%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU683^2 : 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 : n005.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 08:25:01 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 25 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 222 ( 15 ~; 11 |; 13 &; 151 @)
% ( 3 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 60 ( 17 ^; 38 !; 5 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
setadjoin: $i > $i > $i ).
thf(decl_26,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_27,type,
dsetconstrI: $o ).
thf(decl_28,type,
uniqinunit: $o ).
thf(decl_29,type,
singleton: $i > $o ).
thf(decl_30,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_31,type,
esk1_0: $i ).
thf(decl_32,type,
epred1_0: $i > $o ).
thf(decl_33,type,
esk2_0: $i ).
thf(decl_34,type,
esk3_0: $i ).
thf(decl_35,type,
esk4_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X2: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HBbILujq71/E---3.1_1722830.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X1
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HBbILujq71/E---3.1_1722830.p',singleton) ).
thf(ex1E2,conjecture,
( dsetconstrI
=> ( uniqinunit
=> ! [X1: $i,X2: $i > $o] :
( ( ex1 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HBbILujq71/E---3.1_1722830.p',ex1E2) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HBbILujq71/E---3.1_1722830.p',dsetconstrI) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X3: $i,X4: $i] :
( ( in @ X3 @ ( setadjoin @ X4 @ emptyset ) )
=> ( X3 = X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HBbILujq71/E---3.1_1722830.p',uniqinunit) ).
thf(c_0_5,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X14: $i] :
( ( in @ X14
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X14 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_6,plain,
( singleton
= ( ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ( Z0
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_7,negated_conjecture,
~ ( dsetconstrI
=> ( uniqinunit
=> ! [X1: $i,X2: $i > $o] :
( ( ex1 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[ex1E2]) ).
thf(c_0_8,plain,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_9,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X14: $i] :
( ( in @ X14
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X14 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_10,negated_conjecture,
~ ( ! [X15: $i,X16: $i > $o,X17: $i] :
( ( in @ X17 @ X15 )
=> ( ( X16 @ X17 )
=> ( in @ X17 @ ( dsetconstr @ X15 @ X16 ) ) ) )
=> ( ! [X18: $i,X19: $i] :
( ( in @ X18 @ ( setadjoin @ X19 @ emptyset ) )
=> ( X18 = X19 ) )
=> ! [X1: $i,X2: $i > $o] :
( ? [X20: $i] :
( ( in @ X20 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X20 @ emptyset ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7]),c_0_8]),uniqinunit]),c_0_9])]) ).
thf(c_0_11,negated_conjecture,
! [X21: $i,X22: $i > $o,X23: $i,X24: $i,X25: $i] :
( ( ~ ( in @ X23 @ X21 )
| ~ ( X22 @ X23 )
| ( in @ X23 @ ( dsetconstr @ X21 @ X22 ) ) )
& ( ~ ( in @ X24 @ ( setadjoin @ X25 @ emptyset ) )
| ( X24 = X25 ) )
& ( in @ esk2_0 @ ( dsetconstr @ esk1_0 @ epred1_0 ) )
& ( ( dsetconstr @ esk1_0 @ epred1_0 )
= ( setadjoin @ esk2_0 @ emptyset ) )
& ( in @ esk3_0 @ esk1_0 )
& ( in @ esk4_0 @ esk1_0 )
& ( epred1_0 @ esk3_0 )
& ( epred1_0 @ esk4_0 )
& ( esk3_0 != esk4_0 ) ),
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_10])])])])]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X3: $i] :
( ( X1 = X3 )
| ~ ( in @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
( ( dsetconstr @ esk1_0 @ epred1_0 )
= ( setadjoin @ esk2_0 @ emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
( ( X1 = esk2_0 )
| ~ ( in @ X1 @ ( dsetconstr @ esk1_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
| ~ ( in @ X1 @ X3 )
| ~ ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( X1 = esk2_0 )
| ~ ( in @ X1 @ esk1_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_17,negated_conjecture,
in @ esk4_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,negated_conjecture,
epred1_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_19,negated_conjecture,
esk2_0 = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] :
( ( X1 = esk4_0 )
| ~ ( in @ X1 @ esk1_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(rw,[status(thm)],[c_0_16,c_0_19]) ).
