TSTP Solution File: SYO540^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO540^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 08:57:19 EDT 2024
% Result : Theorem 2.74s 1.66s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 11 unt; 4 typ; 1 def)
% Number of atoms : 81 ( 52 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 103 ( 25 ~; 24 |; 28 &; 25 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-3 aty)
% Number of variables : 33 ( 19 ^ 12 !; 2 ?; 33 :)
% 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(11,axiom,
? [A: ( $i > $o ) > $i] :
! [B: $i > $o] :
( ? [C: $i] : ( B @ C )
=> ( B @ ( A @ B ) ) ),
introduced(axiom_of_choice) ).
thf(37,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( eps
@ ^ [B: $i] : ( B = sk2 ) )
= sk2 ) ),
inference(choice,[status(esa)],[11]) ).
thf(38,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( eps
@ ^ [B: $i] : ( B = sk2 ) )
= sk2 ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(39,plain,
( ( eps
@ ^ [A: $i] : ( A = sk2 ) )
= sk2 ),
inference(simp,[status(thm)],[38]) ).
thf(1,conjecture,
! [A: $o,B: $i] :
( ( if @ A @ B @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $o,B: $i] :
( ( if @ A @ B @ B )
= B ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $o,B: $i] :
( ( eps
@ ^ [C: $i] :
( ( A
& ( C = B ) )
| ( ~ A
& ( C = B ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( eps
@ ^ [A: $i] :
( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk2 ) ) ) )
!= sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( eps
@ ^ [A: $i] :
( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk2 ) ) ) )
!= sk2 ),
inference(lifteq,[status(thm)],[5]) ).
thf(12,plain,
! [A: $i] :
( ~ ( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk2 ) ) )
| ( sk1
& ( ( eps
@ ^ [B: $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 ) )
| ( ~ sk1
& ( ( eps
@ ^ [B: $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 ) ) ),
inference(choice,[status(esa)],[11]) ).
thf(13,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 )
| ( ( eps
@ ^ [B: $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 )
| sk1
| ( A != sk2 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(22,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 )
| ( ( eps
@ ^ [B: $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 )
| ( A != sk2 )
| sk1 ),
inference(lifteq,[status(thm)],[13]) ).
thf(23,plain,
( ( ( eps
@ ^ [A: $i] :
( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk2 ) ) ) )
= sk2 )
| sk1 ),
inference(simp,[status(thm)],[22]) ).
thf(34,plain,
sk1,
inference(simplifyReflect,[status(thm)],[23,6]) ).
thf(35,plain,
( ( eps
@ ^ [A: $i] :
( ( $true
& ( A = sk2 ) )
| ( ~ $true
& ( A = sk2 ) ) ) )
!= sk2 ),
inference(rewrite,[status(thm)],[6,34]) ).
thf(36,plain,
( ( eps
@ ^ [A: $i] : ( A = sk2 ) )
!= sk2 ),
inference(simp,[status(thm)],[35]) ).
thf(40,plain,
$false,
inference(simplifyReflect,[status(thm)],[39,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.08 % Problem : SYO540^1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.09 % Command : run_Leo-III %s %d
% 0.07/0.28 % Computer : n018.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Mon May 20 10:40:53 EDT 2024
% 0.07/0.28 % CPUTime :
% 0.77/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.04/0.89 % [INFO] Parsing done (107ms).
% 1.04/0.89 % [INFO] Running in sequential loop mode.
% 1.33/1.12 % [INFO] eprover registered as external prover.
% 1.33/1.12 % [INFO] cvc4 registered as external prover.
% 1.33/1.13 % [INFO] Scanning for conjecture ...
% 1.53/1.18 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.64/1.20 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.64/1.21 % [INFO] Problem is higher-order (TPTP THF).
% 1.64/1.21 % [INFO] Type checking passed.
% 1.64/1.21 % [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 ...
% 2.74/1.65 % [INFO] Killing All external provers ...
% 2.74/1.66 % Time passed: 1215ms (effective reasoning time: 758ms)
% 2.74/1.66 % 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)>
% 2.74/1.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1215 ms resp. 758 ms w/o parsing
% 2.74/1.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.74/1.74 % [INFO] Killing All external provers ...
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