%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV434^4 : 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 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 27 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 204 ( 28 ~; 24 |; 4 &; 135 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 89 ( 54 ^; 35 !; 0 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_27,type,
mfalse: $i > $o ).
thf(decl_29,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimpl: ( $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_43,type,
icl_atom: ( $i > $o ) > $i > $o ).
thf(decl_47,type,
icl_impl: ( $i > $o ) > ( $i > $o ) > $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,
s: $i > $o ).
thf(decl_53,type,
esk1_2: ( $i > $o ) > $i > $i ).
thf(decl_55,type,
esk3_0: $i ).
thf(decl_56,type,
esk4_0: $i ).
thf(decl_57,type,
esk5_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.p',mor) ).
thf(icl_atom,axiom,
( icl_atom
= ( ^ [X11: $i > $o] : ( mbox @ rel @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.p',icl_atom) ).
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.uL9yvwL8KP/E---3.1_264911.p',mbox) ).
thf(icl_impl,axiom,
( icl_impl
= ( ^ [X19: $i > $o,X20: $i > $o] : ( mbox @ rel @ ( mimpl @ X19 @ X20 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.p',icl_impl) ).
thf(mfalse,axiom,
( mfalse
= ( ^ [X1: $i] : ~ $true ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.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.uL9yvwL8KP/E---3.1_264911.p',icl_says) ).
thf(icl_s4_valid,axiom,
( iclval
= ( ^ [X22: $i > $o] : ( mvalid @ X22 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.p',icl_s4_valid) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.p',mvalid) ).
thf(trust,conjecture,
iclval @ ( icl_impl @ ( icl_says @ icl_false @ ( icl_atom @ s ) ) @ ( icl_atom @ s ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.p',trust) ).
thf(icl_false,axiom,
( icl_false
= ( ^ [Z0: $i] : ~ $true ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.p',icl_false) ).
thf(refl_axiom,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X19 ) @ X19 ) ),
file('/export/starexec/sandbox/tmp/tmp.uL9yvwL8KP/E---3.1_264911.p',refl_axiom) ).
thf(c_0_13,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_14,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
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,
( icl_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X25: $i] :
( ( rel @ Z1 @ X25 )
=> ( Z0 @ X25 ) ) ) ),
inference(fof_simplification,[status(thm)],[icl_atom]) ).
thf(c_0_17,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_18,plain,
( icl_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X26: $i] :
( ( rel @ Z2 @ X26 )
=> ( ~ ( Z0 @ X26 )
| ( Z1 @ X26 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[icl_impl]) ).
thf(c_0_19,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_20,plain,
( mfalse
= ( ^ [Z0: $i] : ~ $true ) ),
inference(fof_simplification,[status(thm)],[mfalse]) ).
thf(c_0_21,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_22,plain,
( iclval
= ( ^ [Z0: $i > $o] :
! [X28: $i] : ( Z0 @ X28 ) ) ),
inference(fof_simplification,[status(thm)],[icl_s4_valid]) ).
thf(c_0_23,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_24,negated_conjecture,
~ ( iclval @ ( icl_impl @ ( icl_says @ icl_false @ ( icl_atom @ s ) ) @ ( icl_atom @ s ) ) ),
inference(assume_negation,[status(cth)],[trust]) ).
thf(c_0_25,plain,
( icl_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X25: $i] :
( ( rel @ Z1 @ X25 )
=> ( Z0 @ X25 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_26,plain,
( icl_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X26: $i] :
( ( rel @ Z2 @ X26 )
=> ( ~ ( Z0 @ X26 )
| ( Z1 @ X26 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_19]),c_0_17]) ).
thf(c_0_27,axiom,
( icl_false
= ( ^ [Z0: $i] : ~ $true ) ),
inference(apply_def,[status(thm)],[icl_false,c_0_20]) ).
thf(c_0_28,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_21,c_0_15]),c_0_17]) ).
