TSTP Solution File: SYO443^1 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO443^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 09:00:16 EDT 2024
% Result : Theorem 20.70s 4.53s
% Output : Refutation 20.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 28
% Syntax : Number of formulae : 80 ( 14 unt; 18 typ; 7 def)
% Number of atoms : 236 ( 18 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 491 ( 106 ~; 111 |; 2 &; 268 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 78 ( 11 ^ 67 !; 0 ?; 78 :)
% 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(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(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(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: $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 ).
thf(1,conjecture,
mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
~ ( ~ ( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( p @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( q @ C ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( p @ B ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( q @ B ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( p @ B ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( q @ B ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( p @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( q @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
~ ~ ( ~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( p @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( q @ C ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( p @ B ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( q @ B ) ) )
| ~ ! [A: $i] :
( ~ ( ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( p @ B ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( q @ B ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( p @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( q @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[6]) ).
thf(12,plain,
( ( rel_s5 @ sk2 @ sk3 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
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(76,plain,
! [B: $i,A: $i] :
( sk1
| ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk2 @ sk3 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,24]) ).
thf(77,plain,
( sk1
| ( rel_s5 @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(9,plain,
( ( rel_s5 @ sk2 @ 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(250,plain,
! [C: $i,B: $i,A: $i] :
( sk1
| ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk2 @ sk4 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9,22]) ).
thf(251,plain,
! [A: $i] :
( sk1
| ~ ( rel_s5 @ A @ sk2 )
| ( rel_s5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).
thf(367,plain,
! [A: $i] :
( sk1
| ( rel_s5 @ A @ sk4 )
| ( ( rel_s5 @ sk3 @ sk2 )
!= ( rel_s5 @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[77,251]) ).
thf(368,plain,
( sk1
| ( rel_s5 @ sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[367:[bind(A,$thf( sk3 ))]]) ).
thf(13,plain,
( ~ sk1
| ( rel_s5 @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(14,plain,
( ~ sk1
| ( rel_s5 @ sk6 @ sk7 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk6 @ sk7 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14,22]) ).
thf(243,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s5 @ A @ sk6 )
| ( rel_s5 @ A @ sk7 ) ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( A )),bind(B,$thf( sk6 )),bind(C,$thf( sk7 ))]]) ).
thf(1705,plain,
! [A: $i] :
( ~ sk1
| ( rel_s5 @ A @ sk7 )
| ( ( rel_s5 @ sk5 @ sk6 )
!= ( rel_s5 @ A @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[13,243]) ).
thf(1706,plain,
( ~ sk1
| ( rel_s5 @ sk5 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[1705:[bind(A,$thf( sk5 ))]]) ).
thf(10,plain,
( ~ sk1
| ( p @ sk6 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ A )
| ~ ( p @ A )
| ~ ( rel_s5 @ sk5 @ B )
| ( q @ B ) ),
inference(cnf,[status(esa)],[7]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ A )
| ~ ( p @ A )
| ~ ( rel_s5 @ sk5 @ B )
| ( q @ B ) ),
inference(simp,[status(thm)],[17]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ A )
| ~ ( rel_s5 @ sk5 @ B )
| ( q @ B )
| ( ( p @ sk6 )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,18]) ).
thf(26,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ sk6 )
| ~ ( rel_s5 @ sk5 @ A )
| ( q @ A ) ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( sk6 ))]]) ).
thf(34,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ sk6 )
| ~ ( rel_s5 @ sk5 @ A )
| ( q @ A ) ),
inference(simp,[status(thm)],[26]) ).
thf(605,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ A )
| ( q @ A )
| ( ( rel_s5 @ sk5 @ sk6 )
!= ( rel_s5 @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[13,34]) ).
thf(606,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ A )
| ( q @ A ) ),
inference(pattern_uni,[status(thm)],[605:[]]) ).
thf(1763,plain,
! [A: $i] :
( ~ sk1
| ( q @ A )
| ( ( rel_s5 @ sk5 @ sk7 )
!= ( rel_s5 @ sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1706,606]) ).
