TSTP Solution File: SYO449^1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO449^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 09:00:18 EDT 2024
% Result : Theorem 51.04s 8.42s
% Output : Refutation 51.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 27
% Syntax : Number of formulae : 83 ( 12 unt; 17 typ; 7 def)
% Number of atoms : 245 ( 21 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 487 ( 99 ~; 106 |; 2 &; 276 @)
% ( 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 : 69 ( 8 ^ 61 !; 0 ?; 69 :)
% 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(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(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(q_type,type,
q: $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $o ).
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 @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ) ),
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 ) )
| ( q @ C ) )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ~ ( p @ C )
| ! [D: $i] :
( ~ ( rel_s5 @ C @ D )
| ( q @ D ) ) ) )
| ~ ( ~ ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ~ ( p @ C )
| ! [D: $i] :
( ~ ( rel_s5 @ C @ D )
| ( q @ D ) ) )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ! [D: $i] :
( ~ ( rel_s5 @ C @ D )
| ~ ( p @ D ) )
| ( q @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
( ( rel_s5 @ sk4 @ sk5 )
| sk3 ),
inference(cnf,[status(esa)],[6]) ).
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(92,plain,
! [B: $i,A: $i] :
( sk3
| ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk4 @ sk5 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,24]) ).
thf(93,plain,
( sk3
| ( rel_s5 @ sk5 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(8,plain,
( ( p @ sk4 )
| sk3 ),
inference(cnf,[status(esa)],[6]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ~ ( rel_s5 @ sk2 @ A )
| ~ ( rel_s5 @ A @ B )
| ~ ( p @ B )
| ( q @ A )
| sk3 ),
inference(cnf,[status(esa)],[6]) ).
thf(63,plain,
! [B: $i,A: $i] :
( sk3
| ~ ( rel_s5 @ sk2 @ A )
| ~ ( rel_s5 @ A @ B )
| ( q @ A )
| ( ( p @ sk4 )
!= ( p @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,7]) ).
thf(64,plain,
! [A: $i] :
( sk3
| ~ ( rel_s5 @ sk2 @ A )
| ~ ( rel_s5 @ A @ sk4 )
| ( q @ A ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(2302,plain,
! [A: $i] :
( sk3
| ~ ( rel_s5 @ sk2 @ A )
| ( q @ A )
| ( ( rel_s5 @ sk5 @ sk4 )
!= ( rel_s5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[93,64]) ).
thf(2303,plain,
( sk3
| ~ ( rel_s5 @ sk2 @ sk5 )
| ( q @ sk5 ) ),
inference(pattern_uni,[status(thm)],[2302:[bind(A,$thf( sk5 ))]]) ).
thf(12,plain,
( ~ sk3
| ( rel_s5 @ sk6 @ sk7 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ~ sk3
| ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk6 @ sk7 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,24]) ).
thf(103,plain,
( ~ sk3
| ( rel_s5 @ sk7 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( sk6 )),bind(B,$thf( sk7 ))]]) ).
thf(9,plain,
( ~ sk3
| ( rel_s5 @ sk2 @ sk6 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ~ sk3
| ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk2 @ sk6 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9,24]) ).
thf(101,plain,
( ~ sk3
| ( rel_s5 @ sk6 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( sk2 )),bind(B,$thf( sk6 ))]]) ).
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(191,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk3
| ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk6 @ sk2 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[101,22]) ).
thf(192,plain,
! [A: $i] :
( ~ sk3
| ~ ( rel_s5 @ A @ sk6 )
| ( rel_s5 @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( A )),bind(B,$thf( sk6 )),bind(C,$thf( sk2 ))]]) ).
thf(5143,plain,
! [A: $i] :
( ~ sk3
| ( rel_s5 @ A @ sk2 )
| ( ( rel_s5 @ sk7 @ sk6 )
!= ( rel_s5 @ A @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[103,192]) ).
thf(5144,plain,
( ~ sk3
| ( rel_s5 @ sk7 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5143:[bind(A,$thf( sk7 ))]]) ).
thf(5196,plain,
! [B: $i,A: $i] :
( ~ sk3
| ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk7 @ sk2 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5144,24]) ).
thf(5197,plain,
( ~ sk3
| ( rel_s5 @ sk2 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[5196:[bind(A,$thf( sk7 )),bind(B,$thf( sk2 ))]]) ).
thf(11,plain,
( ~ sk3
| ( p @ sk7 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ sk3
| ~ ( rel_s5 @ sk2 @ A )
| ~ ( p @ A )
| ~ ( rel_s5 @ A @ B )
| ( q @ B ) ),
inference(cnf,[status(esa)],[6]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ sk3
| ~ ( rel_s5 @ sk2 @ A )
| ~ ( p @ A )
| ~ ( rel_s5 @ A @ B )
| ( q @ B ) ),
inference(simp,[status(thm)],[17]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ~ sk3
| ~ ( rel_s5 @ sk2 @ A )
| ~ ( rel_s5 @ A @ B )
| ( q @ B )
| ( ( p @ sk7 )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,18]) ).