thf(c_0_29,plain,
( iclval
= ( ^ [Z0: $i > $o] :
! [X28: $i] : ( Z0 @ X28 ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_30,negated_conjecture,
~ ! [X39: $i,X38: $i] :
( ( rel @ X39 @ X38 )
=> ( ~ ! [X36: $i] :
( ( rel @ X38 @ X36 )
=> ( ~ $true
| ! [X35: $i] :
( ( rel @ X36 @ X35 )
=> ( s @ X35 ) ) ) )
| ! [X37: $i] :
( ( rel @ X38 @ X37 )
=> ( s @ X37 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]) ).
thf(c_0_31,plain,
! [X19: $i > $o,X30: $i] :
( ~ ! [X29: $i] :
( ( rel @ X30 @ X29 )
=> ( X19 @ X29 ) )
| ( X19 @ X30 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[refl_axiom,c_0_19]),c_0_17]),c_0_23]) ).
thf(c_0_32,negated_conjecture,
! [X50: $i,X51: $i] :
( ( rel @ esk3_0 @ esk4_0 )
& ( ~ ( rel @ esk4_0 @ X50 )
| ~ $true
| ~ ( rel @ X50 @ X51 )
| ( s @ X51 ) )
& ( rel @ esk4_0 @ esk5_0 )
& ~ ( s @ esk5_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_30])])])])]) ).
thf(c_0_33,plain,
! [X40: $i > $o,X41: $i] :
( ( ( rel @ X41 @ ( esk1_2 @ X40 @ X41 ) )
| ( X40 @ X41 ) )
& ( ~ ( X40 @ ( esk1_2 @ X40 @ X41 ) )
| ( X40 @ X41 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])])]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i,X3: $i] :
( ( s @ X3 )
| ~ ( rel @ esk4_0 @ X1 )
| ~ $true
| ~ ( rel @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_35,plain,
! [X2: $i > $o,X1: $i] :
( ( X2 @ X1 )
| ~ ( X2 @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_36,plain,
! [X2: $i > $o,X1: $i] :
( ( rel @ X1 @ ( esk1_2 @ X2 @ X1 ) )
| ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_37,negated_conjecture,
! [X3: $i,X1: $i] :
( ( s @ X3 )
| ~ ( rel @ X1 @ X3 )
| ~ ( rel @ esk4_0 @ X1 ) ),
inference(cn,[status(thm)],[c_0_34]) ).
thf(c_0_38,plain,
! [X1: $i] : ( rel @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_39,negated_conjecture,
~ ( s @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i] :
( ( s @ X1 )
| ~ ( rel @ esk4_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_41,negated_conjecture,
rel @ esk4_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV434^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n011.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 16:03:31 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.22 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.uL9yvwL8KP/E---3.1_264911.p
% 0.08/0.24 % Version: 3.5.1-ho
% 0.08/0.24 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.24 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.24 % Starting post_as_ho11 with 300s (1) cores
% 0.08/0.24 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.24 % post_as_ho11 with pid 264941 completed with status 0
% 0.08/0.24 % Result found by post_as_ho11
% 0.08/0.24 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.24 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.24 % Starting post_as_ho11 with 300s (1) cores
% 0.08/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.24 % No SInE strategy applied
% 0.08/0.24 % Search class: HGUNF-FFSF22-SHSSMMBN
% 0.08/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.24 % SubtermCWHack with pid 264944 completed with status 0
% 0.08/0.24 % Result found by SubtermCWHack
% 0.08/0.24 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.24 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.24 % Starting post_as_ho11 with 300s (1) cores
% 0.08/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.24 % No SInE strategy applied
% 0.08/0.24 % Search class: HGUNF-FFSF22-SHSSMMBN
% 0.08/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.24 % Preprocessing time : 0.001 s
% 0.08/0.24
% 0.08/0.24 % Proof found!
