%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU590^2 : 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 : 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 : Wed Sep 30 08:26:50 AM UTC 2026
% Result : Theorem 0.11s 0.25s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 3 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 315 ( 22 ~; 19 |; 6 &; 236 @)
% ( 3 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 78 ( 22 ^; 56 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
subset: $i > $i > $o ).
thf(decl_26,type,
subsetI1: $o ).
thf(decl_27,type,
subsetE: $o ).
thf(decl_28,type,
binintersect: $i > $i > $i ).
thf(decl_29,type,
binintersectI: $o ).
thf(decl_30,type,
esk1_2: $i > $i > $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
esk4_0: $i ).
thf(binintersect,axiom,
( binintersect
= ( ^ [X1: $i,X2: $i] :
( dsetconstr @ X1
@ ^ [X3: $i] : ( in @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZyJBIpj9UY/E---3.1_3193165.p',binintersect) ).
thf(binintersectSubset5,conjecture,
( subsetI1
=> ( subsetE
=> ( binintersectI
=> ! [X1: $i,X2: $i,X4: $i] :
( ( subset @ X4 @ X1 )
=> ( ( subset @ X4 @ X2 )
=> ( subset @ X4 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZyJBIpj9UY/E---3.1_3193165.p',binintersectSubset5) ).
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.ZyJBIpj9UY/E---3.1_3193165.p',binintersectI) ).
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.ZyJBIpj9UY/E---3.1_3193165.p',subsetE) ).
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.ZyJBIpj9UY/E---3.1_3193165.p',subsetI1) ).
thf(c_0_5,plain,
( binintersect
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ Z0
@ ^ [Z2: $i] : ( in @ Z2 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[binintersect]) ).
thf(c_0_6,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( binintersectI
=> ! [X1: $i,X2: $i,X4: $i] :
( ( subset @ X4 @ X1 )
=> ( ( subset @ X4 @ X2 )
=> ( subset @ X4 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[binintersectSubset5]) ).
thf(c_0_7,axiom,
( binintersectI
= ( ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( in @ Z0 @ X2 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[binintersectI,c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X17: $i,X18: $i] :
( ! [X19: $i] :
( ( in @ X19 @ X17 )
=> ( in @ X19 @ X18 ) )
=> ( subset @ X17 @ X18 ) )
=> ( ! [X20: $i,X21: $i,X22: $i] :
( ( subset @ X20 @ X21 )
=> ( ( in @ X22 @ X20 )
=> ( in @ X22 @ X21 ) ) )
=> ( ! [X23: $i,X24: $i,X25: $i] :
( ( in @ X25 @ X23 )
=> ( ( in @ X25 @ X24 )
=> ( in @ X25
@ ( dsetconstr @ X23
@ ^ [Z0: $i] : ( in @ Z0 @ X24 ) ) ) ) )
=> ! [X1: $i,X2: $i,X4: $i] :
( ( subset @ X4 @ X1 )
=> ( ( subset @ X4 @ X2 )
=> ( subset @ X4
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( in @ Z0 @ X2 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_5]),subsetE]),subsetI1]),c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X26: $i,X27: $i,X29: $i,X30: $i,X31: $i,X32: $i,X33: $i,X34: $i] :
( ( ( in @ ( esk1_2 @ X26 @ X27 ) @ X26 )
| ( subset @ X26 @ X27 ) )
& ( ~ ( in @ ( esk1_2 @ X26 @ X27 ) @ X27 )
| ( subset @ X26 @ X27 ) )
& ( ~ ( subset @ X29 @ X30 )
| ~ ( in @ X31 @ X29 )
| ( in @ X31 @ X30 ) )
& ( ~ ( in @ X34 @ X32 )
| ~ ( in @ X34 @ X33 )
| ( in @ X34
@ ( dsetconstr @ X32
@ ^ [Z0: $i] : ( in @ Z0 @ X33 ) ) ) )
& ( subset @ esk4_0 @ esk2_0 )
& ( subset @ esk4_0 @ esk3_0 )
& ~ ( subset @ esk4_0
@ ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ Z0 @ 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_8])])])])])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
| ~ ( in @ ( esk1_2 @ X1 @ X2 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ Z0 @ X3 ) ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
subset @ esk4_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( subset @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ Z0 @ X3 ) ) )
| ~ ( in
@ ( esk1_2 @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ Z0 @ X3 ) ) )
@ X3 )
| ~ ( in
@ ( esk1_2 @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ Z0 @ X3 ) ) )
@ X2 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk3_0 )
| ~ ( in @ X1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ Z0 @ esk3_0 ) ) )
| ~ ( in
@ ( esk1_2 @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ Z0 @ esk3_0 ) ) )
@ esk4_0 )
| ~ ( in
@ ( esk1_2 @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ Z0 @ esk3_0 ) ) )
@ X2 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 )
| ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_18,negated_conjecture,
subset @ esk4_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
( ( subset @ esk4_0
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( in @ Z0 @ esk3_0 ) ) )
| ~ ( in
@ ( esk1_2 @ esk4_0
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( in @ Z0 @ esk3_0 ) ) )
@ X1 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk2_0 )
| ~ ( in @ X1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
thf(c_0_21,negated_conjecture,
~ ( subset @ esk4_0
@ ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ Z0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_22,negated_conjecture,
~ ( in
@ ( esk1_2 @ esk4_0
@ ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ Z0 @ esk3_0 ) ) )
@ esk4_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_17]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU590^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n008.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 13:54:39 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.23 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.ZyJBIpj9UY/E---3.1_3193165.p
% 0.11/0.25 % Version: 3.5.1-ho
% 0.11/0.25 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.11/0.25 % Starting lpo1_def_fix with 300s (1) cores
% 0.11/0.25 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.11/0.25 % ehoh_best_sine_rwall with pid 3193179 completed with status 0
% 0.11/0.25 % Result found by ehoh_best_sine_rwall
% 0.11/0.25 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.11/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.25 % Search class: HGUNF-FFSF22-MSFFMFNN
% 0.11/0.25 % partial match(1): HGUNF-FFSF22-SSFFMFNN
% 0.11/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.25 % SubtermCWHack with pid 3193183 completed with status 0
% 0.11/0.25 % Result found by SubtermCWHack
% 0.11/0.25 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.11/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.25 % Search class: HGUNF-FFSF22-MSFFMFNN
% 0.11/0.25 % partial match(1): HGUNF-FFSF22-SSFFMFNN
% 0.11/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.25 % Preprocessing time : 0.001 s
% 0.11/0.25
% 0.11/0.25 % Proof found!
