%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU598^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 : Wed Sep 30 08:24:40 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 10 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 329 ( 25 ~; 26 |; 7 &; 232 @)
% ( 5 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 79 ( 0 ^; 79 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
subset: $i > $i > $o ).
thf(decl_25,type,
subsetI1: $o ).
thf(decl_26,type,
subsetE: $o ).
thf(decl_27,type,
setextsub: $o ).
thf(decl_28,type,
binintersect: $i > $i > $i ).
thf(decl_29,type,
binintersectI: $o ).
thf(decl_30,type,
binintersectRsub: $o ).
thf(decl_31,type,
esk1_2: $i > $i > $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(binintersectSubset4,conjecture,
( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectRsub
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ X1 )
=> ( ( binintersect @ X1 @ X2 )
= X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f2ac56oURW/E---3.1_1323375.p',binintersectSubset4) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X1 )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f2ac56oURW/E---3.1_1323375.p',setextsub) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f2ac56oURW/E---3.1_1323375.p',subsetI1) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f2ac56oURW/E---3.1_1323375.p',subsetE) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f2ac56oURW/E---3.1_1323375.p',binintersectI) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.f2ac56oURW/E---3.1_1323375.p',binintersectRsub) ).
thf(c_0_6,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectRsub
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ X1 )
=> ( ( binintersect @ X1 @ X2 )
= X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[binintersectSubset4]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X19: $i,X20: $i] :
( ! [X21: $i] :
( ( in @ X21 @ X19 )
=> ( in @ X21 @ X20 ) )
=> ( subset @ X19 @ X20 ) )
=> ( ! [X22: $i,X23: $i,X24: $i] :
( ( subset @ X22 @ X23 )
=> ( ( in @ X24 @ X22 )
=> ( in @ X24 @ X23 ) ) )
=> ( ! [X25: $i,X26: $i] :
( ( subset @ X25 @ X26 )
=> ( ( subset @ X26 @ X25 )
=> ( X25 = X26 ) ) )
=> ( ! [X27: $i,X28: $i,X29: $i] :
( ( in @ X29 @ X27 )
=> ( ( in @ X29 @ X28 )
=> ( in @ X29 @ ( binintersect @ X27 @ X28 ) ) ) )
=> ( ! [X30: $i,X31: $i] : ( subset @ ( binintersect @ X30 @ X31 ) @ X31 )
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ X1 )
=> ( ( binintersect @ X1 @ X2 )
= X2 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,setextsub]),subsetI1]),subsetE]),binintersectI]),binintersectRsub]) ).
thf(c_0_8,negated_conjecture,
! [X32: $i,X33: $i,X35: $i,X36: $i,X37: $i,X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i] :
( ( ( in @ ( esk1_2 @ X32 @ X33 ) @ X32 )
| ( subset @ X32 @ X33 ) )
& ( ~ ( in @ ( esk1_2 @ X32 @ X33 ) @ X33 )
| ( subset @ X32 @ X33 ) )
& ( ~ ( subset @ X35 @ X36 )
| ~ ( in @ X37 @ X35 )
| ( in @ X37 @ X36 ) )
& ( ~ ( subset @ X38 @ X39 )
| ~ ( subset @ X39 @ X38 )
| ( X38 = X39 ) )
& ( ~ ( in @ X42 @ X40 )
| ~ ( in @ X42 @ X41 )
| ( in @ X42 @ ( binintersect @ X40 @ X41 ) ) )
& ( subset @ ( binintersect @ X43 @ X44 ) @ X44 )
& ( subset @ esk3_0 @ esk2_0 )
& ( ( binintersect @ esk2_0 @ esk3_0 )
!= 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_7])])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
subset @ esk3_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
| ~ ( in @ ( esk1_2 @ X1 @ X2 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk2_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ X1 @ X2 )
| ~ ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 )
| ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ ( binintersect @ X2 @ X3 ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] :
( ( subset @ X1 @ esk2_0 )
| ~ ( in @ ( esk1_2 @ X1 @ esk2_0 ) @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ ( esk1_2 @ ( binintersect @ X1 @ X2 ) @ X3 ) @ X2 )
| ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( subset @ X1 @ ( binintersect @ X2 @ X3 ) )
| ~ ( in @ ( esk1_2 @ X1 @ ( binintersect @ X2 @ X3 ) ) @ X3 )
| ~ ( in @ ( esk1_2 @ X1 @ ( binintersect @ X2 @ X3 ) ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] : ( subset @ ( binintersect @ X1 @ esk3_0 ) @ esk2_0 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ ( binintersect @ X2 @ X1 ) )
| ~ ( in @ ( esk1_2 @ X1 @ ( binintersect @ X2 @ X1 ) ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ esk2_0 )
| ~ ( in @ X1 @ ( binintersect @ X2 @ esk3_0 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
thf(c_0_23,negated_conjecture,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( subset @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] : ( subset @ X1 @ ( binintersect @ X1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ ( binintersect @ X1 @ esk3_0 ) @ X2 ) @ esk2_0 )
| ( subset @ ( binintersect @ X1 @ esk3_0 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i] :
( ( binintersect @ X1 @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_11])]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk1_2 @ esk3_0 @ X1 ) @ esk2_0 )
| ( subset @ esk3_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_28,negated_conjecture,
subset @ esk3_0 @ ( binintersect @ esk2_0 @ esk3_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
thf(c_0_29,negated_conjecture,
( ( binintersect @ esk2_0 @ esk3_0 )
!= esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_28]),c_0_11])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU598^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:58:52 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.f2ac56oURW/E---3.1_1323375.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.25 % Starting post_as_ho2 with 300s (1) cores
% 0.08/0.25 % post_as_ho8 with pid 1323389 completed with status 0
% 0.08/0.25 % Result found by post_as_ho8
% 0.08/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.08/0.25 % Search class: HGUSF-FFSF22-SFFFMFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 1323394 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.08/0.25 % Search class: HGUSF-FFSF22-SFFFMFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 14
% 0.08/0.25 % Removed by relevancy pruning/SinE : 8
% 0.08/0.25 % Initial clauses : 8
% 0.08/0.25 % Removed in clause preprocessing : 0
% 0.08/0.25 % Initial clauses in saturation : 8
% 0.08/0.25 % Processed clauses : 37
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 6
% 0.08/0.25 % ...remaining for further processing : 31
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 0
% 0.08/0.25 % Backward-rewritten : 1
% 0.08/0.25 % Generated clauses : 82
% 0.08/0.25 % ...of the previous two non-redundant : 63
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 82
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 16
% 0.08/0.25 % ...of those cached : 8
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 30
% 0.08/0.25 % Positive orientable unit clauses : 8
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 1
% 0.08/0.25 % Non-unit-clauses : 21
% 0.08/0.25 % Current number of unprocessed clauses: 32
% 0.08/0.25 % ...number of literals in the above : 64
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 1
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 57
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 57
% 0.08/0.25 % Non-unit clause-clause subsumptions : 6
% 0.08/0.25 % Unit Clause-clause subsumption calls : 21
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 21
% 0.08/0.25 % BW rewrite match successes : 1
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 2094
% 0.08/0.25 % Search garbage collected termcells : 397
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.004 s
% 0.08/0.25 % System time : 0.002 s
% 0.08/0.25 % Total time : 0.006 s
% 0.08/0.25 % Maximum resident set size: 3636 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.007 s
% 0.08/0.25 % System time : 0.005 s
% 0.08/0.25 % Total time : 0.013 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------