thf(1764,plain,
( ~ sk1
| ( q @ sk7 ) ),
inference(pattern_uni,[status(thm)],[1763:[bind(A,$thf( sk7 ))]]) ).
thf(8,plain,
( ~ sk1
| ~ ( q @ sk7 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(1812,plain,
( ~ sk1
| ( ( q @ sk7 )
!= ( q @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[1764,8]) ).
thf(1813,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[1812:[]]) ).
thf(1836,plain,
( $false
| ( rel_s5 @ sk3 @ sk4 ) ),
inference(rewrite,[status(thm)],[368,1813]) ).
thf(1837,plain,
rel_s5 @ sk3 @ sk4,
inference(simp,[status(thm)],[1836]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( rel_s5 @ sk2 @ A )
| ~ ( p @ A )
| ~ ( rel_s5 @ A @ B )
| ( q @ B )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(181,plain,
! [B: $i,A: $i] :
( sk1
| ~ ( p @ A )
| ~ ( rel_s5 @ A @ B )
| ( q @ B )
| ( ( rel_s5 @ sk2 @ sk3 )
!= ( rel_s5 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,15]) ).
thf(182,plain,
! [A: $i] :
( sk1
| ~ ( p @ sk3 )
| ~ ( rel_s5 @ sk3 @ A )
| ( q @ A ) ),
inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( sk3 ))]]) ).
thf(197,plain,
! [A: $i] :
( sk1
| ~ ( p @ sk3 )
| ~ ( rel_s5 @ sk3 @ A )
| ( q @ A ) ),
inference(simp,[status(thm)],[182]) ).
thf(16,plain,
( ( p @ sk3 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(1832,plain,
( ( p @ sk3 )
| $false ),
inference(rewrite,[status(thm)],[16,1813]) ).
thf(1833,plain,
p @ sk3,
inference(simp,[status(thm)],[1832]) ).
thf(2575,plain,
! [A: $i] :
( $false
| ~ $true
| ~ ( rel_s5 @ sk3 @ A )
| ( q @ A ) ),
inference(rewrite,[status(thm)],[197,1813,1833]) ).
thf(2576,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk3 @ A )
| ( q @ A ) ),
inference(simp,[status(thm)],[2575]) ).
thf(2589,plain,
! [A: $i] :
( ( q @ A )
| ( ( rel_s5 @ sk3 @ sk4 )
!= ( rel_s5 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1837,2576]) ).
thf(2590,plain,
q @ sk4,
inference(pattern_uni,[status(thm)],[2589:[bind(A,$thf( sk4 ))]]) ).
thf(11,plain,
( ~ ( q @ sk4 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(1834,plain,
( ~ ( q @ sk4 )
| $false ),
inference(rewrite,[status(thm)],[11,1813]) ).
thf(1835,plain,
~ ( q @ sk4 ),
inference(simp,[status(thm)],[1834]) ).
thf(2614,plain,
$false,
inference(rewrite,[status(thm)],[2590,1835]) ).
thf(2615,plain,
$false,
inference(simp,[status(thm)],[2614]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO443^1 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.17 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n012.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 : Mon May 20 09:03:39 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.92/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.08 % [INFO] Parsing done (157ms).
% 1.47/1.09 % [INFO] Running in sequential loop mode.
% 1.94/1.32 % [INFO] nitpick registered as external prover.
% 1.94/1.32 % [INFO] Scanning for conjecture ...
% 2.09/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.35/1.46 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.35/1.46 % [INFO] Problem is higher-order (TPTP THF).
% 2.35/1.46 % [INFO] Type checking passed.
% 2.35/1.46 % [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 ...
% 20.70/4.51 % [INFO] Killing All external provers ...
% 20.70/4.52 % Time passed: 3987ms (effective reasoning time: 3427ms)
% 20.70/4.52 % 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)>
% 20.70/4.52 % Axioms used in derivation (2): a3, a2
% 20.70/4.52 % No. of inferences in proof: 55
% 20.70/4.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3987 ms resp. 3427 ms w/o parsing
% 20.88/4.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.93/4.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------