%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU657^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:24:54 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 28 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 265 ( 4 ~; 0 |; 11 &; 239 @)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 35 ( 6 ^; 23 !; 6 ?; 35 :)
% 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,
setunion: $i > $i ).
thf(decl_27,type,
iskpair: $i > $o ).
thf(decl_28,type,
kpair: $i > $i > $i ).
thf(decl_29,type,
kfst: $i > $i ).
thf(decl_30,type,
kfstpairEq: $o ).
thf(decl_31,type,
ksnd: $i > $i ).
thf(decl_32,type,
ksndpairEq: $o ).
thf(decl_33,type,
esk1_0: $i ).
thf(decl_34,type,
esk2_0: $i ).
thf(decl_35,type,
esk3_0: $i ).
thf(kpair,axiom,
( kpair
= ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cnw4lEGzoV/E---3.1_2907513.p',kpair) ).
thf(kpairsurjEq,conjecture,
( kfstpairEq
=> ( ksndpairEq
=> ! [X4: $i] :
( ( iskpair @ X4 )
=> ( ( kpair @ ( kfst @ X4 ) @ ( ksnd @ X4 ) )
= X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cnw4lEGzoV/E---3.1_2907513.p',kpairsurjEq) ).
thf(iskpair,axiom,
( iskpair
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
& ( X1
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cnw4lEGzoV/E---3.1_2907513.p',iskpair) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.cnw4lEGzoV/E---3.1_2907513.p',kfstpairEq) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.cnw4lEGzoV/E---3.1_2907513.p',ksndpairEq) ).
thf(c_0_5,plain,
( kpair
= ( ^ [Z0: $i,Z1: $i] : ( setadjoin @ ( setadjoin @ Z0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Z0 @ ( setadjoin @ Z1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fof_simplification,[status(thm)],[kpair]) ).
thf(c_0_6,negated_conjecture,
~ ( kfstpairEq
=> ( ksndpairEq
=> ! [X4: $i] :
( ( iskpair @ X4 )
=> ( ( kpair @ ( kfst @ X4 ) @ ( ksnd @ X4 ) )
= X4 ) ) ) ),
inference(assume_negation,[status(cth)],[kpairsurjEq]) ).
thf(c_0_7,plain,
( iskpair
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ Z0 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ Z0 ) )
& ( Z0
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iskpair]) ).
thf(c_0_8,axiom,
( kfstpairEq
= ( ! [X2: $i,X3: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
= X2 ) ) ),
inference(apply_def,[status(thm)],[kfstpairEq,c_0_5]) ).
thf(c_0_9,axiom,
( ksndpairEq
= ( ! [X2: $i,X3: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
= X3 ) ) ),
inference(apply_def,[status(thm)],[ksndpairEq,c_0_5]) ).
thf(c_0_10,negated_conjecture,
~ ( ! [X10: $i,X11: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) )
= X10 )
=> ( ! [X12: $i,X13: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X13 @ emptyset ) ) @ emptyset ) ) )
= X13 )
=> ! [X4: $i] :
( ? [X14: $i] :
( ( in @ X14 @ ( setunion @ X4 ) )
& ? [X15: $i] :
( ( in @ X15 @ ( setunion @ X4 ) )
& ( X4
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X15 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ ( kfst @ X4 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X4 ) @ ( setadjoin @ ( ksnd @ X4 ) @ emptyset ) ) @ emptyset ) )
= X4 ) ) ) ),
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]),c_0_8]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X16: $i,X17: $i,X18: $i,X19: $i] :
( ( ( kfst @ ( setadjoin @ ( setadjoin @ X16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X16 @ ( setadjoin @ X17 @ emptyset ) ) @ emptyset ) ) )
= X16 )
& ( ( ksnd @ ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) ) )
= X19 )
& ( in @ esk2_0 @ ( setunion @ esk1_0 ) )
& ( in @ esk3_0 @ ( setunion @ esk1_0 ) )
& ( esk1_0
= ( setadjoin @ ( setadjoin @ esk2_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) @ emptyset ) ) )
& ( ( setadjoin @ ( setadjoin @ ( kfst @ esk1_0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ esk1_0 ) @ ( setadjoin @ ( ksnd @ esk1_0 ) @ emptyset ) ) @ emptyset ) )
!= esk1_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,
! [X2: $i,X1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
( esk1_0
= ( setadjoin @ ( setadjoin @ esk2_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
( ( setadjoin @ ( setadjoin @ ( kfst @ esk1_0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ esk1_0 ) @ ( setadjoin @ ( ksnd @ esk1_0 ) @ emptyset ) ) @ emptyset ) )
!= esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
( ( kfst @ esk1_0 )
= esk2_0 ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_17,negated_conjecture,
( ( ksnd @ esk1_0 )
= esk3_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]),c_0_17]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU657^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n010.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 14:03:17 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.cnw4lEGzoV/E---3.1_2907513.p
% 0.09/0.23 % Version: 3.5.1-ho
% 0.09/0.23 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.23 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.23 % Starting lpo1_def_fix with 300s (1) cores
% 0.09/0.23 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.09/0.23 % ehoh_best8_lambda with pid 2907529 completed with status 0
% 0.09/0.23 % Result found by ehoh_best8_lambda
% 0.09/0.23 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.23 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.23 % Starting lpo1_def_fix with 300s (1) cores
% 0.09/0.23 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.09/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = Auto)
% 0.09/0.23 % No SInE strategy applied
% 0.09/0.23 % Search class: HUUSS-FFSS21-MSFFMFNN
% 0.09/0.23 % partial match(2): HHUSS-FFSF21-MSFFMFNN
% 0.09/0.23 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.23 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.23 % SubtermCWHack with pid 2907534 completed with status 0
% 0.09/0.23 % Result found by SubtermCWHack
% 0.09/0.23 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.23 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.23 % Starting lpo1_def_fix with 300s (1) cores
% 0.09/0.23 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.09/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = Auto)
% 0.09/0.23 % No SInE strategy applied
% 0.09/0.23 % Search class: HUUSS-FFSS21-MSFFMFNN
% 0.09/0.23 % partial match(2): HHUSS-FFSF21-MSFFMFNN
% 0.09/0.23 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.23 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.23 % Preprocessing time : 0.001 s
% 0.09/0.23
% 0.09/0.23 % Proof found!
