%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET692+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:15:00 PM UTC 2026
% Result : Theorem 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 6 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 110 ( 50 ~; 45 |; 9 &)
% ( 5 <=>; 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 : 43 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI19,conjecture,
! [X1,X2] :
( equal_set(X1,intersection(X1,X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI19) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( equal_set(X1,intersection(X1,X2))
<=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[thI19]) ).
fof(c_0_5,negated_conjecture,
( ( subset(esk4_0,esk5_0)
| equal_set(esk4_0,intersection(esk4_0,esk5_0)) )
& ( ~ subset(esk4_0,esk5_0)
| ~ equal_set(esk4_0,intersection(esk4_0,esk5_0)) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X12,X13] :
( ( equal_set(X12,X13)
| ~ subset(X13,X12)
| ~ subset(X12,X13) )
& ( ~ equal_set(X12,X13)
| subset(X13,X12) )
& ( ~ equal_set(X12,X13)
| subset(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
cnf(c_0_7,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ equal_set(esk4_0,intersection(esk4_0,esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X6,X7,X8,X9,X10] :
( ( subset(X9,X10)
| ~ member(esk1_2(X9,X10),X10) )
& ( subset(X9,X10)
| member(esk1_2(X9,X10),X9) )
& ( member(X8,X7)
| ~ member(X8,X6)
| ~ subset(X6,X7) ) ),
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_10,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(esk4_0,intersection(esk4_0,esk5_0))
| ~ subset(intersection(esk4_0,esk5_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X16,X17,X18] :
( ( member(X16,intersection(X17,X18))
| ~ member(X16,X18)
| ~ member(X16,X17) )
& ( ~ member(X16,intersection(X17,X18))
| member(X16,X18) )
& ( ~ member(X16,intersection(X17,X18))
| member(X16,X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])])]) ).
cnf(c_0_14,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(esk4_0,intersection(esk4_0,esk5_0))
| member(esk1_2(intersection(esk4_0,esk5_0),esk4_0),intersection(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(esk4_0,intersection(esk4_0,esk5_0))
| ~ member(esk1_2(intersection(esk4_0,esk5_0),esk4_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_16,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk1_2(esk4_0,intersection(esk4_0,esk5_0)),intersection(esk4_0,esk5_0))
| member(esk1_2(intersection(esk4_0,esk5_0),esk4_0),intersection(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk1_2(intersection(esk4_0,esk5_0),esk4_0),esk4_0)
| ~ member(esk1_2(esk4_0,intersection(esk4_0,esk5_0)),intersection(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk1_2(esk4_0,intersection(esk4_0,esk5_0)),intersection(esk4_0,esk5_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_20,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk1_2(esk4_0,intersection(esk4_0,esk5_0)),esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_23,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| member(esk1_2(intersection(esk4_0,esk5_0),esk4_0),intersection(esk4_0,esk5_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_11]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk1_2(intersection(esk4_0,esk5_0),esk4_0),esk4_0)
| member(esk1_2(esk4_0,intersection(esk4_0,esk5_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_25,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| member(esk1_2(intersection(esk4_0,esk5_0),esk4_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
~ subset(esk4_0,esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_22]) ).
cnf(c_0_27,plain,
( ~ equal_set(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,negated_conjecture,
( subset(esk4_0,esk5_0)
| equal_set(esk4_0,intersection(esk4_0,esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_29,negated_conjecture,
member(esk1_2(esk4_0,esk5_0),esk4_0),
inference(spm,[status(thm)],[c_0_26,c_0_11]) ).
cnf(c_0_30,negated_conjecture,
( subset(esk4_0,esk5_0)
| subset(esk4_0,intersection(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( ~ subset(esk4_0,X1)
| member(esk1_2(esk4_0,esk5_0),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
subset(esk4_0,intersection(esk4_0,esk5_0)),
inference(sr,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_33,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,negated_conjecture,
member(esk1_2(esk4_0,esk5_0),intersection(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
~ member(esk1_2(esk4_0,esk5_0),esk5_0),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET692+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.34 % Computer : n008.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8046.5625MB
% 0.11/0.34 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 05:33:08 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.39 Running first-order theorem proving
% 0.15/0.39 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Version: 3.5.1
% 0.15/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.42 % Starting sh5l with 300s (1) cores
% 0.15/0.42 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 240923 completed with status 0
% 0.15/0.42 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.42 % No SInE strategy applied
% 0.15/0.42 % Search class: FGHSF-FFMF21-SFFFFFNN
% 0.15/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.42 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.42 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S033N with 136s (1) cores
% 0.15/0.42 % G-E--_208_B00_00_F1_SE_CS_SP_PS_S033N with pid 240934 completed with status 0
% 0.15/0.42 % Result found by G-E--_208_B00_00_F1_SE_CS_SP_PS_S033N
% 0.15/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.42 % No SInE strategy applied
% 0.15/0.42 % Search class: FGHSF-FFMF21-SFFFFFNN
% 0.15/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.42 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.42 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S033N with 136s (1) cores
% 0.15/0.42 % Preprocessing time : 0.002 s
% 0.15/0.42 % Presaturation interreduction done
% 0.15/0.42
% 0.15/0.42 % Proof found!
