TSTP Solution File: SYO450^3 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SYO450^3 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n021.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 : Mon Jun 24 20:55:28 EDT 2024
% Result : Theorem 5.51s 2.21s
% Output : Refutation 5.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 12 unt; 0 typ; 5 def)
% Number of atoms : 140 ( 11 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 281 ( 61 ~; 47 |; 0 &; 173 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 39 ( 5 ^ 34 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_m_type,type,
rel_m: $i > $i > $o ).
thf(mbox_m_type,type,
mbox_m: ( $i > $o ) > $i > $o ).
thf(mbox_m_def,definition,
( mbox_m
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_m @ B @ C )
| ( A @ C ) ) ) ) ).
thf(mdia_m_type,type,
mdia_m: ( $i > $o ) > $i > $o ).
thf(mdia_m_def,definition,
( mdia_m
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_m @ ( mnot @ A ) ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(r_type,type,
r: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(3,axiom,
mreflexive @ rel_m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(13,plain,
! [A: $i] : ( rel_m @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [A: $i] : ( rel_m @ A @ A ),
inference(cnf,[status(esa)],[13]) ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mbox_m @ ( mimplies @ p @ ( mdia_m @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_m @ ( mimplies @ q @ ( mimplies @ ( mbox_m @ p ) @ ( mdia_m @ r ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_m @ ( mimplies @ p @ ( mdia_m @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_m @ ( mimplies @ q @ ( mimplies @ ( mbox_m @ p ) @ ( mdia_m @ r ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_m @ A @ B )
| ~ ( p @ B )
| ~ ! [C: $i] :
( ~ ( rel_m @ B @ C )
| ~ ( ~ ( q @ C )
| ( r @ C ) ) ) )
| ~ ! [B: $i] :
( ~ ( rel_m @ A @ B )
| ~ ( ~ ( q @ B )
| ~ ! [C: $i] :
( ~ ( rel_m @ B @ C )
| ( p @ C ) )
| ~ ! [C: $i] :
( ~ ( rel_m @ B @ C )
| ~ ( r @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [A: $i] :
( ~ ( rel_m @ sk1 @ A )
| ~ ( p @ A )
| ~ ( q @ ( sk2 @ A ) )
| ( r @ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ~ ( p @ B )
| ~ ( q @ ( sk2 @ B ) )
| ( r @ ( sk2 @ B ) )
| ( ( rel_m @ A @ A )
!= ( rel_m @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,7]) ).
thf(102,plain,
( ~ ( p @ sk1 )
| ~ ( q @ ( sk2 @ sk1 ) )
| ( r @ ( sk2 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( rel_m @ sk1 @ A )
| ~ ( rel_m @ A @ B )
| ( p @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ~ ( rel_m @ sk1 @ A )
| ~ ( rel_m @ A @ B )
| ( p @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( rel_m @ sk1 @ A )
| ( p @ B )
| ( ( rel_m @ A @ B )
!= ( rel_m @ sk1 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11]) ).
thf(33,plain,
( ~ ( rel_m @ sk1 @ sk1 )
| ( p @ sk1 ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(35,plain,
( ~ $true
| ( p @ sk1 ) ),
inference(rewrite,[status(thm)],[33,14]) ).
thf(36,plain,
p @ sk1,
inference(simp,[status(thm)],[35]) ).
thf(5,plain,
! [A: $i] :
( ~ ( rel_m @ sk1 @ A )
| ~ ( p @ A )
| ( rel_m @ A @ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( p @ B )
| ( rel_m @ B @ ( sk2 @ B ) )
| ( ( rel_m @ A @ A )
!= ( rel_m @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,5]) ).
thf(44,plain,
( ~ ( p @ sk1 )
| ( rel_m @ sk1 @ ( sk2 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(59,plain,
( ~ $true
| ( rel_m @ sk1 @ ( sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[44,36]) ).
thf(60,plain,
rel_m @ sk1 @ ( sk2 @ sk1 ),
inference(simp,[status(thm)],[59]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ~ ( rel_m @ sk1 @ A )
| ~ ( rel_m @ A @ B )
| ~ ( r @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( rel_m @ sk1 @ A )
| ~ ( rel_m @ A @ B )
| ~ ( r @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_m @ sk1 @ B )
| ~ ( r @ C )
| ( ( rel_m @ A @ A )
!= ( rel_m @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14,10]) ).
thf(20,plain,
! [A: $i] :
( ~ ( rel_m @ sk1 @ A )
| ~ ( r @ A ) ),
inference(pattern_uni,[status(thm)],[19:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(67,plain,
! [A: $i] :
( ~ ( r @ A )
| ( ( rel_m @ sk1 @ ( sk2 @ sk1 ) )
!= ( rel_m @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60,20]) ).
thf(68,plain,
~ ( r @ ( sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( sk2 @ sk1 ))]]) ).
thf(8,plain,
! [A: $i] :
( ~ ( rel_m @ sk1 @ A )
| ( q @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(12,plain,
! [A: $i] :
( ~ ( rel_m @ sk1 @ A )
| ( q @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(69,plain,
! [A: $i] :
( ( q @ A )
| ( ( rel_m @ sk1 @ ( sk2 @ sk1 ) )
!= ( rel_m @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60,12]) ).
thf(70,plain,
q @ ( sk2 @ sk1 ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( sk2 @ sk1 ))]]) ).
thf(282,plain,
( ~ $true
| ~ $true
| $false ),
inference(rewrite,[status(thm)],[102,36,68,70]) ).
thf(283,plain,
$false,
inference(simp,[status(thm)],[282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO450^3 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13 % Command : run_Leo-III %s %d SAT
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Jun 23 09:37:10 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.98/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/0.98 % [INFO] Parsing done (134ms).
% 1.29/0.99 % [INFO] Running in sequential loop mode.
% 1.80/1.19 % [INFO] nitpick registered as external prover.
% 1.80/1.19 % [INFO] Scanning for conjecture ...
% 2.01/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.01/1.31 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.01/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 2.01/1.32 % [INFO] Type checking passed.
% 2.01/1.32 % [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 ...
% 5.51/2.20 % [INFO] Killing All external provers ...
% 5.51/2.20 % Time passed: 1669ms (effective reasoning time: 1209ms)
% 5.51/2.20 % 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)>
% 5.51/2.21 % Axioms used in derivation (1): a1
% 5.51/2.21 % No. of inferences in proof: 32
% 5.51/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1669 ms resp. 1209 ms w/o parsing
% 5.51/2.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.51/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------