%------------------------------------------------------------------------------
% File : E---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 : 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 08:16:01 AM UTC 2026
% Result : Theorem 0.24s 0.32s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 14 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 176 ( 35 ~; 25 |; 1 &; 115 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 58 ( 32 ^; 26 !; 0 ?; 58 :)
% 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_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.dPU2OyMtu7/E---3.1_1992761.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dPU2OyMtu7/E---3.1_1992761.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dPU2OyMtu7/E---3.1_1992761.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dPU2OyMtu7/E---3.1_1992761.p',mimplies) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dPU2OyMtu7/E---3.1_1992761.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.dPU2OyMtu7/E---3.1_1992761.p',mbox_s4) ).
thf(law2,axiom,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dPU2OyMtu7/E---3.1_1992761.p',law2) ).
thf(belief2,axiom,
mvalid @ ( mbox_s4 @ ( class @ second ) ),
file('/export/starexec/sandbox2/tmp/tmp.dPU2OyMtu7/E---3.1_1992761.p',belief2) ).
thf(belief1,axiom,
mvalid @ ( mbox_s4 @ ( dest @ paris ) ),
file('/export/starexec/sandbox2/tmp/tmp.dPU2OyMtu7/E---3.1_1992761.p',belief1) ).
thf(con,conjecture,
mvalid @ ( mbox_s4 @ ( price @ seventy ) ),
file('/export/starexec/sandbox2/tmp/tmp.dPU2OyMtu7/E---3.1_1992761.p',con) ).
thf(c_0_10,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_11,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_12,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_13,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_14,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_10,c_0_11]),c_0_12]) ).
thf(c_0_15,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_13,c_0_11]),c_0_12]) ).
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,
! [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_14]),c_0_15]),c_0_16]),c_0_17])]) ).
thf(c_0_19,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_20,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_21,negated_conjecture,
~ ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_22,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_18])])]) ).
thf(c_0_23,plain,
! [X76: $i,X77: $i] :
( ~ ( rel_s4 @ X76 @ X77 )
| ( class @ second @ X77 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
thf(c_0_24,plain,
! [X74: $i,X75: $i] :
( ~ ( rel_s4 @ X74 @ X75 )
| ( dest @ paris @ X75 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_20])]) ).
thf(c_0_25,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_21,c_0_16]),c_0_17])]) ).
thf(c_0_26,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_22]) ).
thf(c_0_27,plain,
! [X3: $i,X7: $i] :
( ( class @ second @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_28,plain,
! [X3: $i,X7: $i] :
( ( dest @ paris @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_29,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_25])])])]) ).
thf(c_0_30,plain,
! [X7: $i,X3: $i] :
( ( price @ seventy @ X3 )
| ~ ( rel_s4 @ X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_31,negated_conjecture,
rel_s4 @ esk2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_32,negated_conjecture,
~ ( price @ seventy @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP264^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n013.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 11:41:36 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.26 Running higher-order theorem proving
% 0.24/0.29 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.dPU2OyMtu7/E---3.1_1992761.p
% 0.24/0.32 % Version: 3.5.1-ho
% 0.24/0.32 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.24/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.32 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.24/0.32 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.24/0.32 % Starting almost_fo_3_lam with 300s (1) cores
% 0.24/0.32 % Starting post_as_ho1 with 300s (1) cores
% 0.24/0.32 % ho_unfolding_3 with pid 1992785 completed with status 0
% 0.24/0.32 % Result found by ho_unfolding_3
% 0.24/0.32 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.24/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.32 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.24/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.32 % No SInE strategy applied
% 0.24/0.32 % Search class: HHHNM-FFSF11-SHSSMFNN
% 0.24/0.32 % partial match(1): HHHNF-FFSF11-SHSSMFNN
% 0.24/0.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.32 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.32 % Starting ho_unfolding_3 with 151s (1) cores
% 0.24/0.32 % Starting lpo1_def_fix with 136s (1) cores
% 0.24/0.32 % Starting lpo1_lambda_fix with 136s (1) cores
% 0.24/0.32 % Starting new_ho_7 with 136s (1) cores
% 0.24/0.32 % ho_unfolding_3 with pid 1992790 completed with status 0
% 0.24/0.32 % Result found by ho_unfolding_3
% 0.24/0.32 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.24/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.32 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.24/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.32 % No SInE strategy applied
% 0.24/0.32 % Search class: HHHNM-FFSF11-SHSSMFNN
% 0.24/0.32 % partial match(1): HHHNF-FFSF11-SHSSMFNN
% 0.24/0.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.32 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.32 % Starting ho_unfolding_3 with 151s (1) cores
% 0.24/0.32 % Preprocessing time : 0.002 s
% 0.24/0.32 % Presaturation interreduction done
% 0.24/0.32
% 0.24/0.32 % Proof found!
