%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU594^2 : 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 : n012.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 08:24:39 AM UTC 2026
% Result : Theorem 0.04s 0.17s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 16 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 198 ( 16 ~; 14 |; 6 &; 134 @)
% ( 5 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 60 ( 13 ^; 47 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
in__Cong: $o ).
thf(decl_26,type,
subset: $i > $i > $o ).
thf(decl_27,type,
subsetI1: $o ).
thf(decl_28,type,
binintersect: $i > $i > $i ).
thf(decl_29,type,
binintersectEL: $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(binintersect,axiom,
( binintersect
= ( ^ [X1: $i,X2: $i] :
( dsetconstr @ X1
@ ^ [X3: $i] : ( in @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Eqb0a1uOM8/E---3.1_142136.p',binintersect) ).
thf(binintersectSubset3,conjecture,
( in__Cong
=> ( subsetI1
=> ( binintersectEL
=> ! [X1: $i,X2: $i] :
( ( ( binintersect @ X1 @ X2 )
= X2 )
=> ( subset @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Eqb0a1uOM8/E---3.1_142136.p',binintersectSubset3) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Eqb0a1uOM8/E---3.1_142136.p',binintersectEL) ).
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.Eqb0a1uOM8/E---3.1_142136.p',subsetI1) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
<=> ( in @ X4 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Eqb0a1uOM8/E---3.1_142136.p',in__Cong) ).
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,
~ ( in__Cong
=> ( subsetI1
=> ( binintersectEL
=> ! [X1: $i,X2: $i] :
( ( ( binintersect @ X1 @ X2 )
= X2 )
=> ( subset @ X2 @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[binintersectSubset3]) ).
thf(c_0_7,axiom,
( binintersectEL
= ( ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( in @ Z0 @ X2 ) ) )
=> ( in @ X3 @ X1 ) ) ) ),
inference(apply_def,[status(thm)],[binintersectEL,c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X17: $i,X18: $i] :
( ( X17 = X18 )
=> ! [X19: $i,X20: $i] :
( ( X19 = X20 )
=> ( ( in @ X19 @ X17 )
<=> ( in @ X20 @ X18 ) ) ) )
=> ( ! [X21: $i,X22: $i] :
( ! [X23: $i] :
( ( in @ X23 @ X21 )
=> ( in @ X23 @ X22 ) )
=> ( subset @ X21 @ X22 ) )
=> ( ! [X24: $i,X25: $i,X26: $i] :
( ( in @ X26
@ ( dsetconstr @ X24
@ ^ [Z0: $i] : ( in @ Z0 @ X25 ) ) )
=> ( in @ X26 @ X24 ) )
=> ! [X1: $i,X2: $i] :
( ( ( dsetconstr @ X1
@ ^ [Z0: $i] : ( in @ Z0 @ X2 ) )
= X2 )
=> ( subset @ X2 @ X1 ) ) ) ) ),
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_7]),c_0_5]),subsetI1]),in__Cong]) ).
thf(c_0_9,negated_conjecture,
! [X27: $i,X28: $i,X29: $i,X30: $i,X31: $i,X32: $i,X34: $i,X35: $i,X36: $i] :
( ( ~ ( in @ X29 @ X27 )
| ( in @ X30 @ X28 )
| ( X29 != X30 )
| ( X27 != X28 ) )
& ( ~ ( in @ X30 @ X28 )
| ( in @ X29 @ X27 )
| ( X29 != X30 )
| ( X27 != X28 ) )
& ( ( in @ ( esk1_2 @ X31 @ X32 ) @ X31 )
| ( subset @ X31 @ X32 ) )
& ( ~ ( in @ ( esk1_2 @ X31 @ X32 ) @ X32 )
| ( subset @ X31 @ X32 ) )
& ( ~ ( in @ X36
@ ( dsetconstr @ X34
@ ^ [Z0: $i] : ( in @ Z0 @ X35 ) ) )
| ( in @ X36 @ X34 ) )
& ( ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ Z0 @ esk3_0 ) )
= esk3_0 )
& ~ ( subset @ esk3_0 @ esk2_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,X3: $i] :
( ( in @ X1 @ X2 )
| ~ ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ Z0 @ X3 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ Z0 @ esk3_0 ) )
= esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
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_9]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk2_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,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_15,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_16,negated_conjecture,
~ ( subset @ esk3_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU594^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.13 % Computer : n012.cluster.edu
% 0.04/0.13 % Model : x86_64 x86_64
% 0.04/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.13 % Memory : 8046.5625MB
% 0.04/0.13 % OS : Linux 6.8.0-71-generic
% 0.04/0.13 % CPULimit : 300
% 0.04/0.13 % WCLimit : 300
% 0.04/0.13 % DateTime : Tue Sep 29 13:53:48 UTC 2026
% 0.04/0.13 % CPUTime :
% 0.04/0.13 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.15 Running higher-order theorem proving
% 0.04/0.16 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.Eqb0a1uOM8/E---3.1_142136.p
% 0.04/0.17 % Version: 3.5.1-ho
% 0.04/0.17 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.04/0.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.17 % Starting new_ho_10 with 1500s (5) cores
% 0.04/0.17 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.04/0.17 % Starting lpo1_def_fix with 300s (1) cores
% 0.04/0.17 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.04/0.17 % ehoh_best_sine_rwall with pid 142150 completed with status 0
% 0.04/0.17 % Result found by ehoh_best_sine_rwall
% 0.04/0.17 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.04/0.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.17 % Starting new_ho_10 with 1500s (5) cores
% 0.04/0.17 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.04/0.17 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.04/0.17 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.04/0.17 % Search class: HGUSF-FFSF22-MSFFMFNN
% 0.04/0.17 % partial match(1): HGUSF-FFSF22-SSFFMFNN
% 0.04/0.17 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.04/0.17 % Starting SubtermCWHack with 28s (1) cores
% 0.04/0.17 % SubtermCWHack with pid 142153 completed with status 0
% 0.04/0.17 % Result found by SubtermCWHack
% 0.04/0.17 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.04/0.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.17 % Starting new_ho_10 with 1500s (5) cores
% 0.04/0.17 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.04/0.17 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.04/0.17 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.04/0.17 % Search class: HGUSF-FFSF22-MSFFMFNN
% 0.04/0.17 % partial match(1): HGUSF-FFSF22-SSFFMFNN
% 0.04/0.17 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.04/0.17 % Starting SubtermCWHack with 28s (1) cores
% 0.04/0.17 % Preprocessing time : 0.001 s
% 0.04/0.17
% 0.04/0.17 % Proof found!