% 0.15/0.42 % SZS status Theorem
% 0.15/0.42 % SZS output start CNFRefutation
% See solution above
% 0.15/0.43 % Parsed axioms : 12
% 0.15/0.43 % Removed by relevancy pruning/SinE : 0
% 0.15/0.43 % Initial clauses : 31
% 0.15/0.43 % Removed in clause preprocessing : 0
% 0.15/0.43 % Initial clauses in saturation : 31
% 0.15/0.43 % Processed clauses : 106
% 0.15/0.43 % ...of these trivial : 4
% 0.15/0.43 % ...subsumed : 4
% 0.15/0.43 % ...remaining for further processing : 98
% 0.15/0.43 % Other redundant clauses eliminated : 3
% 0.15/0.43 % Clauses deleted for lack of memory : 0
% 0.15/0.43 % Backward-subsumed : 12
% 0.15/0.43 % Backward-rewritten : 0
% 0.15/0.43 % Generated clauses : 142
% 0.15/0.43 % ...of the previous two non-redundant : 124
% 0.15/0.43 % ...aggressively subsumed : 0
% 0.15/0.43 % Contextual simplify-reflections : 4
% 0.15/0.43 % Paramodulations : 134
% 0.15/0.43 % Factorizations : 0
% 0.15/0.43 % NegExts : 0
% 0.15/0.43 % Equation resolutions : 3
% 0.15/0.43 % Disequality decompositions : 0
% 0.15/0.43 % Total rewrite steps : 9
% 0.15/0.43 % ...of those cached : 2
% 0.15/0.43 % Propositional unsat checks : 0
% 0.15/0.43 % Propositional check models : 0
% 0.15/0.43 % Propositional check unsatisfiable : 0
% 0.15/0.43 % Propositional clauses : 0
% 0.15/0.43 % Propositional clauses after purity: 0
% 0.15/0.43 % Propositional unsat core size : 0
% 0.15/0.43 % Propositional preprocessing time : 0.000
% 0.15/0.43 % Propositional encoding time : 0.000
% 0.15/0.43 % Propositional solver time : 0.000
% 0.15/0.43 % Success case prop preproc time : 0.000
% 0.15/0.43 % Success case prop encoding time : 0.000
% 0.15/0.43 % Success case prop solver time : 0.000
% 0.15/0.43 % Current number of processed clauses : 47
% 0.15/0.43 % Positive orientable unit clauses : 11
% 0.15/0.43 % Positive unorientable unit clauses: 0
% 0.15/0.43 % Negative unit clauses : 3
% 0.15/0.43 % Non-unit-clauses : 33
% 0.15/0.43 % Current number of unprocessed clauses: 77
% 0.15/0.43 % ...number of literals in the above : 201
% 0.15/0.43 % Current number of archived formulas : 0
% 0.15/0.43 % Current number of archived clauses : 48
% 0.15/0.43 % Clause-clause subsumption calls (NU) : 623
% 0.15/0.43 % Rec. Clause-clause subsumption calls : 573
% 0.15/0.43 % Non-unit clause-clause subsumptions : 10
% 0.15/0.43 % Unit Clause-clause subsumption calls : 35
% 0.15/0.43 % Rewrite failures with RHS unbound : 0
% 0.15/0.43 % BW rewrite match attempts : 3
% 0.15/0.43 % BW rewrite match successes : 0
% 0.15/0.43 % Condensation attempts : 0
% 0.15/0.43 % Condensation successes : 0
% 0.15/0.43 % Termbank termtop insertions : 3597
% 0.15/0.43 % Search garbage collected termcells : 473
% 0.15/0.43
% 0.15/0.43 % -------------------------------------------------
% 0.15/0.43 % User time : 0.012 s
% 0.15/0.43 % System time : 0.003 s
% 0.15/0.43 % Total time : 0.015 s
% 0.15/0.43 % Maximum resident set size: 3648 pages
% 0.15/0.43
% 0.15/0.43 % -------------------------------------------------
% 0.15/0.43 % User time : 0.047 s
% 0.15/0.43 % System time : 0.018 s
% 0.15/0.43 % Total time : 0.065 s
% 0.15/0.43 % Maximum resident set size: 4864 pages
% 0.15/0.43 % E exiting
%------------------------------------------------------------------------------