TSTP Solution File: SYO061^4 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO061^4 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 08:59:08 EDT 2024
% Result : Theorem 5.42s 2.93s
% Output : Refutation 5.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 34 ( 10 unt; 9 typ; 3 def)
% Number of atoms : 73 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 16 ~; 16 |; 0 &; 89 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 19 ( 3 ^ 16 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(irel_type,type,
irel: $i > $i > $o ).
thf(iatom_type,type,
iatom: ( $i > $o ) > $i > $o ).
thf(iatom_def,definition,
( iatom
= ( ^ [A: $i > $o] : A ) ) ).
thf(iimplies_type,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(iimplies_def,definition,
( iimplies
= ( ^ [A: $i > $o,B: $i > $o] : ( mimplies @ ( mbox_s4 @ A ) @ ( mbox_s4 @ B ) ) ) ) ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf(ivalid_def,definition,
( ivalid
= ( '!' @ $i ) ) ).
thf(a_type,type,
a: $i > $o ).
thf(b_type,type,
b: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(1,conjecture,
ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( a @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
irel @ sk1 @ sk2,
inference(cnf,[status(esa)],[6]) ).
thf(5,axiom,
ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(14,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( a @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( irel @ A @ ( sk3 @ A ) )
| ~ ( irel @ A @ B )
| ( b @ B ) ),
inference(cnf,[status(esa)],[14]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( irel @ A @ ( sk3 @ A ) )
| ( b @ B )
| ( ( irel @ sk1 @ sk2 )
!= ( irel @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,15]) ).
thf(70,plain,
( ( irel @ sk1 @ ( sk3 @ sk1 ) )
| ( b @ sk2 ) ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(7,plain,
~ ( b @ sk2 ),
inference(cnf,[status(esa)],[6]) ).
thf(78,plain,
( ( irel @ sk1 @ ( sk3 @ sk1 ) )
| $false ),
inference(rewrite,[status(thm)],[70,7]) ).
thf(79,plain,
irel @ sk1 @ ( sk3 @ sk1 ),
inference(simp,[status(thm)],[78]) ).
thf(9,plain,
! [A: $i] :
( ~ ( irel @ sk1 @ A )
| ( a @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(80,plain,
! [A: $i] :
( ( a @ A )
| ( ( irel @ sk1 @ ( sk3 @ sk1 ) )
!= ( irel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,9]) ).
thf(81,plain,
a @ ( sk3 @ sk1 ),
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ~ ( a @ ( sk3 @ A ) )
| ~ ( irel @ A @ B )
| ( b @ B ) ),
inference(cnf,[status(esa)],[14]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( a @ ( sk3 @ A ) )
| ( b @ B )
| ( ( irel @ sk1 @ sk2 )
!= ( irel @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,16]) ).
thf(24,plain,
( ~ ( a @ ( sk3 @ sk1 ) )
| ( b @ sk2 ) ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(51,plain,
( ~ ( a @ ( sk3 @ sk1 ) )
| $false ),
inference(rewrite,[status(thm)],[24,7]) ).
thf(52,plain,
~ ( a @ ( sk3 @ sk1 ) ),
inference(simp,[status(thm)],[51]) ).
thf(91,plain,
$false,
inference(rewrite,[status(thm)],[81,52]) ).
thf(92,plain,
$false,
inference(simp,[status(thm)],[91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO061^4 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n032.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 10:31:24 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.16/1.10 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.75/1.36 % [INFO] Parsing done (255ms).
% 1.75/1.38 % [INFO] Running in sequential loop mode.
% 2.47/1.82 % [INFO] nitpick registered as external prover.
% 2.47/1.82 % [INFO] Scanning for conjecture ...
% 2.79/1.98 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.79/2.01 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.79/2.02 % [INFO] Problem is higher-order (TPTP THF).
% 2.79/2.02 % [INFO] Type checking passed.
% 2.79/2.03 % [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 ...
% 5.42/2.92 % [INFO] Killing All external provers ...
% 5.42/2.93 % Time passed: 2410ms (effective reasoning time: 1542ms)
% 5.42/2.93 % 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)>
% 5.42/2.93 % Axioms used in derivation (1): axiom1
% 5.42/2.93 % No. of inferences in proof: 22
% 5.42/2.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2410 ms resp. 1542 ms w/o parsing
% 5.43/2.99 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.43/2.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------