TSTP Solution File: SYO470^6 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO470^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 09:00:35 EDT 2024
% Result : Theorem 9.80s 3.38s
% Output : Refutation 9.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 28
% Syntax : Number of formulae : 84 ( 18 unt; 17 typ; 7 def)
% Number of atoms : 216 ( 17 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 498 ( 103 ~; 95 |; 2 &; 294 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 81 ( 8 ^ 73 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ 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(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(mdia_s5_type,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(mdia_s5_def,definition,
( mdia_s5
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ A ) ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i > $i > $i ).
thf(1,conjecture,
mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
~ ( ~ ( ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ~ ! [D: $i] :
( ~ ( rel_s5 @ C @ D )
| ( p @ D ) ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( p @ B ) ) )
| ~ ( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( p @ B ) )
| ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ~ ! [D: $i] :
( ~ ( rel_s5 @ C @ D )
| ( p @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
~ ~ ( ~ ! [A: $i] :
( ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ~ ! [D: $i] :
( ~ ( rel_s5 @ C @ D )
| ( p @ D ) ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( p @ B ) ) )
| ~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( p @ B ) )
| ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ~ ! [D: $i] :
( ~ ( rel_s5 @ C @ D )
| ( p @ D ) ) ) ) ) ),
inference(miniscope,[status(thm)],[6]) ).
thf(14,plain,
( ( rel_s5 @ sk2 @ sk3 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk6 @ A )
| ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ B @ ( sk7 @ B @ A ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk6 @ A )
| ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ B @ ( sk7 @ B @ A ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk6 @ A )
| ( rel_s5 @ B @ ( sk7 @ B @ A ) )
| ( ( rel_s5 @ A @ B )
!= ( rel_s5 @ sk6 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(82,plain,
( ~ sk1
| ~ ( rel_s5 @ sk6 @ sk6 )
| ( rel_s5 @ sk6 @ ( sk7 @ sk6 @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(3,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(19,plain,
! [A: $i] : ( rel_s5 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,plain,
! [A: $i] : ( rel_s5 @ A @ A ),
inference(cnf,[status(esa)],[19]) ).
thf(322,plain,
( ~ sk1
| ~ $true
| ( rel_s5 @ sk6 @ ( sk7 @ sk6 @ sk6 ) ) ),
inference(rewrite,[status(thm)],[82,20]) ).
thf(323,plain,
( ~ sk1
| ( rel_s5 @ sk6 @ ( sk7 @ sk6 @ sk6 ) ) ),
inference(simp,[status(thm)],[322]) ).
thf(8,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk6 @ A )
| ( p @ A ) ),
inference(cnf,[status(esa)],[7]) ).
thf(18,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk6 @ A )
| ( p @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(341,plain,
! [A: $i] :
( ~ sk1
| ( p @ A )
| ( ( rel_s5 @ sk6 @ ( sk7 @ sk6 @ sk6 ) )
!= ( rel_s5 @ sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[323,18]) ).
thf(342,plain,
( ~ sk1
| ( p @ ( sk7 @ sk6 @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[341:[bind(A,$thf( sk7 @ sk6 @ sk6 ))]]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk6 @ A )
| ~ ( rel_s5 @ A @ B )
| ~ ( p @ ( sk7 @ B @ A ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk6 @ A )
| ~ ( rel_s5 @ A @ B )
| ~ ( p @ ( sk7 @ B @ A ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk6 @ A )
| ~ ( p @ ( sk7 @ B @ A ) )
| ( ( rel_s5 @ A @ B )
!= ( rel_s5 @ sk6 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(36,plain,
( ~ sk1
| ~ ( rel_s5 @ sk6 @ sk6 )
| ~ ( p @ ( sk7 @ sk6 @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(38,plain,
( ~ sk1
| ~ $true
| ~ ( p @ ( sk7 @ sk6 @ sk6 ) ) ),
inference(rewrite,[status(thm)],[36,20]) ).
thf(39,plain,
( ~ sk1
| ~ ( p @ ( sk7 @ sk6 @ sk6 ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(359,plain,
( ~ sk1
| ( ( p @ ( sk7 @ sk6 @ sk6 ) )
!= ( p @ ( sk7 @ sk6 @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[342,39]) ).
thf(360,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[359:[]]) ).
thf(382,plain,
( ( rel_s5 @ sk2 @ sk3 )
| $false ),
inference(rewrite,[status(thm)],[14,360]) ).
thf(383,plain,
rel_s5 @ sk2 @ sk3,
inference(simp,[status(thm)],[382]) ).
thf(9,plain,
( ( rel_s5 @ sk3 @ sk4 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(4,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(21,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(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( rel_s5 @ B @ C )
| ( rel_s5 @ A @ C ) ),
inference(cnf,[status(esa)],[21]) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( sk1
| ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk3 @ sk4 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9,22]) ).