thf(c_0_21,negated_conjecture,
in @ esk3_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_22,negated_conjecture,
epred1_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_23,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU683^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n005.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 14:08:16 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.22 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.HBbILujq71/E---3.1_1722830.p
% 0.10/0.24 % Version: 3.5.1-ho
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLMNHSA.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % Starting new_ho_7 with 300s (1) cores
% 0.10/0.24 % Starting lpo8_lambda_fix with 300s (1) cores
% 0.10/0.24 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.10/0.24 % new_ho_10 with pid 1722843 completed with status 0
% 0.10/0.24 % Result found by new_ho_10
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLMNHSA.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.24 % No SInE strategy applied
% 0.10/0.24 % Search class: HHUSF-FFSM22-SHSFMSBN
% 0.10/0.24 % partial match(2): HHUSF-FFSF32-SHSFMSBN
% 0.10/0.24 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.24 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.24 % Starting new_ho_10 with 901s (1) cores
% 0.10/0.24 % Starting sh5l with 151s (1) cores
% 0.10/0.24 % Starting ehoh_best_sine_rwall with 151s (1) cores
% 0.10/0.24 % Starting lpo1_def_fix with 146s (1) cores
% 0.10/0.24 % SubtermCWHack with pid 1722847 completed with status 0
% 0.10/0.24 % Result found by SubtermCWHack
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLMNHSA.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.24 % No SInE strategy applied
% 0.10/0.24 % Search class: HHUSF-FFSM22-SHSFMSBN
% 0.10/0.24 % partial match(2): HHUSF-FFSF32-SHSFMSBN
% 0.10/0.24 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.24 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.24 % Preprocessing time : 0.001 s
% 0.10/0.24
% 0.10/0.24 % Proof found!
% 0.10/0.24 % SZS status Theorem
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24 % Parsed axioms : 13
% 0.10/0.24 % Removed by relevancy pruning/SinE : 0
% 0.10/0.24 % Initial clauses : 17
% 0.10/0.24 % Removed in clause preprocessing : 8
% 0.10/0.24 % Initial clauses in saturation : 9
% 0.10/0.24 % Processed clauses : 15
% 0.10/0.24 % ...of these trivial : 0
% 0.10/0.24 % ...subsumed : 0
% 0.10/0.24 % ...remaining for further processing : 15
% 0.10/0.24 % Other redundant clauses eliminated : 0
% 0.10/0.24 % Clauses deleted for lack of memory : 0
% 0.10/0.24 % Backward-subsumed : 0
% 0.10/0.24 % Backward-rewritten : 4
% 0.10/0.24 % Generated clauses : 6
% 0.10/0.24 % ...of the previous two non-redundant : 9
% 0.10/0.24 % ...aggressively subsumed : 0
% 0.10/0.24 % Contextual simplify-reflections : 0
% 0.10/0.24 % Paramodulations : 6
% 0.10/0.24 % Factorizations : 0
% 0.10/0.24 % NegExts : 0
% 0.10/0.24 % Equation resolutions : 0
% 0.10/0.24 % Disequality decompositions : 0
% 0.10/0.24 % Total rewrite steps : 7
% 0.10/0.24 % ...of those cached : 4
% 0.10/0.24 % Propositional unsat checks : 0
% 0.10/0.24 % Propositional check models : 0
% 0.10/0.24 % Propositional check unsatisfiable : 0
% 0.10/0.24 % Propositional clauses : 0
% 0.10/0.24 % Propositional clauses after purity: 0
% 0.10/0.24 % Propositional unsat core size : 0
% 0.10/0.24 % Propositional preprocessing time : 0.000
% 0.10/0.24 % Propositional encoding time : 0.000
% 0.10/0.24 % Propositional solver time : 0.000
% 0.10/0.24 % Success case prop preproc time : 0.000
% 0.10/0.24 % Success case prop encoding time : 0.000
% 0.10/0.24 % Success case prop solver time : 0.000
% 0.10/0.24 % Current number of processed clauses : 11
% 0.10/0.24 % Positive orientable unit clauses : 7
% 0.10/0.24 % Positive unorientable unit clauses: 0
% 0.10/0.24 % Negative unit clauses : 1
% 0.10/0.24 % Non-unit-clauses : 3
% 0.10/0.24 % Current number of unprocessed clauses: 2
% 0.10/0.24 % ...number of literals in the above : 4
% 0.10/0.24 % Current number of archived formulas : 0
% 0.10/0.24 % Current number of archived clauses : 4
% 0.10/0.24 % Clause-clause subsumption calls (NU) : 3
% 0.10/0.24 % Rec. Clause-clause subsumption calls : 3
% 0.10/0.24 % Non-unit clause-clause subsumptions : 0
% 0.10/0.24 % Unit Clause-clause subsumption calls : 0
% 0.10/0.24 % Rewrite failures with RHS unbound : 0
% 0.10/0.24 % BW rewrite match attempts : 1
% 0.10/0.24 % BW rewrite match successes : 1
% 0.10/0.24 % Condensation attempts : 0
% 0.10/0.24 % Condensation successes : 0
% 0.10/0.24 % Termbank termtop insertions : 1145
% 0.10/0.24 % Search garbage collected termcells : 368
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.002 s
% 0.10/0.24 % System time : 0.004 s
% 0.10/0.24 % Total time : 0.006 s
% 0.10/0.24 % Maximum resident set size: 3640 pages
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.014 s
% 0.10/0.24 % System time : 0.012 s
% 0.10/0.24 % Total time : 0.026 s
% 0.10/0.24 % Maximum resident set size: 4864 pages
% 0.10/0.24 % E exiting
%------------------------------------------------------------------------------