%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP010^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 08:04:00 AM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 6 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 8 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 62 ( 8 ~; 0 |; 0 &; 52 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
d: $tType ).
thf(decl_sort2,type,
u: $tType ).
thf(decl_sort3,type,
du: $tType ).
thf(decl_23,type,
tyop_2Emin_2Ebool: d ).
thf(decl_24,type,
tyop_2Emin_2Efun: d > d > d ).
thf(decl_25,type,
s: d > u > du ).
thf(decl_45,type,
c_2Ecardinal_2Ecardleq_2E2: du > du > u ).
thf(decl_59,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
! [X1: d,X2: d,X23: u,X24: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X23 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X24 ) ) ) )
<=> ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X23 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X24 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.A5vn1q6JjR/E---3.1_560954.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
thf(c_0_1,negated_conjecture,
~ ! [X1: d,X2: d,X23: u,X24: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X23 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X24 ) ) ) )
<=> ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X23 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X24 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm_2Ecardinal_2ECARD__NOT__LE]) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: d,X2: d,X23: u,X24: u] : $true,
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
~ $true,
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2])]) ).
thf(c_0_4,negated_conjecture,
~ $true,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
$false,
inference(cn,[status(thm)],[c_0_4]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP010^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 19:25:18 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.14 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.A5vn1q6JjR/E---3.1_560954.p
% 0.08/0.15 % Version: 3.5.1-ho
% 0.08/0.15 % Preprocessing class: HSLSSLSMSSSNSFA.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting additional_ho_4 with 1500s (5) cores
% 0.08/0.15 % Starting pre_casc_8 with 300s (1) cores
% 0.08/0.15 % Starting pre_casc_5 with 300s (1) cores
% 0.08/0.15 % Starting pre_casc_6 with 300s (1) cores
% 0.08/0.15 % pre_casc_8 with pid 560968 completed with status 0
% 0.08/0.15 % Result found by pre_casc_8
% 0.08/0.15 % Preprocessing class: HSLSSLSMSSSNSFA.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting additional_ho_4 with 1500s (5) cores
% 0.08/0.15 % Starting pre_casc_8 with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,5,,5,20000,3.0,true))
% 0.08/0.15 % SinE strategy is GSinE(CountTerms,hypos,5,,5,20000,3.0,true)
% 0.08/0.15 % Search class: HGHSM-FFMF31-DSFFFSBN
% 0.08/0.15 % partial match(2): HGHSM-FFMM31-DSFFFFBN
% 0.08/0.15 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.15 % SubtermCWHack with pid 560972 completed with status 0
% 0.08/0.15 % Result found by SubtermCWHack
% 0.08/0.15 % Preprocessing class: HSLSSLSMSSSNSFA.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting additional_ho_4 with 1500s (5) cores
% 0.08/0.15 % Starting pre_casc_8 with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,5,,5,20000,3.0,true))
% 0.08/0.15 % SinE strategy is GSinE(CountTerms,hypos,5,,5,20000,3.0,true)
% 0.08/0.15 % Search class: HGHSM-FFMF31-DSFFFSBN
% 0.08/0.15 % partial match(2): HGHSM-FFMM31-DSFFFFBN
% 0.08/0.15 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.15 % Preprocessing time : 0.001 s
% 0.08/0.15
% 0.08/0.15 % Proof found!
% 0.08/0.15 % SZS status Theorem
% 0.08/0.15 % SZS output start CNFRefutation
% See solution above
% 0.08/0.15 % Parsed axioms : 84
% 0.08/0.15 % Removed by relevancy pruning/SinE : 71
% 0.08/0.15 % Initial clauses : 18
% 0.08/0.15 % Removed in clause preprocessing : 0
% 0.08/0.15 % Initial clauses in saturation : 18
% 0.08/0.15 % Processed clauses : 1
% 0.08/0.15 % ...of these trivial : 0
% 0.08/0.15 % ...subsumed : 0
% 0.08/0.15 % ...remaining for further processing : 0
% 0.08/0.15 % Other redundant clauses eliminated : 0
% 0.08/0.15 % Clauses deleted for lack of memory : 0
% 0.08/0.15 % Backward-subsumed : 0
% 0.08/0.15 % Backward-rewritten : 0
% 0.08/0.15 % Generated clauses : 0
% 0.08/0.15 % ...of the previous two non-redundant : 0
% 0.08/0.15 % ...aggressively subsumed : 0
% 0.08/0.15 % Contextual simplify-reflections : 0
% 0.08/0.15 % Paramodulations : 0
% 0.08/0.15 % Factorizations : 0
% 0.08/0.15 % NegExts : 0
% 0.08/0.15 % Equation resolutions : 0
% 0.08/0.15 % Disequality decompositions : 0
% 0.08/0.15 % Total rewrite steps : 0
% 0.08/0.15 % ...of those cached : 0
% 0.08/0.15 % Propositional unsat checks : 0
% 0.08/0.15 % Propositional check models : 0
% 0.08/0.15 % Propositional check unsatisfiable : 0
% 0.08/0.15 % Propositional clauses : 0
% 0.08/0.15 % Propositional clauses after purity: 0
% 0.08/0.15 % Propositional unsat core size : 0
% 0.08/0.15 % Propositional preprocessing time : 0.000
% 0.08/0.15 % Propositional encoding time : 0.000
% 0.08/0.15 % Propositional solver time : 0.000
% 0.08/0.15 % Success case prop preproc time : 0.000
% 0.08/0.15 % Success case prop encoding time : 0.000
% 0.08/0.15 % Success case prop solver time : 0.000
% 0.08/0.15 % Current number of processed clauses : 0
% 0.08/0.15 % Positive orientable unit clauses : 0
% 0.08/0.15 % Positive unorientable unit clauses: 0
% 0.08/0.15 % Negative unit clauses : 0
% 0.08/0.15 % Non-unit-clauses : 0
% 0.08/0.15 % Current number of unprocessed clauses: 17
% 0.08/0.15 % ...number of literals in the above : 27
% 0.08/0.15 % Current number of archived formulas : 0
% 0.08/0.15 % Current number of archived clauses : 0
% 0.08/0.15 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.15 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.15 % Non-unit clause-clause subsumptions : 0
% 0.08/0.15 % Unit Clause-clause subsumption calls : 0
% 0.08/0.15 % Rewrite failures with RHS unbound : 0
% 0.08/0.15 % BW rewrite match attempts : 0
% 0.08/0.15 % BW rewrite match successes : 0
% 0.08/0.15 % Condensation attempts : 0
% 0.08/0.15 % Condensation successes : 0
% 0.08/0.15 % Termbank termtop insertions : 3309
% 0.08/0.15 % Search garbage collected termcells : 581
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.004 s
% 0.08/0.15 % System time : 0.000 s
% 0.08/0.15 % Total time : 0.004 s
% 0.08/0.15 % Maximum resident set size: 3684 pages
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.006 s
% 0.08/0.15 % System time : 0.003 s
% 0.08/0.15 % Total time : 0.008 s
% 0.08/0.15 % Maximum resident set size: 4864 pages
% 0.08/0.15 % E exiting
%------------------------------------------------------------------------------