thf(252,plain,
! [A: $i] :
( sk1
| ~ ( rel_s5 @ A @ sk3 )
| ( rel_s5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[251:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(555,plain,
! [A: $i] :
( $false
| ~ ( rel_s5 @ A @ sk3 )
| ( rel_s5 @ A @ sk4 ) ),
inference(rewrite,[status(thm)],[252,360]) ).
thf(556,plain,
! [A: $i] :
( ~ ( rel_s5 @ A @ sk3 )
| ( rel_s5 @ A @ sk4 ) ),
inference(simp,[status(thm)],[555]) ).
thf(575,plain,
! [A: $i] :
( ( rel_s5 @ A @ sk4 )
| ( ( rel_s5 @ sk2 @ sk3 )
!= ( rel_s5 @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[383,556]) ).
thf(576,plain,
rel_s5 @ sk2 @ sk4,
inference(pattern_uni,[status(thm)],[575:[bind(A,$thf( sk2 ))]]) ).
thf(5,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( rel_s5 @ A @ B )
=> ( rel_s5 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ B @ A ) ),
inference(cnf,[status(esa)],[23]) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk2 @ sk4 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[576,24]) ).
thf(599,plain,
rel_s5 @ sk4 @ sk2,
inference(pattern_uni,[status(thm)],[598:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(15,plain,
( ( rel_s5 @ sk2 @ sk5 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( sk1
| ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk2 @ sk5 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,22]) ).
thf(264,plain,
! [A: $i] :
( sk1
| ~ ( rel_s5 @ A @ sk2 )
| ( rel_s5 @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk5 ))]]) ).
thf(640,plain,
! [A: $i] :
( $false
| ~ ( rel_s5 @ A @ sk2 )
| ( rel_s5 @ A @ sk5 ) ),
inference(rewrite,[status(thm)],[264,360]) ).
thf(641,plain,
! [A: $i] :
( ~ ( rel_s5 @ A @ sk2 )
| ( rel_s5 @ A @ sk5 ) ),
inference(simp,[status(thm)],[640]) ).
thf(658,plain,
! [A: $i] :
( ( rel_s5 @ A @ sk5 )
| ( ( rel_s5 @ sk4 @ sk2 )
!= ( rel_s5 @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[599,641]) ).
thf(659,plain,
rel_s5 @ sk4 @ sk5,
inference(pattern_uni,[status(thm)],[658:[bind(A,$thf( sk4 ))]]) ).
thf(10,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk4 @ A )
| ( p @ A )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(366,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk4 @ A )
| ( p @ A )
| $false ),
inference(rewrite,[status(thm)],[10,360]) ).
thf(367,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk4 @ A )
| ( p @ A ) ),
inference(simp,[status(thm)],[366]) ).
thf(704,plain,
! [A: $i] :
( ( p @ A )
| ( ( rel_s5 @ sk4 @ sk5 )
!= ( rel_s5 @ sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[659,367]) ).
thf(705,plain,
p @ sk5,
inference(pattern_uni,[status(thm)],[704:[bind(A,$thf( sk5 ))]]) ).
thf(13,plain,
( ~ ( p @ sk5 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(370,plain,
( ~ ( p @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[13,360]) ).
thf(371,plain,
~ ( p @ sk5 ),
inference(simp,[status(thm)],[370]) ).
thf(715,plain,
$false,
inference(rewrite,[status(thm)],[705,371]) ).
thf(716,plain,
$false,
inference(simp,[status(thm)],[715]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : SYO470^6 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.11 % Command : run_Leo-III %s %d
% 0.12/0.31 % Computer : n027.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon May 20 08:44:54 EDT 2024
% 0.12/0.31 % CPUTime :
% 0.89/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/1.14 % [INFO] Parsing done (227ms).
% 1.49/1.15 % [INFO] Running in sequential loop mode.
% 2.01/1.49 % [INFO] nitpick registered as external prover.
% 2.01/1.50 % [INFO] Scanning for conjecture ...
% 2.47/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.53/1.69 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.53/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 2.53/1.70 % [INFO] Type checking passed.
% 2.53/1.70 % [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 ...
% 9.80/3.37 % [INFO] Killing All external provers ...
% 9.80/3.38 % Time passed: 2923ms (effective reasoning time: 2221ms)
% 9.80/3.38 % 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)>
% 9.80/3.38 % Axioms used in derivation (3): a1, a2, a3
% 9.80/3.38 % No. of inferences in proof: 60
% 9.80/3.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2923 ms resp. 2221 ms w/o parsing
% 9.99/3.51 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.99/3.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------