% 0.08/0.24 % SZS status Theorem
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.24 % Parsed axioms : 58
% 0.08/0.24 % Removed by relevancy pruning/SinE : 0
% 0.08/0.24 % Initial clauses : 39
% 0.08/0.24 % Removed in clause preprocessing : 31
% 0.08/0.24 % Initial clauses in saturation : 8
% 0.08/0.24 % Processed clauses : 8
% 0.08/0.24 % ...of these trivial : 0
% 0.08/0.24 % ...subsumed : 0
% 0.08/0.24 % ...remaining for further processing : 8
% 0.08/0.24 % Other redundant clauses eliminated : 0
% 0.08/0.24 % Clauses deleted for lack of memory : 0
% 0.08/0.24 % Backward-subsumed : 0
% 0.08/0.24 % Backward-rewritten : 0
% 0.08/0.24 % Generated clauses : 6
% 0.08/0.24 % ...of the previous two non-redundant : 5
% 0.08/0.24 % ...aggressively subsumed : 0
% 0.08/0.24 % Contextual simplify-reflections : 0
% 0.08/0.24 % Paramodulations : 6
% 0.08/0.24 % Factorizations : 0
% 0.08/0.24 % NegExts : 0
% 0.08/0.24 % Equation resolutions : 0
% 0.08/0.24 % Disequality decompositions : 0
% 0.08/0.24 % Total rewrite steps : 1
% 0.08/0.24 % ...of those cached : 0
% 0.08/0.24 % Propositional unsat checks : 0
% 0.08/0.24 % Propositional check models : 0
% 0.08/0.24 % Propositional check unsatisfiable : 0
% 0.08/0.24 % Propositional clauses : 0
% 0.08/0.24 % Propositional clauses after purity: 0
% 0.08/0.24 % Propositional unsat core size : 0
% 0.08/0.24 % Propositional preprocessing time : 0.000
% 0.08/0.24 % Propositional encoding time : 0.000
% 0.08/0.24 % Propositional solver time : 0.000
% 0.08/0.24 % Success case prop preproc time : 0.000
% 0.08/0.24 % Success case prop encoding time : 0.000
% 0.08/0.24 % Success case prop solver time : 0.000
% 0.08/0.24 % Current number of processed clauses : 8
% 0.08/0.24 % Positive orientable unit clauses : 3
% 0.08/0.24 % Positive unorientable unit clauses: 0
% 0.08/0.24 % Negative unit clauses : 1
% 0.08/0.24 % Non-unit-clauses : 4
% 0.08/0.24 % Current number of unprocessed clauses: 4
% 0.08/0.24 % ...number of literals in the above : 13
% 0.08/0.24 % Current number of archived formulas : 0
% 0.08/0.24 % Current number of archived clauses : 0
% 0.08/0.24 % Clause-clause subsumption calls (NU) : 2
% 0.08/0.24 % Rec. Clause-clause subsumption calls : 2
% 0.08/0.24 % Non-unit clause-clause subsumptions : 0
% 0.08/0.24 % Unit Clause-clause subsumption calls : 1
% 0.08/0.24 % Rewrite failures with RHS unbound : 0
% 0.08/0.24 % BW rewrite match attempts : 3
% 0.08/0.24 % BW rewrite match successes : 0
% 0.08/0.24 % Condensation attempts : 0
% 0.08/0.24 % Condensation successes : 0
% 0.08/0.24 % Termbank termtop insertions : 2151
% 0.08/0.24 % Search garbage collected termcells : 596
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.004 s
% 0.08/0.24 % System time : 0.002 s
% 0.08/0.24 % Total time : 0.006 s
% 0.08/0.24 % Maximum resident set size: 3680 pages
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.007 s
% 0.08/0.24 % System time : 0.005 s
% 0.08/0.24 % Total time : 0.013 s
% 0.08/0.24 % Maximum resident set size: 4608 pages
% 0.08/0.24 % E exiting
%------------------------------------------------------------------------------