thf(30,plain,
! [A: $i] :
( ~ sk3
| ~ ( rel_s5 @ sk2 @ sk7 )
| ~ ( rel_s5 @ sk7 @ A )
| ( q @ A ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk7 ))]]) ).
thf(41,plain,
! [A: $i] :
( ~ sk3
| ~ ( rel_s5 @ sk2 @ sk7 )
| ~ ( rel_s5 @ sk7 @ A )
| ( q @ A ) ),
inference(simp,[status(thm)],[30]) ).
thf(1062,plain,
! [A: $i] :
( ~ sk3
| ~ ( rel_s5 @ sk2 @ sk7 )
| ( q @ A )
| ( ( rel_s5 @ sk7 @ sk6 )
!= ( rel_s5 @ sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,41]) ).
thf(1063,plain,
( ~ sk3
| ~ ( rel_s5 @ sk2 @ sk7 )
| ( q @ sk6 ) ),
inference(pattern_uni,[status(thm)],[1062:[bind(A,$thf( sk6 ))]]) ).
thf(5309,plain,
( ~ sk3
| ( q @ sk6 )
| ( ( rel_s5 @ sk2 @ sk7 )
!= ( rel_s5 @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[5197,1063]) ).
thf(5310,plain,
( ~ sk3
| ( q @ sk6 ) ),
inference(pattern_uni,[status(thm)],[5309:[]]) ).
thf(16,plain,
( ~ sk3
| ~ ( q @ sk6 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(5385,plain,
( ~ sk3
| ( ( q @ sk6 )
!= ( q @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[5310,16]) ).
thf(5386,plain,
~ sk3,
inference(pattern_uni,[status(thm)],[5385:[]]) ).
thf(5399,plain,
( $false
| ~ ( rel_s5 @ sk2 @ sk5 )
| ( q @ sk5 ) ),
inference(rewrite,[status(thm)],[2303,5386]) ).
thf(5400,plain,
( ~ ( rel_s5 @ sk2 @ sk5 )
| ( q @ sk5 ) ),
inference(simp,[status(thm)],[5399]) ).
thf(14,plain,
( ( rel_s5 @ sk2 @ sk4 )
| sk3 ),
inference(cnf,[status(esa)],[6]) ).
thf(5413,plain,
( ( rel_s5 @ sk2 @ sk4 )
| $false ),
inference(rewrite,[status(thm)],[14,5386]) ).
thf(5414,plain,
rel_s5 @ sk2 @ sk4,
inference(simp,[status(thm)],[5413]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( sk3
| ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk4 @ sk5 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10,22]) ).
thf(196,plain,
! [A: $i] :
( sk3
| ~ ( rel_s5 @ A @ sk4 )
| ( rel_s5 @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( sk5 ))]]) ).
thf(5431,plain,
! [A: $i] :
( $false
| ~ ( rel_s5 @ A @ sk4 )
| ( rel_s5 @ A @ sk5 ) ),
inference(rewrite,[status(thm)],[196,5386]) ).
thf(5432,plain,
! [A: $i] :
( ~ ( rel_s5 @ A @ sk4 )
| ( rel_s5 @ A @ sk5 ) ),
inference(simp,[status(thm)],[5431]) ).
thf(5795,plain,
! [A: $i] :
( ( rel_s5 @ A @ sk5 )
| ( ( rel_s5 @ sk2 @ sk4 )
!= ( rel_s5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[5414,5432]) ).
thf(5796,plain,
rel_s5 @ sk2 @ sk5,
inference(pattern_uni,[status(thm)],[5795:[bind(A,$thf( sk2 ))]]) ).
thf(13,plain,
( ~ ( q @ sk5 )
| sk3 ),
inference(cnf,[status(esa)],[6]) ).
thf(5421,plain,
( ~ ( q @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[13,5386]) ).
thf(5422,plain,
~ ( q @ sk5 ),
inference(simp,[status(thm)],[5421]) ).
thf(6890,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[5400,5796,5422]) ).
thf(6891,plain,
$false,
inference(simp,[status(thm)],[6890]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO449^1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 08:42:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.92/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/1.13 % [INFO] Parsing done (218ms).
% 1.38/1.14 % [INFO] Running in sequential loop mode.
% 1.83/1.38 % [INFO] nitpick registered as external prover.
% 1.83/1.38 % [INFO] Scanning for conjecture ...
% 2.25/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.25/1.53 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.25/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.25/1.53 % [INFO] Type checking passed.
% 2.34/1.53 % [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 ...
% 51.04/8.39 % [INFO] Killing All external provers ...
% 51.04/8.41 % Time passed: 7859ms (effective reasoning time: 7247ms)
% 51.04/8.41 % 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)>
% 51.04/8.42 % Axioms used in derivation (2): a3, a2
% 51.04/8.42 % No. of inferences in proof: 59
% 51.04/8.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7859 ms resp. 7247 ms w/o parsing
% 51.24/8.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 51.24/8.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------