%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : AGT032^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 07:44:28 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 15 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 132 ( 21 ~; 7 |; 0 &; 101 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 71 ( 30 ^; 38 !; 3 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_34,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_41,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(decl_42,type,
mserial: ( $i > $i > $o ) > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
a1: $i > $i > $o ).
thf(decl_57,type,
jan: mu ).
thf(decl_59,type,
cola: mu ).
thf(decl_62,type,
likes: mu > mu > $i > $o ).
thf(decl_72,type,
esk6_1: $i > $i ).
thf(decl_75,type,
esk9_0: $i ).
thf(msymmetric,axiom,
( msymmetric
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i] :
( ( X13 @ X15 @ X16 )
=> ( X13 @ X16 @ X15 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',msymmetric) ).
thf(mserial,axiom,
( mserial
= ( ^ [X13: $i > $i > $o] :
! [X15: $i] :
? [X16: $i] : ( X13 @ X15 @ X16 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',mserial) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X11: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X11 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',mexists_ind) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',mnot) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X8: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X8 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',mforall_ind) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',mvalid) ).
thf(axioms_B_a1,axiom,
msymmetric @ a1,
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',axioms_B_a1) ).
thf(axioms_D_a1,axiom,
mserial @ a1,
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',axioms_D_a1) ).
thf(conj,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X1: mu] :
( mexists_ind
@ ^ [X2: mu] : ( likes @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',conj) ).
thf(axiom_a1_1,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ jan @ cola ) ),
file('/export/starexec/sandbox2/tmp/tmp.XStQwrXlDv/E---3.1_389974.p',axiom_a1_1) ).
thf(c_0_11,plain,
( msymmetric
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i] :
( ( Z0 @ X15 @ X16 )
=> ( Z0 @ X16 @ X15 ) ) ) ),
inference(fof_simplification,[status(thm)],[msymmetric]) ).
thf(c_0_12,plain,
( mserial
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i] :
? [X16: $i] : ( Z0 @ X15 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mserial]) ).
thf(c_0_13,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X22: mu] :
~ ( Z0 @ X22 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_14,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_15,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_16,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X14: $i] :
( ~ ( Z0 @ Z2 @ X14 )
| ( Z1 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_17,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_18,plain,
! [X81: $i,X82: $i] :
( ( a1 @ X81 @ X82 )
=> ( a1 @ X82 @ X81 ) ),
inference(apply_def,[status(thm)],[axioms_B_a1,c_0_11]) ).
thf(c_0_19,plain,
! [X87: $i] :
? [X88: $i] : ( a1 @ X87 @ X88 ),
inference(apply_def,[status(thm)],[axioms_D_a1,c_0_12]) ).
thf(c_0_20,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [X1: mu] :
( mexists_ind
@ ^ [X2: mu] : ( likes @ X1 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_21,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X22: mu] :
~ ( Z0 @ X22 @ Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_22,plain,
! [X26: $i,X25: $i] :
( ~ ( a1 @ X26 @ X25 )
| ( likes @ jan @ cola @ X25 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom_a1_1,c_0_16]),c_0_17])]) ).
thf(c_0_23,plain,
! [X194: $i,X195: $i] :
( ~ ( a1 @ X194 @ X195 )
| ( a1 @ X195 @ X194 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
thf(c_0_24,plain,
! [X200: $i] : ( a1 @ X200 @ ( esk6_1 @ X200 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
thf(c_0_25,negated_conjecture,
~ ! [X137: $i] :
~ ! [X136: mu] :
~ ~ ! [X135: mu] :
~ ( likes @ X136 @ X135 @ X137 ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_20]),c_0_21]),c_0_17])]) ).
thf(c_0_26,plain,
! [X138: $i,X139: $i] :
( ~ ( a1 @ X138 @ X139 )
| ( likes @ jan @ cola @ X139 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_22])]) ).
