%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU672^2 : 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 : n026.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 08:24:58 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 23 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 295 ( 11 ~; 6 |; 16 &; 252 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 77 ( 48 ^; 21 !; 8 ?; 77 :)
% 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,
subset: $i > $i > $o ).
thf(decl_28,type,
kpair: $i > $i > $i ).
thf(decl_29,type,
cartprod: $i > $i > $i ).
thf(decl_30,type,
singleton: $i > $o ).
thf(decl_31,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_32,type,
breln: $i > $i > $i > $o ).
thf(decl_33,type,
func: $i > $i > $i > $o ).
thf(decl_34,type,
esk1_0: $i ).
thf(decl_35,type,
esk2_0: $i ).
thf(decl_36,type,
esk3_0: $i ).
thf(decl_37,type,
esk4_1: $i > $i ).
thf(decl_38,type,
esk5_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X3: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agIi6DTOSH/E---3.1_655100.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agIi6DTOSH/E---3.1_655100.p',singleton) ).
thf(func,axiom,
( func
= ( ^ [X1: $i,X4: $i,X6: $i] :
( ( breln @ X1 @ X4 @ X6 )
& ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ex1 @ X4
@ ^ [X7: $i] : ( in @ ( kpair @ X2 @ X7 ) @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agIi6DTOSH/E---3.1_655100.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agIi6DTOSH/E---3.1_655100.p',breln) ).
thf(funcImageSingleton,conjecture,
! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X7: $i] : ( in @ ( kpair @ X2 @ X7 ) @ X8 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agIi6DTOSH/E---3.1_655100.p',funcImageSingleton) ).
thf(c_0_5,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X13: $i] :
( ( in @ X13
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X13 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_6,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_7,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X14: $i] :
( ( in @ X14
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X14 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_8,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_9,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X13: $i] :
( ( in @ X13
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X13 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_10,negated_conjecture,
~ ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X7: $i] : ( in @ ( kpair @ X2 @ X7 ) @ X8 ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcImageSingleton]) ).
thf(c_0_11,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X14: $i] :
( ( in @ X14
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X14 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
thf(c_0_12,negated_conjecture,
~ ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X15: $i] :
( ( in @ X15 @ X1 )
=> ? [X16: $i] :
( ( in @ X16
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X15 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X15 @ Z0 ) @ X8 ) )
= ( setadjoin @ X16 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ? [X17: $i] :
( ( in @ X17
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X8 ) )
= ( setadjoin @ X17 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10]),c_0_11]),c_0_6]) ).
thf(c_0_13,negated_conjecture,
! [X21: $i,X24: $i] :
( ( subset @ esk3_0 @ ( cartprod @ esk1_0 @ esk2_0 ) )
& ( ( in @ ( esk4_1 @ X21 )
@ ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X21 @ Z0 ) @ esk3_0 ) ) )
| ~ ( in @ X21 @ esk1_0 ) )
& ( ( ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X21 @ Z0 ) @ esk3_0 ) )
= ( setadjoin @ ( esk4_1 @ X21 ) @ emptyset ) )
| ~ ( in @ X21 @ esk1_0 ) )
& ( in @ esk5_0 @ esk1_0 )
& ( ~ ( in @ X24
@ ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk5_0 @ Z0 ) @ esk3_0 ) ) )
| ( ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk5_0 @ Z0 ) @ esk3_0 ) )
!= ( setadjoin @ X24 @ emptyset ) ) ) ),
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_12])])])])])]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1
@ ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk5_0 @ Z0 ) @ esk3_0 ) ) )
| ( ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk5_0 @ Z0 ) @ esk3_0 ) )
!= ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk4_1 @ X1 )
@ ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk3_0 ) ) )
| ~ ( in @ X1 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
in @ esk5_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
( ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk5_0 @ Z0 ) @ esk3_0 ) )
!= ( setadjoin @ ( esk4_1 @ esk5_0 ) @ emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i] :
( ( ( dsetconstr @ esk2_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk3_0 ) )
= ( setadjoin @ ( esk4_1 @ X1 ) @ emptyset ) )
| ~ ( in @ X1 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU672^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n026.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:09:42 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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.agIi6DTOSH/E---3.1_655100.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.09/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.25 % Starting sh2l with 300s (1) cores
% 0.09/0.25 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.09/0.25 % ehoh_best_sine_rwall with pid 655114 completed with status 0
% 0.09/0.25 % Result found by ehoh_best_sine_rwall
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.09/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.25 % Search class: HHHSF-FFSF21-MHSFMFNN
% 0.09/0.25 % partial match(2): HHHSF-FFSF11-SHSFMFNN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % SubtermCWHack with pid 655119 completed with status 0
% 0.09/0.25 % Result found by SubtermCWHack
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.09/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.25 % Search class: HHHSF-FFSF21-MHSFMFNN
% 0.09/0.25 % partial match(2): HHHSF-FFSF11-SHSFMFNN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % Preprocessing time : 0.001 s
% 0.09/0.25
% 0.09/0.25 % Proof found!