% 0.09/0.23 % SZS status Theorem
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23 % Parsed axioms : 15
% 0.09/0.23 % Removed by relevancy pruning/SinE : 0
% 0.09/0.23 % Initial clauses : 16
% 0.09/0.23 % Removed in clause preprocessing : 10
% 0.09/0.23 % Initial clauses in saturation : 6
% 0.09/0.23 % Processed clauses : 9
% 0.09/0.23 % ...of these trivial : 0
% 0.09/0.23 % ...subsumed : 0
% 0.09/0.23 % ...remaining for further processing : 8
% 0.09/0.23 % Other redundant clauses eliminated : 0
% 0.09/0.23 % Clauses deleted for lack of memory : 0
% 0.09/0.23 % Backward-subsumed : 0
% 0.09/0.23 % Backward-rewritten : 0
% 0.09/0.23 % Generated clauses : 4
% 0.09/0.23 % ...of the previous two non-redundant : 4
% 0.09/0.23 % ...aggressively subsumed : 0
% 0.09/0.23 % Contextual simplify-reflections : 0
% 0.09/0.23 % Paramodulations : 4
% 0.09/0.23 % Factorizations : 0
% 0.09/0.23 % NegExts : 0
% 0.09/0.23 % Equation resolutions : 0
% 0.09/0.23 % Disequality decompositions : 0
% 0.09/0.23 % Total rewrite steps : 4
% 0.09/0.23 % ...of those cached : 1
% 0.09/0.23 % Propositional unsat checks : 0
% 0.09/0.23 % Propositional check models : 0
% 0.09/0.23 % Propositional check unsatisfiable : 0
% 0.09/0.23 % Propositional clauses : 0
% 0.09/0.23 % Propositional clauses after purity: 0
% 0.09/0.23 % Propositional unsat core size : 0
% 0.09/0.23 % Propositional preprocessing time : 0.000
% 0.09/0.23 % Propositional encoding time : 0.000
% 0.09/0.23 % Propositional solver time : 0.000
% 0.09/0.23 % Success case prop preproc time : 0.000
% 0.09/0.23 % Success case prop encoding time : 0.000
% 0.09/0.23 % Success case prop solver time : 0.000
% 0.09/0.23 % Current number of processed clauses : 8
% 0.09/0.23 % Positive orientable unit clauses : 8
% 0.09/0.23 % Positive unorientable unit clauses: 0
% 0.09/0.23 % Negative unit clauses : 0
% 0.09/0.23 % Non-unit-clauses : 0
% 0.09/0.23 % Current number of unprocessed clauses: 1
% 0.09/0.23 % ...number of literals in the above : 1
% 0.09/0.23 % Current number of archived formulas : 0
% 0.09/0.23 % Current number of archived clauses : 0
% 0.09/0.23 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.23 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.23 % Non-unit clause-clause subsumptions : 0
% 0.09/0.23 % Unit Clause-clause subsumption calls : 0
% 0.09/0.23 % Rewrite failures with RHS unbound : 0
% 0.09/0.23 % BW rewrite match attempts : 1
% 0.09/0.23 % BW rewrite match successes : 0
% 0.09/0.23 % Condensation attempts : 0
% 0.09/0.23 % Condensation successes : 0
% 0.09/0.23 % Termbank termtop insertions : 869
% 0.09/0.23 % Search garbage collected termcells : 167
% 0.09/0.23
% 0.09/0.23 % -------------------------------------------------
% 0.09/0.23 % User time : 0.003 s
% 0.09/0.23 % System time : 0.002 s
% 0.09/0.23 % Total time : 0.005 s
% 0.09/0.23 % Maximum resident set size: 3636 pages
% 0.09/0.23
% 0.09/0.23 % -------------------------------------------------
% 0.09/0.23 % User time : 0.005 s
% 0.09/0.23 % System time : 0.004 s
% 0.09/0.23 % Total time : 0.009 s
% 0.09/0.23 % Maximum resident set size: 4864 pages
% 0.09/0.23 % E exiting
%------------------------------------------------------------------------------