thf(c_0_27,plain,
! [X3: $i,X14: $i] :
( ( a1 @ X14 @ X3 )
| ~ ( a1 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_28,plain,
! [X3: $i] : ( a1 @ X3 @ ( esk6_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_29,negated_conjecture,
! [X249: mu,X250: mu] :
~ ( likes @ X249 @ X250 @ esk9_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,
! [X3: $i,X14: $i] :
( ( likes @ jan @ cola @ X14 )
| ~ ( a1 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,plain,
! [X3: $i] : ( a1 @ ( esk6_1 @ X3 ) @ X3 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_32,negated_conjecture,
! [X1: mu,X2: mu] :
~ ( likes @ X1 @ X2 @ esk9_0 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_33,plain,
! [X3: $i] : ( likes @ jan @ cola @ X3 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_34,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_32,c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : AGT032^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.15 % Computer : n018.cluster.edu
% 0.08/0.15 % Model : x86_64 x86_64
% 0.08/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.15 % Memory : 8046.5625MB
% 0.08/0.15 % 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 17:32:47 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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.XStQwrXlDv/E---3.1_389974.p
% 0.08/0.24 % Version: 3.5.1-ho
% 0.08/0.24 % Preprocessing class: HSMSSMSSMLLNHSN.
% 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 new_ho_12 with 300s (1) cores
% 0.08/0.24 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.24 % new_ho_12 with pid 390002 completed with status 0
% 0.08/0.24 % Result found by new_ho_12
% 0.08/0.24 % Preprocessing class: HSMSSMSSMLLNHSN.
% 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 new_ho_12 with 300s (1) cores
% 0.08/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.24 % No SInE strategy applied
% 0.08/0.24 % Search class: HGUNM-FFMF32-SHSSMFNN
% 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 390011 completed with status 0
% 0.08/0.24 % Result found by SubtermCWHack
% 0.08/0.24 % Preprocessing class: HSMSSMSSMLLNHSN.
% 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 new_ho_12 with 300s (1) cores
% 0.08/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.24 % No SInE strategy applied
% 0.08/0.24 % Search class: HGUNM-FFMF32-SHSSMFNN
% 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 : 118
% 0.08/0.24 % Removed by relevancy pruning/SinE : 0
% 0.08/0.24 % Initial clauses : 91
% 0.08/0.24 % Removed in clause preprocessing : 45
% 0.08/0.24 % Initial clauses in saturation : 46
% 0.08/0.24 % Processed clauses : 28
% 0.08/0.24 % ...of these trivial : 0
% 0.08/0.24 % ...subsumed : 3
% 0.08/0.24 % ...remaining for further processing : 25
% 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 : 1
% 0.08/0.24 % Generated clauses : 25
% 0.08/0.24 % ...of the previous two non-redundant : 19
% 0.08/0.24 % ...aggressively subsumed : 0
% 0.08/0.24 % Contextual simplify-reflections : 0
% 0.08/0.24 % Paramodulations : 25
% 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 : 6
% 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 : 24
% 0.08/0.24 % Positive orientable unit clauses : 13
% 0.08/0.24 % Positive unorientable unit clauses: 0
% 0.08/0.24 % Negative unit clauses : 1
% 0.08/0.24 % Non-unit-clauses : 10
% 0.08/0.24 % Current number of unprocessed clauses: 37
% 0.08/0.24 % ...number of literals in the above : 104
% 0.08/0.24 % Current number of archived formulas : 0
% 0.08/0.24 % Current number of archived clauses : 1
% 0.08/0.24 % Clause-clause subsumption calls (NU) : 15
% 0.08/0.24 % Rec. Clause-clause subsumption calls : 15
% 0.08/0.24 % Non-unit clause-clause subsumptions : 3
% 0.08/0.24 % Unit Clause-clause subsumption calls : 2
% 0.08/0.24 % Rewrite failures with RHS unbound : 0
% 0.08/0.24 % BW rewrite match attempts : 1
% 0.08/0.24 % BW rewrite match successes : 1
% 0.08/0.24 % Condensation attempts : 0
% 0.08/0.24 % Condensation successes : 0
% 0.08/0.24 % Termbank termtop insertions : 8943
% 0.08/0.24 % Search garbage collected termcells : 3237
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.010 s
% 0.08/0.24 % System time : 0.003 s
% 0.08/0.24 % Total time : 0.013 s
% 0.08/0.24 % Maximum resident set size: 4232 pages
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.012 s
% 0.08/0.24 % System time : 0.005 s
% 0.08/0.24 % Total time : 0.017 s
% 0.08/0.24 % Maximum resident set size: 4864 pages
% 0.08/0.24 % E exiting
%------------------------------------------------------------------------------