%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV435^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:39:44 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 33 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 23 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 77 ( 12 ~; 8 |; 3 &; 48 @)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 35 ^; 14 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_27,type,
mfalse: $i > $o ).
thf(decl_28,type,
mtrue: $i > $o ).
thf(decl_30,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_42,type,
rel: $i > $i > $o ).
thf(decl_44,type,
icl_princ: ( $i > $o ) > $i > $o ).
thf(decl_48,type,
icl_true: $i > $o ).
thf(decl_49,type,
icl_false: $i > $o ).
thf(decl_50,type,
icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_51,type,
iclval: ( $i > $o ) > $o ).
thf(decl_52,type,
a: $i > $o ).
thf(decl_53,type,
esk1_0: $i ).
thf(decl_54,type,
esk2_0: $i ).
thf(mtrue,axiom,
( mtrue
= ( ^ [X1: $i] : $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',mtrue) ).
thf(mfalse,axiom,
( mfalse
= ( ^ [X1: $i] : ~ $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',mfalse) ).
thf(icl_says,axiom,
( icl_says
= ( ^ [X19: $i > $o,X21: $i > $o] : ( mbox @ rel @ ( mor @ X19 @ X21 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',icl_says) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',mor) ).
thf(mbox,axiom,
( mbox
= ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
! [X12: $i] :
( ( X10 @ X1 @ X12 )
=> ( X11 @ X12 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',mbox) ).
thf(icl_s4_valid,axiom,
( iclval
= ( ^ [X22: $i > $o] : ( mvalid @ X22 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',icl_s4_valid) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',mvalid) ).
thf(icl_princ,axiom,
( icl_princ
= ( ^ [X11: $i > $o] : X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',icl_princ) ).
thf(icl_true,axiom,
( icl_true
= ( ^ [Z0: $i] : $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',icl_true) ).
thf(untrust,conjecture,
iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',untrust) ).
thf(icl_false,axiom,
( icl_false
= ( ^ [Z0: $i] : ~ $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',icl_false) ).
thf(ax1,axiom,
( ( icl_princ @ a )
= icl_true ),
file('/export/starexec/sandbox2/tmp/tmp.VYTFJ40t9w/E---3.1_1480081.p',ax1) ).
thf(c_0_12,plain,
( mtrue
= ( ^ [Z0: $i] : $true ) ),
inference(fof_simplification,[status(thm)],[mtrue]) ).
thf(c_0_13,plain,
( mfalse
= ( ^ [Z0: $i] : ~ $true ) ),
inference(fof_simplification,[status(thm)],[mfalse]) ).
thf(c_0_14,plain,
( icl_says
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X25: $i] :
( ( rel @ Z2 @ X25 )
=> ( ( Z0 @ X25 )
| ( Z1 @ X25 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[icl_says]) ).
thf(c_0_15,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_16,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X12: $i] :
( ( Z0 @ Z2 @ X12 )
=> ( Z1 @ X12 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_17,plain,
( iclval
= ( ^ [Z0: $i > $o] :
! [X26: $i] : ( Z0 @ X26 ) ) ),
inference(fof_simplification,[status(thm)],[icl_s4_valid]) ).
thf(c_0_18,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_19,plain,
( icl_princ
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[icl_princ]) ).
thf(c_0_20,axiom,
( icl_true
= ( ^ [Z0: $i] : $true ) ),
inference(apply_def,[status(thm)],[icl_true,c_0_12]) ).
thf(c_0_21,negated_conjecture,
~ ( iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ) ),
inference(assume_negation,[status(cth)],[untrust]) ).
thf(c_0_22,axiom,
( icl_false
= ( ^ [Z0: $i] : ~ $true ) ),
inference(apply_def,[status(thm)],[icl_false,c_0_13]) ).
thf(c_0_23,plain,
( icl_says
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X25: $i] :
( ( rel @ Z2 @ X25 )
=> ( ( Z0 @ X25 )
| ( Z1 @ X25 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_24,plain,
( iclval
= ( ^ [Z0: $i > $o] :
! [X26: $i] : ( Z0 @ X26 ) ) ),
inference(apply_def,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_25,plain,
! [X29: $i] :
( ( a @ X29 )
<=> $true ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ax1,c_0_19]),c_0_20])]) ).
