1,esk2_0)),X2),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET697+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 21 05:33:05 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.49 Running first-order theorem proving
% 0.18/0.49 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
% 0.45/0.57 % Version: 3.5.1
% 0.45/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.45/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.45/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.45/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.45/0.57 % Starting sh5l with 300s (1) cores
% 0.45/0.57 % sh5l with pid 1784517 completed with status 0
% 0.45/0.57 % Result found by sh5l
% 0.45/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.45/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.45/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.45/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.45/0.57 % Starting sh5l with 300s (1) cores
% 0.45/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.45/0.57 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.45/0.57 % Search class: FGHNF-FFSS21-SFFFFFNN
% 0.45/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.45/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.45/0.57 % SubtermCWHack with pid 1784520 completed with status 0
% 0.45/0.57 % Result found by SubtermCWHack
% 0.45/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.45/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.45/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.45/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.45/0.57 % Starting sh5l with 300s (1) cores
% 0.45/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.45/0.57 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.45/0.57 % Search class: FGHNF-FFSS21-SFFFFFNN
% 0.45/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.45/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.45/0.57 % Preprocessing time : 0.001 s
% 0.45/0.57
% 0.45/0.57 % Proof found!
% 0.45/0.57 % SZS status Theorem
% 0.45/0.57 % SZS output start CNFRefutation
% See solution above
% 0.45/0.57 % Parsed axioms : 12
% 0.45/0.57 % Removed by relevancy pruning/SinE : 5
% 0.45/0.57 % Initial clauses : 19
% 0.45/0.57 % Removed in clause preprocessing : 0
% 0.45/0.57 % Initial clauses in saturation : 19
% 0.45/0.57 % Processed clauses : 135
% 0.45/0.57 % ...of these trivial : 0
% 0.45/0.57 % ...subsumed : 26
% 0.45/0.57 % ...remaining for further processing : 109
% 0.45/0.57 % Other redundant clauses eliminated : 0
% 0.45/0.57 % Clauses deleted for lack of memory : 0
% 0.45/0.57 % Backward-subsumed : 1
% 0.45/0.57 % Backward-rewritten : 10
% 0.45/0.57 % Generated clauses : 356
% 0.45/0.57 % ...of the previous two non-redundant : 320
% 0.45/0.57 % ...aggressively subsumed : 0
% 0.45/0.57 % Contextual simplify-reflections : 2
% 0.45/0.57 % Paramodulations : 356
% 0.45/0.57 % Factorizations : 0
% 0.45/0.57 % NegExts : 0
% 0.45/0.57 % Equation resolutions : 0
% 0.45/0.57 % Disequality decompositions : 0
% 0.45/0.57 % Total rewrite steps : 37
% 0.45/0.57 % ...of those cached : 17
% 0.45/0.57 % Propositional unsat checks : 0
% 0.45/0.57 % Propositional check models : 0
% 0.45/0.57 % Propositional check unsatisfiable : 0
% 0.45/0.57 % Propositional clauses : 0
% 0.45/0.57 % Propositional clauses after purity: 0
% 0.45/0.57 % Propositional unsat core size : 0
% 0.45/0.57 % Propositional preprocessing time : 0.000
% 0.45/0.57 % Propositional encoding time : 0.000
% 0.45/0.57 % Propositional solver time : 0.000
% 0.45/0.57 % Success case prop preproc time : 0.000
% 0.45/0.57 % Success case prop encoding time : 0.000
% 0.45/0.57 % Success case prop solver time : 0.000
% 0.45/0.57 % Current number of processed clauses : 98
% 0.45/0.57 % Positive orientable unit clauses : 32
% 0.45/0.57 % Positive unorientable unit clauses: 0
% 0.45/0.57 % Negative unit clauses : 2
% 0.45/0.57 % Non-unit-clauses : 64
% 0.45/0.57 % Current number of unprocessed clauses: 204
% 0.45/0.57 % ...number of literals in the above : 442
% 0.45/0.57 % Current number of archived formulas : 0
% 0.45/0.57 % Current number of archived clauses : 11
% 0.45/0.57 % Clause-clause subsumption calls (NU) : 431
% 0.45/0.57 % Rec. Clause-clause subsumption calls : 410
% 0.45/0.57 % Non-unit clause-clause subsumptions : 23
% 0.45/0.57 % Unit Clause-clause subsumption calls : 78
% 0.45/0.57 % Rewrite failures with RHS unbound : 0
% 0.45/0.57 % BW rewrite match attempts : 42
% 0.45/0.57 % BW rewrite match successes : 2
% 0.45/0.57 % Condensation attempts : 0
% 0.45/0.57 % Condensation successes : 0
% 0.45/0.57 % Termbank termtop insertions : 6027
% 0.45/0.57 % Search garbage collected termcells : 316
% 0.45/0.57
% 0.45/0.57 % -------------------------------------------------
% 0.45/0.57 % User time : 0.015 s
% 0.45/0.57 % System time : 0.003 s
% 0.45/0.57 % Total time : 0.018 s
% 0.45/0.57 % Maximum resident set size: 3648 pages
% 0.45/0.57
% 0.45/0.57 % -------------------------------------------------
% 0.45/0.57 % User time : 0.018 s
% 0.45/0.57 % System time : 0.009 s
% 0.45/0.57 % Total time : 0.027 s
% 0.45/0.57 % Maximum resident set size: 4608 pages
% 0.45/0.57 % E exiting
%------------------------------------------------------------------------------