%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO395^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:42:54 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 17 equ; 0 cnn)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 273 ( 60 ~; 52 |; 8 &; 153 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 58 ( 40 ^; 18 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
rel_k: $i > $i > $o ).
thf(decl_55,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(decl_57,type,
p: $i > $o ).
thf(decl_58,type,
esk1_0: $i ).
thf(decl_59,type,
esk2_0: $i ).
thf(decl_60,type,
esk3_0: $i ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c3nn0NcfCL/E---3.1_2367519.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c3nn0NcfCL/E---3.1_2367519.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c3nn0NcfCL/E---3.1_2367519.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c3nn0NcfCL/E---3.1_2367519.p',mimplies) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mand @ ( mimplies @ X6 @ X7 ) @ ( mimplies @ X7 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c3nn0NcfCL/E---3.1_2367519.p',mequiv) ).
thf(prove,conjecture,
mvalid @ ( mequiv @ ( mbox_k @ ( mimplies @ ( mnot @ p ) @ p ) ) @ ( mbox_k @ p ) ),
file('/export/starexec/sandbox/tmp/tmp.c3nn0NcfCL/E---3.1_2367519.p',prove) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c3nn0NcfCL/E---3.1_2367519.p',mvalid) ).
thf(mbox_k,axiom,
( mbox_k
= ( ^ [X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( rel_k @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c3nn0NcfCL/E---3.1_2367519.p',mbox_k) ).
thf(c_0_8,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_9,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_10,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_11,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_12,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
| ~ ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv]) ).
thf(c_0_13,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_14,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_9]),c_0_10]) ).
thf(c_0_15,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mbox_k @ ( mimplies @ ( mnot @ p ) @ p ) ) @ ( mbox_k @ p ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(c_0_16,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
| ~ ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_17,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_18,plain,
( mbox_k
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X14: $i] :
( ~ ( rel_k @ Z1 @ X14 )
| ( Z0 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_k]) ).
thf(c_0_19,negated_conjecture,
~ ! [X24: $i] :
~ ( ~ ( ~ ! [X22: $i] :
( ~ ( rel_k @ X24 @ X22 )
| ( p @ X22 ) )
| ! [X23: $i] :
( ~ ( rel_k @ X24 @ X23 )
| ( p @ X23 ) ) )
| ~ ( ~ ! [X23: $i] :
( ~ ( rel_k @ X24 @ X23 )
| ( p @ X23 ) )
| ! [X22: $i] :
( ~ ( rel_k @ X24 @ X22 )
| ( p @ X22 ) ) ) ),
inference(fof_simplification,[status(thm)],[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_15,c_0_9]),c_0_14]),c_0_16]),c_0_17]),c_0_18])]) ).
thf(c_0_20,negated_conjecture,
! [X26: $i,X28: $i] :
( ( ~ ( rel_k @ esk1_0 @ X28 )
| ( p @ X28 )
| ~ ( rel_k @ esk1_0 @ X26 )
| ( p @ X26 ) )
& ( ( rel_k @ esk1_0 @ esk3_0 )
| ~ ( rel_k @ esk1_0 @ X26 )
| ( p @ X26 ) )
& ( ~ ( p @ esk3_0 )
| ~ ( rel_k @ esk1_0 @ X26 )
| ( p @ X26 ) )
& ( ~ ( rel_k @ esk1_0 @ X28 )
| ( p @ X28 )
| ( rel_k @ esk1_0 @ esk2_0 ) )
& ( ( rel_k @ esk1_0 @ esk3_0 )
| ( rel_k @ esk1_0 @ esk2_0 ) )
& ( ~ ( p @ esk3_0 )
| ( rel_k @ esk1_0 @ esk2_0 ) )
& ( ~ ( rel_k @ esk1_0 @ X28 )
| ( p @ X28 )
| ~ ( p @ esk2_0 ) )
& ( ( rel_k @ esk1_0 @ esk3_0 )
| ~ ( p @ esk2_0 ) )
& ( ~ ( p @ esk3_0 )
| ~ ( p @ esk2_0 ) ) ),
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_19])])])])])]) ).
thf(c_0_21,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( p @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_22,negated_conjecture,
( ( rel_k @ esk1_0 @ esk3_0 )
| ~ ( p @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,negated_conjecture,
( ~ ( p @ esk3_0 )
| ~ ( p @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ~ ( p @ esk3_0 )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_25,negated_conjecture,
( ( rel_k @ esk1_0 @ esk2_0 )
| ~ ( p @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,negated_conjecture,
~ ( p @ esk2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
thf(c_0_27,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ( rel_k @ esk1_0 @ esk2_0 )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,negated_conjecture,
( ( rel_k @ esk1_0 @ esk3_0 )
| ( rel_k @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_29,negated_conjecture,
~ ( p @ esk3_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
thf(c_0_30,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk1_0 @ esk3_0 )
| ( p @ X3 )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_31,negated_conjecture,
rel_k @ esk1_0 @ esk2_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_32,negated_conjecture,
! [X3: $i,X14: $i] :
( ( p @ X3 )
| ( p @ X14 )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( rel_k @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_33,negated_conjecture,
rel_k @ esk1_0 @ esk3_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_26]) ).
thf(c_0_34,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29]) ).
thf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_33]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO395^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:49:51 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.c3nn0NcfCL/E---3.1_2367519.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.22/0.27 % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.27 % ehoh_best2_full_lfho with pid 2367550 completed with status 0
% 0.22/0.27 % Result found by ehoh_best2_full_lfho
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGHNF-FFSF00-SHSSMFNN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 2367556 completed with status 0
% 0.22/0.27 % Result found by SubtermCWHack
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGHNF-FFSF00-SHSSMFNN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % Preprocessing time : 0.001 s
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% See solution above
% 0.22/0.27 % Parsed axioms : 70
% 0.22/0.27 % Removed by relevancy pruning/SinE : 0
% 0.22/0.27 % Initial clauses : 45
% 0.22/0.27 % Removed in clause preprocessing : 36
% 0.22/0.27 % Initial clauses in saturation : 9
% 0.22/0.27 % Processed clauses : 14
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 0
% 0.22/0.27 % ...remaining for further processing : 14
% 0.22/0.27 % Other redundant clauses eliminated : 0
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 6
% 0.22/0.27 % Backward-rewritten : 3
% 0.22/0.27 % Generated clauses : 11
% 0.22/0.27 % ...of the previous two non-redundant : 7
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 1
% 0.22/0.27 % Paramodulations : 11
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 0
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 3
% 0.22/0.27 % ...of those cached : 1
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 5
% 0.22/0.27 % Positive orientable unit clauses : 2
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 2
% 0.22/0.27 % Non-unit-clauses : 1
% 0.22/0.27 % Current number of unprocessed clauses: 1
% 0.22/0.27 % ...number of literals in the above : 2
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 9
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 2
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 2
% 0.22/0.27 % Non-unit clause-clause subsumptions : 2
% 0.22/0.27 % Unit Clause-clause subsumption calls : 5
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 2
% 0.22/0.27 % BW rewrite match successes : 2
% 0.22/0.27 % Condensation attempts : 0
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 2689
% 0.22/0.27 % Search garbage collected termcells : 484
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.008 s
% 0.22/0.27 % System time : 0.000 s
% 0.22/0.27 % Total time : 0.008 s
% 0.22/0.27 % Maximum resident set size: 3696 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.012 s
% 0.22/0.27 % System time : 0.003 s
% 0.22/0.27 % Total time : 0.015 s
% 0.22/0.27 % Maximum resident set size: 4864 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------