%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NLP264^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:16:15 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 16 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 191 ( 35 ~; 25 |; 1 &; 130 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 67 ( 34 ^; 33 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_41,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_51,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_55,type,
rel_s4: $i > $i > $o ).
thf(decl_56,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_58,type,
dest: mu > $i > $o ).
thf(decl_59,type,
class: mu > $i > $o ).
thf(decl_60,type,
price: mu > $i > $o ).
thf(decl_63,type,
paris: mu ).
thf(decl_64,type,
second: mu ).
thf(decl_65,type,
seventy: mu ).
thf(decl_67,type,
esk2_0: $i ).
thf(decl_68,type,
esk3_0: $i ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',mimplies) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',mvalid) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X4: $i > $o,X3: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ( X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',mbox_s4) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',mreflexive) ).
thf(belief1,axiom,
mvalid @ ( mbox_s4 @ ( dest @ paris ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',belief1) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',a1) ).
thf(belief2,axiom,
mvalid @ ( mbox_s4 @ ( class @ second ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',belief2) ).
thf(law2,axiom,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',law2) ).
thf(con,conjecture,
mvalid @ ( mbox_s4 @ ( price @ seventy ) ),
file('/export/starexec/sandbox2/tmp/tmp.J0GTGsbh3w/E---3.1_1171700.p',con) ).
thf(c_0_12,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_13,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
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,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_16,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_17,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ Z1 @ X7 )
| ( Z0 @ X7 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_18,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_19,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_12,c_0_13]),c_0_14]) ).
thf(c_0_20,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_15,c_0_13]),c_0_14]) ).
thf(c_0_21,plain,
! [X47: $i,X46: $i] :
( ~ ( rel_s4 @ X47 @ X46 )
| ( dest @ paris @ X46 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[belief1,c_0_16]),c_0_17])]) ).
thf(c_0_22,plain,
! [X34: $i] : ( rel_s4 @ X34 @ X34 ),
inference(apply_def,[status(thm)],[a1,c_0_18]) ).
thf(c_0_23,plain,
! [X49: $i,X48: $i] :
( ~ ( rel_s4 @ X49 @ X48 )
| ( class @ second @ X48 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[belief2,c_0_16]),c_0_17])]) ).
thf(c_0_24,plain,
! [X41: $i,X40: $i] :
( ~ ( rel_s4 @ X41 @ X40 )
| ~ ~ ( ~ ( dest @ paris @ X40 )
| ~ ( class @ second @ X40 ) )
| ( price @ seventy @ X40 ) ),
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)],[law2,c_0_19]),c_0_20]),c_0_16]),c_0_17])]) ).
thf(c_0_25,plain,
! [X74: $i,X75: $i] :
( ~ ( rel_s4 @ X74 @ X75 )
| ( dest @ paris @ X75 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_21])]) ).
thf(c_0_26,plain,
! [X54: $i] : ( rel_s4 @ X54 @ X54 ),
inference(variable_rename,[status(thm)],[c_0_22]) ).
thf(c_0_27,plain,
! [X76: $i,X77: $i] :
( ~ ( rel_s4 @ X76 @ X77 )
| ( class @ second @ X77 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_23])]) ).
thf(c_0_28,negated_conjecture,
~ ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_29,plain,
! [X68: $i,X69: $i] :
( ~ ( rel_s4 @ X68 @ X69 )
| ~ ( dest @ paris @ X69 )
| ~ ( class @ second @ X69 )
| ( price @ seventy @ X69 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
thf(c_0_30,plain,
! [X3: $i,X7: $i] :
( ( dest @ paris @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_31,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_32,plain,
! [X3: $i,X7: $i] :
( ( class @ second @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_33,negated_conjecture,
~ ! [X51: $i,X50: $i] :
( ~ ( rel_s4 @ X51 @ X50 )
| ( price @ seventy @ X50 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_28,c_0_16]),c_0_17])]) ).
