TSTP Solution File: SYO468^6 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO468^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 09:00:33 EDT 2024
% Result : Theorem 52.19s 9.86s
% Output : Refutation 52.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 43 ( 14 unt; 13 typ; 6 def)
% Number of atoms : 93 ( 10 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 166 ( 21 ~; 20 |; 2 &; 119 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 39 ( 8 ^ 31 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mor_def,definition,
( mor
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(msymmetric_type,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(msymmetric_def,definition,
( msymmetric
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ B ) ) ) ) ).
thf(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(mtransitive_def,definition,
( mtransitive
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s5_type,type,
rel_s5: $i > $i > $o ).
thf(mbox_s5_type,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(mbox_s5_def,definition,
( mbox_s5
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ p ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( p @ C ) )
| ( q @ B ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( q @ C ) )
| ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
rel_s5 @ sk1 @ sk3,
inference(cnf,[status(esa)],[6]) ).
thf(5,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( rel_s5 @ A @ B )
=> ( rel_s5 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ B @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(715,plain,
! [B: $i,A: $i] :
( ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk1 @ sk3 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7,19]) ).
thf(716,plain,
rel_s5 @ sk3 @ sk1,
inference(pattern_uni,[status(thm)],[715:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(9,plain,
rel_s5 @ sk1 @ sk2,
inference(cnf,[status(esa)],[6]) ).
thf(4,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(16,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rel_s5 @ A @ B )
& ( rel_s5 @ B @ C ) )
=> ( rel_s5 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( rel_s5 @ B @ C )
| ( rel_s5 @ A @ C ) ),
inference(cnf,[status(esa)],[16]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk1 @ sk2 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9,17]) ).
thf(23,plain,
! [A: $i] :
( ~ ( rel_s5 @ A @ sk1 )
| ( rel_s5 @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(848,plain,
! [A: $i] :
( ( rel_s5 @ A @ sk2 )
| ( ( rel_s5 @ sk3 @ sk1 )
!= ( rel_s5 @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[716,23]) ).
thf(849,plain,
rel_s5 @ sk3 @ sk2,
inference(pattern_uni,[status(thm)],[848:[bind(A,$thf( sk3 ))]]) ).
thf(10,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk3 @ A )
| ( q @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(13,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk3 @ A )
| ( q @ A ) ),
inference(simp,[status(thm)],[10]) ).
thf(4975,plain,
! [A: $i] :
( ( q @ A )
| ( ( rel_s5 @ sk3 @ sk2 )
!= ( rel_s5 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[849,13]) ).
thf(4976,plain,
q @ sk2,
inference(pattern_uni,[status(thm)],[4975:[bind(A,$thf( sk2 ))]]) ).
thf(8,plain,
~ ( q @ sk2 ),
inference(cnf,[status(esa)],[6]) ).
thf(5191,plain,
$false,
inference(rewrite,[status(thm)],[4976,8]) ).
thf(5192,plain,
$false,
inference(simp,[status(thm)],[5191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SYO468^6 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11 % Command : run_Leo-III %s %d
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 10:24:09 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.91/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.14 % [INFO] Parsing done (246ms).
% 1.40/1.15 % [INFO] Running in sequential loop mode.
% 2.03/1.50 % [INFO] nitpick registered as external prover.
% 2.03/1.50 % [INFO] Scanning for conjecture ...
% 2.38/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.51/1.69 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.51/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 2.51/1.70 % [INFO] Type checking passed.
% 2.51/1.70 % [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 ...
% 52.16/9.85 % [INFO] Killing All external provers ...
% 52.19/9.86 % Time passed: 9416ms (effective reasoning time: 8695ms)
% 52.19/9.86 % 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)>
% 52.19/9.86 % Axioms used in derivation (2): a3, a2
% 52.19/9.86 % No. of inferences in proof: 24
% 52.19/9.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9416 ms resp. 8695 ms w/o parsing
% 52.19/9.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 52.19/9.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------