% 0.09/0.25 % SZS status Theorem
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25 % Parsed axioms : 16
% 0.09/0.25 % Removed by relevancy pruning/SinE : 11
% 0.09/0.25 % Initial clauses : 5
% 0.09/0.25 % Removed in clause preprocessing : 0
% 0.09/0.25 % Initial clauses in saturation : 5
% 0.09/0.25 % Processed clauses : 7
% 0.09/0.25 % ...of these trivial : 0
% 0.09/0.25 % ...subsumed : 0
% 0.09/0.25 % ...remaining for further processing : 7
% 0.09/0.25 % Other redundant clauses eliminated : 0
% 0.09/0.25 % Clauses deleted for lack of memory : 0
% 0.09/0.25 % Backward-subsumed : 0
% 0.09/0.25 % Backward-rewritten : 0
% 0.09/0.25 % Generated clauses : 4
% 0.09/0.25 % ...of the previous two non-redundant : 3
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 0
% 0.09/0.25 % Paramodulations : 4
% 0.09/0.25 % Factorizations : 0
% 0.09/0.25 % NegExts : 0
% 0.09/0.25 % Equation resolutions : 0
% 0.09/0.25 % Disequality decompositions : 0
% 0.09/0.25 % Total rewrite steps : 3
% 0.09/0.25 % ...of those cached : 2
% 0.09/0.25 % Propositional unsat checks : 0
% 0.09/0.25 % Propositional check models : 0
% 0.09/0.25 % Propositional check unsatisfiable : 0
% 0.09/0.25 % Propositional clauses : 0
% 0.09/0.25 % Propositional clauses after purity: 0
% 0.09/0.25 % Propositional unsat core size : 0
% 0.09/0.25 % Propositional preprocessing time : 0.000
% 0.09/0.25 % Propositional encoding time : 0.000
% 0.09/0.25 % Propositional solver time : 0.000
% 0.09/0.25 % Success case prop preproc time : 0.000
% 0.09/0.25 % Success case prop encoding time : 0.000
% 0.09/0.25 % Success case prop solver time : 0.000
% 0.09/0.25 % Current number of processed clauses : 7
% 0.09/0.25 % Positive orientable unit clauses : 2
% 0.09/0.25 % Positive unorientable unit clauses: 0
% 0.09/0.25 % Negative unit clauses : 1
% 0.09/0.25 % Non-unit-clauses : 4
% 0.09/0.25 % Current number of unprocessed clauses: 1
% 0.09/0.25 % ...number of literals in the above : 2
% 0.09/0.25 % Current number of archived formulas : 0
% 0.09/0.25 % Current number of archived clauses : 0
% 0.09/0.25 % Clause-clause subsumption calls (NU) : 1
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 1
% 0.09/0.25 % Non-unit clause-clause subsumptions : 0
% 0.09/0.25 % Unit Clause-clause subsumption calls : 1
% 0.09/0.25 % Rewrite failures with RHS unbound : 0
% 0.09/0.25 % BW rewrite match attempts : 0
% 0.09/0.25 % BW rewrite match successes : 0
% 0.09/0.25 % Condensation attempts : 0
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 982
% 0.09/0.25 % Search garbage collected termcells : 271
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.003 s
% 0.09/0.25 % System time : 0.002 s
% 0.09/0.25 % Total time : 0.005 s
% 0.09/0.25 % Maximum resident set size: 3640 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.004 s
% 0.09/0.25 % System time : 0.007 s
% 0.09/0.25 % Total time : 0.011 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------