thf(c_0_34,plain,
! [X3: $i,X7: $i] :
( ( price @ seventy @ X7 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( dest @ paris @ X7 )
| ~ ( class @ second @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_35,plain,
! [X3: $i] : ( dest @ paris @ X3 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_36,plain,
! [X3: $i] : ( class @ second @ X3 ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
thf(c_0_37,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
& ~ ( price @ seventy @ esk3_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
thf(c_0_38,plain,
! [X7: $i,X3: $i] :
( ( price @ seventy @ X3 )
| ~ ( rel_s4 @ X7 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
thf(c_0_39,negated_conjecture,
rel_s4 @ esk2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_40,negated_conjecture,
~ ( price @ seventy @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NLP264^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 11:44:52 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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.J0GTGsbh3w/E---3.1_1171700.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.26 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.26 % ehoh_best2_full_lfho with pid 1171714 completed with status 0
% 0.09/0.26 % Result found by ehoh_best2_full_lfho
% 0.09/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HHHNM-FFSF11-SHSSMFNN
% 0.09/0.26 % partial match(1): HHHNF-FFSF11-SHSSMFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 1171722 completed with status 0
% 0.09/0.26 % Result found by SubtermCWHack
% 0.09/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HHHNM-FFSF11-SHSSMFNN
% 0.09/0.26 % partial match(1): HHHNF-FFSF11-SHSSMFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % Preprocessing time : 0.002 s
% 0.09/0.26
% 0.09/0.26 % Proof found!
% 0.09/0.26 % SZS status Theorem
% 0.09/0.26 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26 % Parsed axioms : 92
% 0.09/0.26 % Removed by relevancy pruning/SinE : 0
% 0.09/0.26 % Initial clauses : 61
% 0.09/0.26 % Removed in clause preprocessing : 44
% 0.09/0.26 % Initial clauses in saturation : 17
% 0.09/0.26 % Processed clauses : 24
% 0.09/0.26 % ...of these trivial : 0
% 0.09/0.26 % ...subsumed : 1
% 0.09/0.26 % ...remaining for further processing : 23
% 0.09/0.26 % Other redundant clauses eliminated : 0
% 0.09/0.26 % Clauses deleted for lack of memory : 0
% 0.09/0.26 % Backward-subsumed : 0
% 0.09/0.26 % Backward-rewritten : 4
% 0.09/0.26 % Generated clauses : 17
% 0.09/0.26 % ...of the previous two non-redundant : 7
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 0
% 0.09/0.26 % Paramodulations : 17
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 0
% 0.09/0.26 % Equation resolutions : 0
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 14
% 0.09/0.26 % ...of those cached : 2
% 0.09/0.26 % Propositional unsat checks : 0
% 0.09/0.26 % Propositional check models : 0
% 0.09/0.26 % Propositional check unsatisfiable : 0
% 0.09/0.26 % Propositional clauses : 0
% 0.09/0.26 % Propositional clauses after purity: 0
% 0.09/0.26 % Propositional unsat core size : 0
% 0.09/0.26 % Propositional preprocessing time : 0.000
% 0.09/0.26 % Propositional encoding time : 0.000
% 0.09/0.26 % Propositional solver time : 0.000
% 0.09/0.26 % Success case prop preproc time : 0.000
% 0.09/0.26 % Success case prop encoding time : 0.000
% 0.09/0.26 % Success case prop solver time : 0.000
% 0.09/0.26 % Current number of processed clauses : 19
% 0.09/0.26 % Positive orientable unit clauses : 11
% 0.09/0.26 % Positive unorientable unit clauses: 0
% 0.09/0.26 % Negative unit clauses : 1
% 0.09/0.26 % Non-unit-clauses : 7
% 0.09/0.26 % Current number of unprocessed clauses: 0
% 0.09/0.26 % ...number of literals in the above : 0
% 0.09/0.26 % Current number of archived formulas : 0
% 0.09/0.26 % Current number of archived clauses : 4
% 0.09/0.26 % Clause-clause subsumption calls (NU) : 3
% 0.09/0.26 % Rec. Clause-clause subsumption calls : 3
% 0.09/0.26 % Non-unit clause-clause subsumptions : 1
% 0.09/0.26 % Unit Clause-clause subsumption calls : 4
% 0.09/0.26 % Rewrite failures with RHS unbound : 0
% 0.09/0.26 % BW rewrite match attempts : 5
% 0.09/0.26 % BW rewrite match successes : 4
% 0.09/0.26 % Condensation attempts : 0
% 0.09/0.26 % Condensation successes : 0
% 0.09/0.26 % Termbank termtop insertions : 3826
% 0.09/0.26 % Search garbage collected termcells : 824
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.005 s
% 0.09/0.26 % System time : 0.005 s
% 0.09/0.26 % Total time : 0.010 s
% 0.09/0.26 % Maximum resident set size: 3712 pages
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.008 s
% 0.09/0.26 % System time : 0.010 s
% 0.09/0.26 % Total time : 0.018 s
% 0.09/0.26 % Maximum resident set size: 4864 pages
% 0.09/0.26 % E exiting
%------------------------------------------------------------------------------