%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV435^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 32 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 25 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 65 ( 9 ~; 5 |; 2 &; 44 @)
% ( 0 <=>; 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 : 48 ( 37 ^; 11 !; 0 ?; 48 :)
% 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_55,type,
esk3_0: $i ).
thf(decl_56,type,
esk4_0: $i ).
thf(mfalse,axiom,
( mfalse
= ( ^ [X1: $i] : ~ $true ) ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',mfalse) ).
thf(icl_says,axiom,
( icl_says
= ( ^ [X19: $i > $o,X21: $i > $o] : ( mbox @ rel @ ( mor @ X19 @ X21 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',icl_says) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.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/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',mbox) ).
thf(icl_s4_valid,axiom,
( iclval
= ( ^ [X22: $i > $o] : ( mvalid @ X22 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',icl_s4_valid) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',mvalid) ).
thf(mtrue,axiom,
( mtrue
= ( ^ [X1: $i] : $true ) ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',mtrue) ).
thf(untrust,conjecture,
iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',untrust) ).
thf(icl_princ,axiom,
( icl_princ
= ( ^ [X11: $i > $o] : X11 ) ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',icl_princ) ).
thf(icl_false,axiom,
( icl_false
= ( ^ [Z0: $i] : ~ $true ) ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',icl_false) ).
thf(icl_true,axiom,
( icl_true
= ( ^ [Z0: $i] : $true ) ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',icl_true) ).
thf(ax1,axiom,
( ( icl_princ @ a )
= icl_true ),
file('/export/starexec/sandbox/tmp/tmp.Vw6zQK1Zdp/E---3.1_265710.p',ax1) ).
thf(c_0_12,plain,
( mfalse
= ( ^ [Z0: $i] : ~ $true ) ),
inference(fof_simplification,[status(thm)],[mfalse]) ).
thf(c_0_13,plain,
( icl_says
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X27: $i] :
( ( rel @ Z2 @ X27 )
=> ( ( Z0 @ X27 )
| ( Z1 @ X27 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[icl_says]) ).
thf(c_0_14,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_15,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_16,plain,
( iclval
= ( ^ [Z0: $i > $o] :
! [X28: $i] : ( Z0 @ X28 ) ) ),
inference(fof_simplification,[status(thm)],[icl_s4_valid]) ).
thf(c_0_17,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_18,plain,
( mtrue
= ( ^ [Z0: $i] : $true ) ),
inference(fof_simplification,[status(thm)],[mtrue]) ).
thf(c_0_19,negated_conjecture,
~ ( iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ) ),
inference(assume_negation,[status(cth)],[untrust]) ).
thf(c_0_20,plain,
( icl_princ
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[icl_princ]) ).
thf(c_0_21,axiom,
( icl_false
= ( ^ [Z0: $i] : ~ $true ) ),
inference(apply_def,[status(thm)],[icl_false,c_0_12]) ).
thf(c_0_22,plain,
( icl_says
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X27: $i] :
( ( rel @ Z2 @ X27 )
=> ( ( Z0 @ X27 )
| ( Z1 @ X27 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_23,plain,
( iclval
= ( ^ [Z0: $i > $o] :
! [X28: $i] : ( Z0 @ X28 ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_24,axiom,
( icl_true
= ( ^ [Z0: $i] : $true ) ),
inference(apply_def,[status(thm)],[icl_true,c_0_18]) ).
thf(c_0_25,negated_conjecture,
~ ! [X36: $i,X35: $i] :
( ( rel @ X36 @ X35 )
=> ( ( a @ X35 )
| ~ $true ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23]) ).
thf(c_0_26,plain,
( a
= ( ^ [Z0: $i] : $true ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ax1,c_0_20]),c_0_24]) ).
thf(c_0_27,negated_conjecture,
( ( rel @ esk3_0 @ esk4_0 )
& ~ ( a @ esk4_0 )
& $true ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
thf(c_0_28,plain,
( a
= ( ^ [Z0: $i] : $true ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_29,negated_conjecture,
~ ( a @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_30,plain,
! [X1: $i] : ( a @ X1 ),
inference(arg_cong,[status(thm)],[c_0_28]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV435^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.15 % Computer : n011.cluster.edu
% 0.07/0.15 % Model : x86_64 x86_64
% 0.07/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.15 % Memory : 8046.5625MB
% 0.07/0.15 % OS : Linux 6.8.0-71-generic
% 0.07/0.15 % CPULimit : 300
% 0.07/0.15 % WCLimit : 300
% 0.07/0.15 % DateTime : Tue Sep 29 16:03:46 UTC 2026
% 0.07/0.15 % CPUTime :
% 0.07/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 Running higher-order theorem proving
% 0.07/0.20 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.Vw6zQK1Zdp/E---3.1_265710.p
% 0.07/0.22 % Version: 3.5.1-ho
% 0.07/0.22 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.07/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.22 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.22 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.22 % Starting post_as_ho11 with 300s (1) cores
% 0.07/0.22 % Starting full_lambda_8 with 300s (1) cores
% 0.07/0.22 % full_lambda_8 with pid 265750 completed with status 0
% 0.07/0.22 % Result found by full_lambda_8
% 0.07/0.22 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.07/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.22 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.22 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.22 % Starting post_as_ho11 with 300s (1) cores
% 0.07/0.22 % Starting full_lambda_8 with 300s (1) cores
% 0.07/0.22 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.22 % No SInE strategy applied
% 0.07/0.22 % Search class: HGUSF-FFSF22-SHSSMMBN
% 0.07/0.22 % partial match(1): HGUNF-FFSF22-SHSSMMBN
% 0.07/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.22 % SubtermCWHack with pid 265758 completed with status 0
% 0.07/0.22 % Result found by SubtermCWHack
% 0.07/0.22 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.07/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.22 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.22 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.22 % Starting post_as_ho11 with 300s (1) cores
% 0.07/0.22 % Starting full_lambda_8 with 300s (1) cores
% 0.07/0.22 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.22 % No SInE strategy applied
% 0.07/0.22 % Search class: HGUSF-FFSF22-SHSSMMBN
% 0.07/0.22 % partial match(1): HGUNF-FFSF22-SHSSMMBN
% 0.07/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.22 % Preprocessing time : 0.001 s
% 0.07/0.22
% 0.07/0.22 % Proof found!
