TSTP Solution File: PHI043^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : PHI043^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:18:32 EDT 2024
% Result : Theorem 3.09s 1.74s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 24
% Syntax : Number of formulae : 29 ( 10 unt; 12 typ; 9 def)
% Number of atoms : 60 ( 13 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 75 ( 6 ~; 1 |; 1 &; 64 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 36 ( 23 ^ 10 !; 3 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: $i > $o,B: $i] :
~ ( A @ B ) ) ) ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(mforall_ind_def,definition,
( mforall_ind
= ( ^ [A: mu > $i > $o,B: $i] :
! [C: mu] : ( A @ C @ B ) ) ) ).
thf(mforall_indset_type,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(mforall_indset_def,definition,
( mforall_indset
= ( ^ [A: ( mu > $i > $o ) > $i > $o,B: $i] :
! [C: mu > $i > $o] : ( A @ C @ B ) ) ) ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mexists_ind_def,definition,
( mexists_ind
= ( ^ [A: mu > $i > $o,B: $i] :
? [C: mu] : ( A @ C @ B ) ) ) ).
thf(rel_type,type,
rel: $i > $i > $o ).
thf(mbox_type,type,
mbox: ( $i > $o ) > $i > $o ).
thf(mbox_def,definition,
( mbox
= ( mbox_generic @ rel ) ) ).
thf(mdia_type,type,
mdia: ( $i > $o ) > $i > $o ).
thf(mdia_def,definition,
( mdia
= ( mdia_generic @ rel ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(p_type,type,
p: ( mu > $i > $o ) > $i > $o ).
thf(1,conjecture,
( mvalid
@ ( mforall_indset
@ ^ [A: mu > $i > $o] : ( mimplies @ ( p @ A ) @ ( mdia @ ( mexists_ind @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',possible_instantiation_of_the_positive) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mforall_indset
@ ^ [A: mu > $i > $o] : ( mimplies @ ( p @ A ) @ ( mdia @ ( mexists_ind @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i,B: mu > $i > $o] :
( ( p @ B @ A )
=> ? [C: $i] :
( ( rel @ A @ C )
& ? [D: mu] : ( B @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
( mvalid
@ ( mnot
@ ( p
@ ^ [A: mu,B: $i] : ( A != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
thf(8,plain,
! [A: $i] :
~ ( p
@ ^ [B: mu,C: $i] : $false
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
( mvalid
@ ( mforall_indset
@ ^ [A: mu > $i > $o] :
( mforall_indset
@ ^ [B: mu > $i > $o] :
( mimplies
@ ( mbox
@ ( mforall_ind
@ ^ [C: mu] : ( mequiv @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( mequiv @ ( p @ A ) @ ( p @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(11,plain,
! [A: $i,B: mu > $i > $o,C: mu > $i > $o] :
( ! [D: $i] :
( ~ ( rel @ A @ D )
| ! [E: mu] :
( ( B @ E @ D )
= ( C @ E @ D ) ) )
=> ( ( p @ B @ A )
= ( p @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
$false,
inference(e,[status(thm)],[5,8,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : PHI043^1 : TPTP v8.2.0. Released v7.5.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n002.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sat May 18 14:49:24 EDT 2024
% 0.17/0.38 % CPUTime :
% 1.04/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/1.04 % [INFO] Parsing done (141ms).
% 1.32/1.04 % [INFO] Running in sequential loop mode.
% 1.87/1.26 % [INFO] eprover registered as external prover.
% 1.87/1.27 % [INFO] cvc4 registered as external prover.
% 1.87/1.27 % [INFO] Scanning for conjecture ...
% 2.10/1.36 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.10/1.38 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.28/1.38 % [INFO] Problem is higher-order (TPTP THF).
% 2.28/1.39 % [INFO] Type checking passed.
% 2.28/1.39 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.09/1.74 % External prover 'e' found a proof!
% 3.09/1.74 % [INFO] Killing All external provers ...
% 3.09/1.74 % Time passed: 1195ms (effective reasoning time: 692ms)
% 3.09/1.74 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.09/1.74 % Axioms used in derivation (2): ax16, ax17
% 3.09/1.74 % No. of inferences in proof: 8
% 3.09/1.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1195 ms resp. 692 ms w/o parsing
% 3.48/1.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.48/1.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------