% 0.11/0.25 % SZS status Theorem
% 0.11/0.25 % SZS output start CNFRefutation
% See solution above
% 0.11/0.25 % Parsed axioms : 12
% 0.11/0.25 % Removed by relevancy pruning/SinE : 7
% 0.11/0.25 % Initial clauses : 7
% 0.11/0.25 % Removed in clause preprocessing : 0
% 0.11/0.25 % Initial clauses in saturation : 7
% 0.11/0.25 % Processed clauses : 28
% 0.11/0.25 % ...of these trivial : 0
% 0.11/0.25 % ...subsumed : 0
% 0.11/0.25 % ...remaining for further processing : 28
% 0.11/0.25 % Other redundant clauses eliminated : 0
% 0.11/0.25 % Clauses deleted for lack of memory : 0
% 0.11/0.25 % Backward-subsumed : 0
% 0.11/0.25 % Backward-rewritten : 0
% 0.11/0.25 % Generated clauses : 49
% 0.11/0.25 % ...of the previous two non-redundant : 43
% 0.11/0.25 % ...aggressively subsumed : 0
% 0.11/0.25 % Contextual simplify-reflections : 0
% 0.11/0.25 % Paramodulations : 49
% 0.11/0.25 % Factorizations : 0
% 0.11/0.25 % NegExts : 0
% 0.11/0.25 % Equation resolutions : 0
% 0.11/0.25 % Disequality decompositions : 0
% 0.11/0.25 % Total rewrite steps : 4
% 0.11/0.25 % ...of those cached : 0
% 0.11/0.25 % Propositional unsat checks : 0
% 0.11/0.25 % Propositional check models : 0
% 0.11/0.25 % Propositional check unsatisfiable : 0
% 0.11/0.25 % Propositional clauses : 0
% 0.11/0.25 % Propositional clauses after purity: 0
% 0.11/0.25 % Propositional unsat core size : 0
% 0.11/0.25 % Propositional preprocessing time : 0.000
% 0.11/0.25 % Propositional encoding time : 0.000
% 0.11/0.25 % Propositional solver time : 0.000
% 0.11/0.25 % Success case prop preproc time : 0.000
% 0.11/0.25 % Success case prop encoding time : 0.000
% 0.11/0.25 % Success case prop solver time : 0.000
% 0.11/0.25 % Current number of processed clauses : 28
% 0.11/0.25 % Positive orientable unit clauses : 7
% 0.11/0.25 % Positive unorientable unit clauses: 0
% 0.11/0.25 % Negative unit clauses : 2
% 0.11/0.25 % Non-unit-clauses : 19
% 0.11/0.25 % Current number of unprocessed clauses: 22
% 0.11/0.25 % ...number of literals in the above : 53
% 0.11/0.25 % Current number of archived formulas : 0
% 0.11/0.25 % Current number of archived clauses : 0
% 0.11/0.25 % Clause-clause subsumption calls (NU) : 73
% 0.11/0.25 % Rec. Clause-clause subsumption calls : 72
% 0.11/0.25 % Non-unit clause-clause subsumptions : 0
% 0.11/0.25 % Unit Clause-clause subsumption calls : 12
% 0.11/0.25 % Rewrite failures with RHS unbound : 0
% 0.11/0.25 % BW rewrite match attempts : 8
% 0.11/0.25 % BW rewrite match successes : 0
% 0.11/0.25 % Condensation attempts : 0
% 0.11/0.25 % Condensation successes : 0
% 0.11/0.25 % Termbank termtop insertions : 2054
% 0.11/0.25 % Search garbage collected termcells : 323
% 0.11/0.25
% 0.11/0.25 % -------------------------------------------------
% 0.11/0.25 % User time : 0.005 s
% 0.11/0.25 % System time : 0.003 s
% 0.11/0.25 % Total time : 0.008 s
% 0.11/0.25 % Maximum resident set size: 3584 pages
% 0.11/0.25
% 0.11/0.25 % -------------------------------------------------
% 0.11/0.25 % User time : 0.008 s
% 0.11/0.25 % System time : 0.006 s
% 0.11/0.25 % Total time : 0.014 s
% 0.11/0.25 % Maximum resident set size: 4864 pages
% 0.11/0.25 % E exiting
%------------------------------------------------------------------------------