% 0.07/0.22 % SZS status Theorem
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22 % Parsed axioms : 59
% 0.07/0.22 % Removed by relevancy pruning/SinE : 0
% 0.07/0.23 % Initial clauses : 39
% 0.07/0.23 % Removed in clause preprocessing : 32
% 0.07/0.23 % Initial clauses in saturation : 7
% 0.07/0.23 % Processed clauses : 3
% 0.07/0.23 % ...of these trivial : 0
% 0.07/0.23 % ...subsumed : 0
% 0.07/0.23 % ...remaining for further processing : 3
% 0.07/0.23 % Other redundant clauses eliminated : 0
% 0.07/0.23 % Clauses deleted for lack of memory : 0
% 0.07/0.23 % Backward-subsumed : 0
% 0.07/0.23 % Backward-rewritten : 1
% 0.07/0.23 % Generated clauses : 1
% 0.07/0.23 % ...of the previous two non-redundant : 1
% 0.07/0.23 % ...aggressively subsumed : 0
% 0.07/0.23 % Contextual simplify-reflections : 0
% 0.07/0.23 % Paramodulations : 0
% 0.07/0.23 % Factorizations : 0
% 0.07/0.23 % NegExts : 0
% 0.07/0.23 % Equation resolutions : 0
% 0.07/0.23 % Disequality decompositions : 0
% 0.07/0.23 % Total rewrite steps : 1
% 0.07/0.23 % ...of those cached : 0
% 0.07/0.23 % Propositional unsat checks : 0
% 0.07/0.23 % Propositional check models : 0
% 0.07/0.23 % Propositional check unsatisfiable : 0
% 0.07/0.23 % Propositional clauses : 0
% 0.07/0.23 % Propositional clauses after purity: 0
% 0.07/0.23 % Propositional unsat core size : 0
% 0.07/0.23 % Propositional preprocessing time : 0.000
% 0.07/0.23 % Propositional encoding time : 0.000
% 0.07/0.23 % Propositional solver time : 0.000
% 0.07/0.23 % Success case prop preproc time : 0.000
% 0.07/0.23 % Success case prop encoding time : 0.000
% 0.07/0.23 % Success case prop solver time : 0.000
% 0.07/0.23 % Current number of processed clauses : 2
% 0.07/0.23 % Positive orientable unit clauses : 2
% 0.07/0.23 % Positive unorientable unit clauses: 0
% 0.07/0.23 % Negative unit clauses : 0
% 0.07/0.23 % Non-unit-clauses : 0
% 0.07/0.23 % Current number of unprocessed clauses: 5
% 0.07/0.23 % ...number of literals in the above : 13
% 0.07/0.23 % Current number of archived formulas : 0
% 0.07/0.23 % Current number of archived clauses : 1
% 0.07/0.23 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.23 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.23 % Non-unit clause-clause subsumptions : 0
% 0.07/0.23 % Unit Clause-clause subsumption calls : 0
% 0.07/0.23 % Rewrite failures with RHS unbound : 0
% 0.07/0.23 % BW rewrite match attempts : 2
% 0.07/0.23 % BW rewrite match successes : 1
% 0.07/0.23 % Condensation attempts : 0
% 0.07/0.23 % Condensation successes : 0
% 0.07/0.23 % Termbank termtop insertions : 1794
% 0.07/0.23 % Search garbage collected termcells : 450
% 0.07/0.23
% 0.07/0.23 % -------------------------------------------------
% 0.07/0.23 % User time : 0.004 s
% 0.07/0.23 % System time : 0.002 s
% 0.07/0.23 % Total time : 0.005 s
% 0.07/0.23 % Maximum resident set size: 3680 pages
% 0.07/0.23
% 0.07/0.23 % -------------------------------------------------
% 0.07/0.23 % User time : 0.005 s
% 0.07/0.23 % System time : 0.006 s
% 0.07/0.23 % Total time : 0.011 s
% 0.07/0.23 % Maximum resident set size: 4864 pages
% 0.07/0.23 % E exiting
%------------------------------------------------------------------------------