TSTP Solution File: SYO539^1 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO539^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% 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 : Tue May 21 09:00:51 EDT 2024
% Result : Theorem 2.47s 1.51s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 10 unt; 5 typ; 1 def)
% Number of atoms : 88 ( 57 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 125 ( 34 ~; 28 |; 30 &; 32 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 37 ( 20 ^ 15 !; 2 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(eps_type,type,
eps: ( $i > $o ) > $i ).
thf(if_type,type,
if: $o > $i > $i > $i ).
thf(if_def,definition,
( if
= ( ^ [A: $o,B: $i,C: $i] :
( eps
@ ^ [D: $i] :
( ( A
& ( D = B ) )
| ( ~ A
& ( D = C ) ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(12,axiom,
? [A: ( $i > $o ) > $i] :
! [B: $i > $o] :
( ? [C: $i] : ( B @ C )
=> ( B @ ( A @ B ) ) ),
introduced(axiom_of_choice) ).
thf(43,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( eps
@ ^ [B: $i] : ( B = sk3 ) )
= sk3 ) ),
inference(choice,[status(esa)],[12]) ).
thf(44,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( eps
@ ^ [B: $i] : ( B = sk3 ) )
= sk3 ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(45,plain,
( ( eps
@ ^ [A: $i] : ( A = sk3 ) )
= sk3 ),
inference(simp,[status(thm)],[44]) ).
thf(1,conjecture,
! [A: $o,B: $i,C: $i] :
( ( ( if @ A @ B @ C )
= B )
| ( ( if @ A @ B @ C )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $o,B: $i,C: $i] :
( ( ( if @ A @ B @ C )
= B )
| ( ( if @ A @ B @ C )
= C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $o,B: $i,C: $i] :
( ( ( eps
@ ^ [D: $i] :
( ( A
& ( D = B ) )
| ( ~ A
& ( D = C ) ) ) )
= B )
| ( ( eps
@ ^ [D: $i] :
( ( A
& ( D = B ) )
| ( ~ A
& ( D = C ) ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( eps
@ ^ [A: $i] :
( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk3 ) ) ) )
!= sk3 ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
( ( eps
@ ^ [A: $i] :
( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk3 ) ) ) )
!= sk3 ),
inference(lifteq,[status(thm)],[5]) ).
thf(13,plain,
! [A: $i] :
( ~ ( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk3 ) ) )
| ( sk1
& ( ( eps
@ ^ [B: $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk3 ) ) ) )
= sk2 ) )
| ( ~ sk1
& ( ( eps
@ ^ [B: $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk3 ) ) ) )
= sk3 ) ) ),
inference(choice,[status(esa)],[12]) ).
thf(20,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk3 ) ) ) )
= sk2 )
| ~ sk1
| ~ sk1
| ( A != sk2 ) ),
inference(cnf,[status(esa)],[13]) ).
thf(24,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk3 ) ) ) )
= sk2 )
| ( A != sk2 )
| ~ sk1
| ~ sk1 ),
inference(lifteq,[status(thm)],[20]) ).
thf(25,plain,
( ( ( eps
@ ^ [A: $i] :
( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk3 ) ) ) )
= sk2 )
| ~ sk1 ),
inference(simp,[status(thm)],[24]) ).
thf(6,plain,
( ( eps
@ ^ [A: $i] :
( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk3 ) ) ) )
!= sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
( ( eps
@ ^ [A: $i] :
( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk3 ) ) ) )
!= sk2 ),
inference(lifteq,[status(thm)],[6]) ).
thf(38,plain,
~ sk1,
inference(simplifyReflect,[status(thm)],[25,8]) ).
thf(39,plain,
( ( eps
@ ^ [A: $i] :
( ( $false
& ( A = sk2 ) )
| ( ~ $false
& ( A = sk3 ) ) ) )
!= sk3 ),
inference(rewrite,[status(thm)],[7,38]) ).
thf(40,plain,
( ( eps
@ ^ [A: $i] : ( A = sk3 ) )
!= sk3 ),
inference(simp,[status(thm)],[39]) ).
thf(49,plain,
$false,
inference(simplifyReflect,[status(thm)],[45,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO539^1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 09:26:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.95 % [INFO] Parsing done (95ms).
% 1.16/0.96 % [INFO] Running in sequential loop mode.
% 1.54/1.16 % [INFO] nitpick registered as external prover.
% 1.54/1.16 % [INFO] Scanning for conjecture ...
% 1.63/1.21 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.82/1.23 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.82/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.82/1.24 % [INFO] Type checking passed.
% 1.82/1.24 % [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 ...
% 2.47/1.50 % [INFO] Killing All external provers ...
% 2.47/1.51 % Time passed: 979ms (effective reasoning time: 539ms)
% 2.47/1.51 % 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)>
% 2.47/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 979 ms resp. 539 ms w/o parsing
% 2.63/1.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.63/1.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------