%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : AGT028^2 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 07:44:31 AM UTC 2026
% Result : Theorem 0.11s 0.29s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 16 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 140 ( 25 ~; 14 |; 1 &; 100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 68 ( 39 ^; 29 !; 0 ?; 68 :)
% 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_28,type,
mimplies: ( $i > $o ) > ( $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_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_57,type,
r4: $i > $i > $o ).
thf(decl_59,type,
john: mu ).
thf(decl_63,type,
good_in_maths: mu > $i > $o ).
thf(decl_64,type,
maths_teacher: mu > $i > $o ).
thf(decl_85,type,
esk17_0: $i ).
thf(decl_86,type,
esk18_1: mu > $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mq4Nz55N8r/E---3.1_1566478.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mq4Nz55N8r/E---3.1_1566478.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mq4Nz55N8r/E---3.1_1566478.p',mor) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X11: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X11 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mq4Nz55N8r/E---3.1_1566478.p',mexists_ind) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X8: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X8 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mq4Nz55N8r/E---3.1_1566478.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/sandbox/tmp/tmp.Mq4Nz55N8r/E---3.1_1566478.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mq4Nz55N8r/E---3.1_1566478.p',mvalid) ).
thf(conj,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X1: mu] : ( mbox @ r4 @ ( good_in_maths @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mq4Nz55N8r/E---3.1_1566478.p',conj) ).
thf(axiom_r1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( maths_teacher @ X1 ) @ ( mbox @ r4 @ ( good_in_maths @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mq4Nz55N8r/E---3.1_1566478.p',axiom_r1) ).
thf(axiom_a6,axiom,
mvalid @ ( maths_teacher @ john ),
file('/export/starexec/sandbox/tmp/tmp.Mq4Nz55N8r/E---3.1_1566478.p',axiom_a6) ).
thf(c_0_10,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
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,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X18: mu] :
~ ( Z0 @ X18 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_14,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
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_10,c_0_11]),c_0_12]) ).
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,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [X1: mu] : ( mbox @ r4 @ ( good_in_maths @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_19,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X18: mu] :
~ ( Z0 @ X18 @ Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_11]),c_0_14]) ).
thf(c_0_20,plain,
! [X23: $i,X22: mu] :
( ~ ( maths_teacher @ X22 @ X23 )
| ! [X21: $i] :
( ~ ( r4 @ X23 @ X21 )
| ( good_in_maths @ X22 @ X21 ) ) ),
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(fof_simplification,[status(thm)],[axiom_r1]),c_0_15]),c_0_14]),c_0_16]),c_0_17])]) ).
thf(c_0_21,negated_conjecture,
~ ! [X102: $i] :
~ ! [X101: mu] :
~ ! [X100: $i] :
( ~ ( r4 @ X102 @ X100 )
| ( good_in_maths @ X101 @ X100 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_18]),c_0_19]),c_0_16]),c_0_17])]) ).
thf(c_0_22,plain,
! [X103: $i,X104: mu,X105: $i] :
( ~ ( maths_teacher @ X104 @ X103 )
| ~ ( r4 @ X103 @ X105 )
| ( good_in_maths @ X104 @ X105 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_20])])]) ).
thf(c_0_23,negated_conjecture,
! [X183: mu] :
( ( r4 @ esk17_0 @ ( esk18_1 @ X183 ) )
& ~ ( good_in_maths @ X183 @ ( esk18_1 @ X183 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
thf(c_0_24,plain,
! [X3: $i,X1: mu,X14: $i] :
( ( good_in_maths @ X1 @ X14 )
| ~ ( maths_teacher @ X1 @ X3 )
| ~ ( r4 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_25,negated_conjecture,
! [X1: mu] : ( r4 @ esk17_0 @ ( esk18_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_26,plain,
! [X93: $i] : ( maths_teacher @ john @ X93 ),
inference(apply_def,[status(thm)],[axiom_a6,c_0_17]) ).
thf(c_0_27,negated_conjecture,
! [X1: mu] :
~ ( good_in_maths @ X1 @ ( esk18_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_28,negated_conjecture,
! [X2: mu,X1: mu] :
( ( good_in_maths @ X1 @ ( esk18_1 @ X2 ) )
| ~ ( maths_teacher @ X1 @ esk17_0 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_29,plain,
! [X175: $i] : ( maths_teacher @ john @ X175 ),
inference(variable_rename,[status(thm)],[c_0_26]) ).