thf(c_0_26,negated_conjecture,
~ ! [X28: $i,X27: $i] :
( ( rel @ X28 @ X27 )
=> ( ( a @ X27 )
| ~ $true ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_19]),c_0_22]),c_0_23]),c_0_24]) ).
thf(c_0_27,plain,
! [X30: $i] :
( ( ~ ( a @ X30 )
| $true )
& ( ~ $true
| ( a @ X30 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
thf(c_0_28,negated_conjecture,
( ( rel @ esk1_0 @ esk2_0 )
& ~ ( a @ esk2_0 )
& $true ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
thf(c_0_29,plain,
! [X1: $i] :
( ( a @ X1 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_30,negated_conjecture,
~ ( a @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_31,plain,
! [X1: $i] : ( a @ X1 ),
inference(cn,[status(thm)],[c_0_29]) ).
thf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV435^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n004.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 16:03:37 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 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.VYTFJ40t9w/E---3.1_1480081.p
% 0.10/0.24 % Version: 3.5.1-ho
% 0.10/0.24 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.10/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho11 with 300s (1) cores
% 0.10/0.24 % Starting full_lambda_8 with 300s (1) cores
% 0.10/0.24 % post_as_ho11 with pid 1480109 completed with status 0
% 0.10/0.24 % Result found by post_as_ho11
% 0.10/0.24 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.10/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho11 with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.24 % No SInE strategy applied
% 0.10/0.24 % Search class: HUUNF-FFSF00-SHSSMFNN
% 0.10/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.24 % SubtermCWHack with pid 1480114 completed with status 0
% 0.10/0.24 % Result found by SubtermCWHack
% 0.10/0.24 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.10/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho11 with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.24 % No SInE strategy applied
% 0.10/0.24 % Search class: HUUNF-FFSF00-SHSSMFNN
% 0.10/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 28s (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 : 57
% 0.10/0.24 % Removed by relevancy pruning/SinE : 0
% 0.10/0.24 % Initial clauses : 36
% 0.10/0.24 % Removed in clause preprocessing : 33
% 0.10/0.24 % Initial clauses in saturation : 3
% 0.10/0.24 % Processed clauses : 2
% 0.10/0.24 % ...of these trivial : 0
% 0.10/0.24 % ...subsumed : 0
% 0.10/0.24 % ...remaining for further processing : 1
% 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 : 0
% 0.10/0.24 % Generated clauses : 0
% 0.10/0.24 % ...of the previous two non-redundant : 0
% 0.10/0.24 % ...aggressively subsumed : 0
% 0.10/0.24 % Contextual simplify-reflections : 0
% 0.10/0.24 % Paramodulations : 0
% 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 : 1
% 0.10/0.24 % ...of those cached : 0
% 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 : 1
% 0.10/0.24 % Positive orientable unit clauses : 1
% 0.10/0.24 % Positive unorientable unit clauses: 0
% 0.10/0.24 % Negative unit clauses : 0
% 0.10/0.24 % Non-unit-clauses : 0
% 0.10/0.24 % Current number of unprocessed clauses: 1
% 0.10/0.24 % ...number of literals in the above : 1
% 0.10/0.24 % Current number of archived formulas : 0
% 0.10/0.24 % Current number of archived clauses : 0
% 0.10/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.24 % Rec. Clause-clause subsumption calls : 0
% 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 : 0
% 0.10/0.24 % BW rewrite match successes : 0
% 0.10/0.24 % Condensation attempts : 0
% 0.10/0.24 % Condensation successes : 0
% 0.10/0.24 % Termbank termtop insertions : 1335
% 0.10/0.24 % Search garbage collected termcells : 202
% 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: 3676 pages
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.004 s
% 0.10/0.24 % System time : 0.009 s
% 0.10/0.24 % Total time : 0.013 s
% 0.10/0.24 % Maximum resident set size: 4864 pages
% 0.10/0.24 % E exiting
%------------------------------------------------------------------------------