TSTP Solution File: SYO446^1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SYO446^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n020.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 20:55:27 EDT 2024
% Result : Theorem 10.11s 2.91s
% Output : Refutation 10.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 13 unt; 0 typ; 6 def)
% Number of atoms : 235 ( 18 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 507 ( 126 ~; 106 |; 2 &; 269 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 14 con; 0-3 aty)
% Number of variables : 69 ( 7 ^ 62 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).
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(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(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 @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_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(15,plain,
( ~ sk1
| ( rel_s5 @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(5,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/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(116,plain,
! [B: $i,A: $i] :
( ~ sk1
| ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk5 @ sk6 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15,24]) ).
thf(117,plain,
( ~ sk1
| ( rel_s5 @ sk6 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(11,plain,
( ( p @ sk3 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(13,plain,
( ( q @ sk4 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(14,plain,
( ( rel_s5 @ sk2 @ sk3 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(10,plain,
( ( rel_s5 @ sk3 @ sk4 )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(4,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/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(173,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)],[10,22]) ).
thf(174,plain,
! [A: $i] :
( sk1
| ~ ( rel_s5 @ A @ sk3 )
| ( rel_s5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(272,plain,
! [A: $i] :
( sk1
| ( rel_s5 @ A @ sk4 )
| ( ( rel_s5 @ sk2 @ sk3 )
!= ( rel_s5 @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,174]) ).
thf(273,plain,
( sk1
| ( rel_s5 @ sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( sk2 ))]]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( rel_s5 @ sk2 @ A )
| ~ ( p @ A )
| ~ ( rel_s5 @ sk2 @ B )
| ~ ( q @ B )
| sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(57,plain,
! [B: $i,A: $i] :
( sk1
| ~ ( p @ A )
| ~ ( rel_s5 @ sk2 @ B )
| ~ ( q @ B )
| ( ( rel_s5 @ sk2 @ sk3 )
!= ( rel_s5 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,12]) ).
thf(58,plain,
! [A: $i] :
( sk1
| ~ ( p @ sk3 )
| ~ ( rel_s5 @ sk2 @ A )
| ~ ( q @ A ) ),
inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( sk3 ))]]) ).
thf(79,plain,
! [A: $i] :
( sk1
| ~ ( p @ sk3 )
| ~ ( rel_s5 @ sk2 @ A )
| ~ ( q @ A ) ),
inference(simp,[status(thm)],[58]) ).
thf(1022,plain,
! [A: $i] :
( sk1
| ~ ( p @ sk3 )
| ~ ( q @ A )
| ( ( rel_s5 @ sk2 @ sk4 )
!= ( rel_s5 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[273,79]) ).
thf(1023,plain,
( sk1
| ~ ( p @ sk3 )
| ~ ( q @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1022:[bind(A,$thf( sk4 ))]]) ).
thf(1069,plain,
( sk1
| ~ ( p @ sk3 )
| ( ( q @ sk4 )
!= ( q @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13,1023]) ).
thf(1070,plain,
( sk1
| ~ ( p @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1069:[]]) ).
thf(1075,plain,
( sk1
| ( ( p @ sk3 )
!= ( p @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[11,1070]) ).
thf(1076,plain,
sk1,
inference(pattern_uni,[status(thm)],[1075:[]]) ).
thf(1082,plain,
( ~ $true
| ( rel_s5 @ sk6 @ sk5 ) ),
inference(rewrite,[status(thm)],[117,1076]) ).
thf(1083,plain,
rel_s5 @ sk6 @ sk5,
inference(simp,[status(thm)],[1082]) ).
thf(1128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ B @ C )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk6 @ sk5 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1083,22]) ).
thf(1129,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk5 @ A )
| ( rel_s5 @ sk6 @ A ) ),
inference(pattern_uni,[status(thm)],[1128:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).
thf(1132,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk5 @ A )
| ( rel_s5 @ sk6 @ A ) ),
inference(simp,[status(thm)],[1129]) ).
thf(17,plain,
( ~ sk1
| ( p @ sk6 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(8,plain,
( ~ sk1
| ( q @ sk7 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ A )
| ~ ( p @ A )
| ~ ( rel_s5 @ A @ B )
| ~ ( q @ B ) ),
inference(cnf,[status(esa)],[7]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ A )
| ~ ( p @ A )
| ~ ( rel_s5 @ A @ B )
| ~ ( q @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ A )
| ~ ( p @ A )
| ~ ( rel_s5 @ A @ B )
| ( ( q @ sk7 )
!= ( q @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,18]) ).
thf(34,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s5 @ sk5 @ A )
| ~ ( p @ A )
| ~ ( rel_s5 @ A @ sk7 ) ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(427,plain,
! [A: $i] :
( ~ sk1
| ~ ( p @ A )
| ~ ( rel_s5 @ A @ sk7 )
| ( ( rel_s5 @ sk5 @ sk6 )
!= ( rel_s5 @ sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15,34]) ).
thf(428,plain,
( ~ sk1
| ~ ( p @ sk6 )
| ~ ( rel_s5 @ sk6 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[427:[bind(A,$thf( sk6 ))]]) ).
thf(580,plain,
( ~ sk1
| ~ ( rel_s5 @ sk6 @ sk7 )
| ( ( p @ sk6 )
!= ( p @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[17,428]) ).
thf(581,plain,
( ~ sk1
| ~ ( rel_s5 @ sk6 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[580:[]]) ).
thf(1096,plain,
( ~ $true
| ~ ( rel_s5 @ sk6 @ sk7 ) ),
inference(rewrite,[status(thm)],[581,1076]) ).
thf(1097,plain,
~ ( rel_s5 @ sk6 @ sk7 ),
inference(simp,[status(thm)],[1096]) ).
thf(1373,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk5 @ A )
| ( ( rel_s5 @ sk6 @ A )
!= ( rel_s5 @ sk6 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[1132,1097]) ).
thf(1374,plain,
~ ( rel_s5 @ sk5 @ sk7 ),
inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( sk7 ))]]) ).
thf(16,plain,
( ~ sk1
| ( rel_s5 @ sk5 @ sk7 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(1094,plain,
( ~ $true
| ( rel_s5 @ sk5 @ sk7 ) ),
inference(rewrite,[status(thm)],[16,1076]) ).
thf(1095,plain,
rel_s5 @ sk5 @ sk7,
inference(simp,[status(thm)],[1094]) ).
thf(1403,plain,
~ $true,
inference(rewrite,[status(thm)],[1374,1095]) ).
thf(1404,plain,
$false,
inference(simp,[status(thm)],[1403]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO446^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13 % Command : run_Leo-III %s %d SAT
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Jun 23 10:15:10 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.82/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.99 % [INFO] Parsing done (144ms).
% 1.20/1.00 % [INFO] Running in sequential loop mode.
% 1.82/1.20 % [INFO] nitpick registered as external prover.
% 1.82/1.21 % [INFO] Scanning for conjecture ...
% 2.07/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.07/1.33 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.07/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 2.07/1.33 % [INFO] Type checking passed.
% 2.07/1.33 % [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 ...
% 10.11/2.91 % [INFO] Killing All external provers ...
% 10.11/2.91 % Time passed: 2381ms (effective reasoning time: 1900ms)
% 10.11/2.91 % 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)>
% 10.11/2.91 % Axioms used in derivation (2): a3, a2
% 10.11/2.91 % No. of inferences in proof: 55
% 10.11/2.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2381 ms resp. 1900 ms w/o parsing
% 10.11/2.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.11/2.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------