% 0.04/0.17 % SZS status Theorem
% 0.04/0.17 % SZS output start CNFRefutation
% See solution above
% 0.04/0.17 % Parsed axioms : 12
% 0.04/0.17 % Removed by relevancy pruning/SinE : 7
% 0.04/0.17 % Initial clauses : 7
% 0.04/0.17 % Removed in clause preprocessing : 2
% 0.04/0.17 % Initial clauses in saturation : 5
% 0.04/0.17 % Processed clauses : 8
% 0.04/0.17 % ...of these trivial : 0
% 0.04/0.17 % ...subsumed : 0
% 0.04/0.17 % ...remaining for further processing : 8
% 0.04/0.17 % Other redundant clauses eliminated : 0
% 0.04/0.17 % Clauses deleted for lack of memory : 0
% 0.04/0.17 % Backward-subsumed : 0
% 0.04/0.17 % Backward-rewritten : 0
% 0.04/0.17 % Generated clauses : 5
% 0.04/0.17 % ...of the previous two non-redundant : 4
% 0.04/0.17 % ...aggressively subsumed : 0
% 0.04/0.17 % Contextual simplify-reflections : 0
% 0.04/0.17 % Paramodulations : 5
% 0.04/0.17 % Factorizations : 0
% 0.04/0.17 % NegExts : 0
% 0.04/0.17 % Equation resolutions : 0
% 0.04/0.17 % Disequality decompositions : 0
% 0.04/0.17 % Total rewrite steps : 0
% 0.04/0.17 % ...of those cached : 0
% 0.04/0.17 % Propositional unsat checks : 0
% 0.04/0.17 % Propositional check models : 0
% 0.04/0.17 % Propositional check unsatisfiable : 0
% 0.04/0.17 % Propositional clauses : 0
% 0.04/0.17 % Propositional clauses after purity: 0
% 0.04/0.17 % Propositional unsat core size : 0
% 0.04/0.17 % Propositional preprocessing time : 0.000
% 0.04/0.17 % Propositional encoding time : 0.000
% 0.04/0.17 % Propositional solver time : 0.000
% 0.04/0.17 % Success case prop preproc time : 0.000
% 0.04/0.17 % Success case prop encoding time : 0.000
% 0.04/0.17 % Success case prop solver time : 0.000
% 0.04/0.17 % Current number of processed clauses : 8
% 0.04/0.17 % Positive orientable unit clauses : 2
% 0.04/0.17 % Positive unorientable unit clauses: 0
% 0.04/0.17 % Negative unit clauses : 1
% 0.04/0.17 % Non-unit-clauses : 5
% 0.04/0.17 % Current number of unprocessed clauses: 1
% 0.04/0.17 % ...number of literals in the above : 2
% 0.04/0.17 % Current number of archived formulas : 0
% 0.04/0.17 % Current number of archived clauses : 0
% 0.04/0.17 % Clause-clause subsumption calls (NU) : 3
% 0.04/0.17 % Rec. Clause-clause subsumption calls : 3
% 0.04/0.17 % Non-unit clause-clause subsumptions : 0
% 0.04/0.17 % Unit Clause-clause subsumption calls : 2
% 0.04/0.17 % Rewrite failures with RHS unbound : 0
% 0.04/0.17 % BW rewrite match attempts : 2
% 0.04/0.17 % BW rewrite match successes : 0
% 0.04/0.17 % Condensation attempts : 0
% 0.04/0.17 % Condensation successes : 0
% 0.04/0.17 % Termbank termtop insertions : 974
% 0.04/0.17 % Search garbage collected termcells : 333
% 0.04/0.17
% 0.04/0.17 % -------------------------------------------------
% 0.04/0.17 % User time : 0.001 s
% 0.04/0.17 % System time : 0.002 s
% 0.04/0.17 % Total time : 0.003 s
% 0.04/0.17 % Maximum resident set size: 3592 pages
% 0.04/0.17
% 0.04/0.17 % -------------------------------------------------
% 0.04/0.17 % User time : 0.002 s
% 0.04/0.17 % System time : 0.004 s
% 0.04/0.17 % Total time : 0.007 s
% 0.04/0.17 % Maximum resident set size: 4864 pages
% 0.04/0.17 % E exiting
%------------------------------------------------------------------------------