thf(c_0_30,negated_conjecture,
! [X1: mu] :
~ ( maths_teacher @ X1 @ esk17_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_31,plain,
! [X3: $i] : ( maths_teacher @ john @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_32,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_30,c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT028^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n001.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 17:35:29 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.25 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.Mq4Nz55N8r/E---3.1_1566478.p
% 0.11/0.28 % Version: 3.5.1-ho
% 0.11/0.28 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.11/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.11/0.28 % Starting post_as_ho3 with 300s (1) cores
% 0.11/0.28 % Starting new_ho_12 with 300s (1) cores
% 0.11/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.11/0.28 % post_as_ho3 with pid 1566512 completed with status 0
% 0.11/0.28 % Result found by post_as_ho3
% 0.11/0.28 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.11/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.11/0.28 % Starting post_as_ho3 with 300s (1) cores
% 0.11/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.28 % No SInE strategy applied
% 0.11/0.28 % Search class: HGUNS-FFMF32-SHSSMFNN
% 0.11/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.28 % SubtermCWHack with pid 1566517 completed with status 0
% 0.11/0.28 % Result found by SubtermCWHack
% 0.11/0.28 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.11/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.11/0.29 % Starting post_as_ho3 with 300s (1) cores
% 0.11/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.29 % No SInE strategy applied
% 0.11/0.29 % Search class: HGUNS-FFMF32-SHSSMFNN
% 0.11/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.29 % Preprocessing time : 0.002 s
% 0.11/0.29
% 0.11/0.29 % Proof found!
% 0.11/0.29 % SZS status Theorem
% 0.11/0.29 % SZS output start CNFRefutation
% See solution above
% 0.11/0.29 % Parsed axioms : 100
% 0.11/0.29 % Removed by relevancy pruning/SinE : 0
% 0.11/0.29 % Initial clauses : 86
% 0.11/0.29 % Removed in clause preprocessing : 47
% 0.11/0.29 % Initial clauses in saturation : 39
% 0.11/0.29 % Processed clauses : 9
% 0.11/0.29 % ...of these trivial : 0
% 0.11/0.29 % ...subsumed : 0
% 0.11/0.29 % ...remaining for further processing : 9
% 0.11/0.29 % Other redundant clauses eliminated : 0
% 0.11/0.29 % Clauses deleted for lack of memory : 0
% 0.11/0.29 % Backward-subsumed : 1
% 0.11/0.29 % Backward-rewritten : 0
% 0.11/0.29 % Generated clauses : 3
% 0.11/0.29 % ...of the previous two non-redundant : 2
% 0.11/0.29 % ...aggressively subsumed : 0
% 0.11/0.29 % Contextual simplify-reflections : 0
% 0.11/0.29 % Paramodulations : 3
% 0.11/0.29 % Factorizations : 0
% 0.11/0.29 % NegExts : 0
% 0.11/0.29 % Equation resolutions : 0
% 0.11/0.29 % Disequality decompositions : 0
% 0.11/0.29 % Total rewrite steps : 0
% 0.11/0.29 % ...of those cached : 0
% 0.11/0.29 % Propositional unsat checks : 0
% 0.11/0.29 % Propositional check models : 0
% 0.11/0.29 % Propositional check unsatisfiable : 0
% 0.11/0.29 % Propositional clauses : 0
% 0.11/0.29 % Propositional clauses after purity: 0
% 0.11/0.29 % Propositional unsat core size : 0
% 0.11/0.29 % Propositional preprocessing time : 0.000
% 0.11/0.29 % Propositional encoding time : 0.000
% 0.11/0.29 % Propositional solver time : 0.000
% 0.11/0.29 % Success case prop preproc time : 0.000
% 0.11/0.29 % Success case prop encoding time : 0.000
% 0.11/0.29 % Success case prop solver time : 0.000
% 0.11/0.29 % Current number of processed clauses : 8
% 0.11/0.29 % Positive orientable unit clauses : 2
% 0.11/0.29 % Positive unorientable unit clauses: 0
% 0.11/0.29 % Negative unit clauses : 2
% 0.11/0.29 % Non-unit-clauses : 4
% 0.11/0.29 % Current number of unprocessed clauses: 32
% 0.11/0.29 % ...number of literals in the above : 106
% 0.11/0.29 % Current number of archived formulas : 0
% 0.11/0.29 % Current number of archived clauses : 1
% 0.11/0.29 % Clause-clause subsumption calls (NU) : 2
% 0.11/0.29 % Rec. Clause-clause subsumption calls : 2
% 0.11/0.29 % Non-unit clause-clause subsumptions : 0
% 0.11/0.29 % Unit Clause-clause subsumption calls : 1
% 0.11/0.29 % Rewrite failures with RHS unbound : 0
% 0.11/0.29 % BW rewrite match attempts : 0
% 0.11/0.29 % BW rewrite match successes : 0
% 0.11/0.29 % Condensation attempts : 0
% 0.11/0.29 % Condensation successes : 0
% 0.11/0.29 % Termbank termtop insertions : 8762
% 0.11/0.29 % Search garbage collected termcells : 3764
% 0.11/0.29
% 0.11/0.29 % -------------------------------------------------
% 0.11/0.29 % User time : 0.008 s
% 0.11/0.29 % System time : 0.006 s
% 0.11/0.29 % Total time : 0.014 s
% 0.11/0.29 % Maximum resident set size: 4184 pages
% 0.11/0.29
% 0.11/0.29 % -------------------------------------------------
% 0.11/0.29 % User time : 0.012 s
% 0.11/0.29 % System time : 0.009 s
% 0.11/0.29 % Total time : 0.021 s
% 0.11/0.29 % Maximum resident set size: 4864 pages
% 0.11/0.29 % E exiting
%------------------------------------------------------------------------------