% 0.24/0.32 % SZS status Theorem
% 0.24/0.32 % SZS output start CNFRefutation
% See solution above
% 0.24/0.32 % Parsed axioms : 92
% 0.24/0.32 % Removed by relevancy pruning/SinE : 0
% 0.24/0.32 % Initial clauses : 61
% 0.24/0.32 % Removed in clause preprocessing : 44
% 0.24/0.32 % Initial clauses in saturation : 17
% 0.24/0.32 % Processed clauses : 24
% 0.24/0.32 % ...of these trivial : 0
% 0.24/0.32 % ...subsumed : 0
% 0.24/0.32 % ...remaining for further processing : 24
% 0.24/0.32 % Other redundant clauses eliminated : 0
% 0.24/0.32 % Clauses deleted for lack of memory : 0
% 0.24/0.32 % Backward-subsumed : 0
% 0.24/0.32 % Backward-rewritten : 0
% 0.24/0.32 % Generated clauses : 2
% 0.24/0.32 % ...of the previous two non-redundant : 0
% 0.24/0.32 % ...aggressively subsumed : 0
% 0.24/0.32 % Contextual simplify-reflections : 3
% 0.24/0.32 % Paramodulations : 2
% 0.24/0.32 % Factorizations : 0
% 0.24/0.32 % NegExts : 0
% 0.24/0.32 % Equation resolutions : 0
% 0.24/0.32 % Disequality decompositions : 0
% 0.24/0.32 % Total rewrite steps : 0
% 0.24/0.32 % ...of those cached : 0
% 0.24/0.32 % Propositional unsat checks : 0
% 0.24/0.32 % Propositional check models : 0
% 0.24/0.32 % Propositional check unsatisfiable : 0
% 0.24/0.32 % Propositional clauses : 0
% 0.24/0.32 % Propositional clauses after purity: 0
% 0.24/0.32 % Propositional unsat core size : 0
% 0.24/0.32 % Propositional preprocessing time : 0.000
% 0.24/0.32 % Propositional encoding time : 0.000
% 0.24/0.32 % Propositional solver time : 0.000
% 0.24/0.32 % Success case prop preproc time : 0.000
% 0.24/0.32 % Success case prop encoding time : 0.000
% 0.24/0.32 % Success case prop solver time : 0.000
% 0.24/0.32 % Current number of processed clauses : 7
% 0.24/0.32 % Positive orientable unit clauses : 5
% 0.24/0.32 % Positive unorientable unit clauses: 0
% 0.24/0.32 % Negative unit clauses : 1
% 0.24/0.32 % Non-unit-clauses : 1
% 0.24/0.32 % Current number of unprocessed clauses: 10
% 0.24/0.32 % ...number of literals in the above : 22
% 0.24/0.32 % Current number of archived formulas : 0
% 0.24/0.32 % Current number of archived clauses : 17
% 0.24/0.32 % Clause-clause subsumption calls (NU) : 4
% 0.24/0.32 % Rec. Clause-clause subsumption calls : 4
% 0.24/0.32 % Non-unit clause-clause subsumptions : 3
% 0.24/0.32 % Unit Clause-clause subsumption calls : 0
% 0.24/0.32 % Rewrite failures with RHS unbound : 0
% 0.24/0.32 % BW rewrite match attempts : 2
% 0.24/0.32 % BW rewrite match successes : 0
% 0.24/0.32 % Condensation attempts : 24
% 0.24/0.32 % Condensation successes : 0
% 0.24/0.32 % Termbank termtop insertions : 3744
% 0.24/0.32 % Search garbage collected termcells : 824
% 0.24/0.32
% 0.24/0.32 % -------------------------------------------------
% 0.24/0.32 % User time : 0.005 s
% 0.24/0.32 % System time : 0.005 s
% 0.24/0.32 % Total time : 0.011 s
% 0.24/0.32 % Maximum resident set size: 4172 pages
% 0.24/0.32
% 0.24/0.32 % -------------------------------------------------
% 0.24/0.32 % User time : 0.025 s
% 0.24/0.32 % System time : 0.013 s
% 0.24/0.32 % Total time : 0.038 s
% 0.24/0.32 % Maximum resident set size: 4864 pages
% 0.24/0.32 % E exiting
%------------------------------------------------------------------------------