TSTP Solution File: SYO543^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SYO543^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% 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 20:52:07 EDT 2024
% Result : Theorem 2.91s 1.68s
% Output : Refutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 81 ( 52 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 107 ( 29 ~; 24 |; 28 &; 25 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 33 ( 19 ^ 12 !; 2 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(epsii_type,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(if_type,type,
if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(if_def,definition,
( if
= ( ^ [A: $o,B: $i > $i,C: $i > $i] :
( epsii
@ ^ [D: $i > $i] :
( ( A
& ( D = B ) )
| ( ~ A
& ( D = C ) ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(11,axiom,
? [A: ( ( $i > $i ) > $o ) > $i > $i] :
! [B: ( $i > $i ) > $o] :
( ? [C: $i > $i] : ( B @ C )
=> ( B @ ( A @ B ) ) ),
introduced(axiom_of_choice) ).
thf(40,plain,
! [A: $i > $i] :
( ( A != sk2 )
| ( ( epsii
@ ^ [B: $i > $i] : ( B = sk2 ) )
= sk2 ) ),
inference(choice,[status(esa)],[11]) ).
thf(41,plain,
! [A: $i > $i] :
( ( A != sk2 )
| ( ( epsii
@ ^ [B: $i > $i] : ( B = sk2 ) )
= sk2 ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(42,plain,
( ( epsii
@ ^ [A: $i > $i] : ( A = sk2 ) )
= sk2 ),
inference(simp,[status(thm)],[41]) ).
thf(1,conjecture,
! [A: $o,B: $i > $i] :
( ( if @ A @ B @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $o,B: $i > $i] :
( ( if @ A @ B @ B )
= B ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $o,B: $i > $i] :
( ( epsii
@ ^ [C: $i > $i] :
( ( A
& ( C = B ) )
| ( ~ A
& ( C = B ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( epsii
@ ^ [A: $i > $i] :
( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk2 ) ) ) )
!= sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( epsii
@ ^ [A: $i > $i] :
( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk2 ) ) ) )
!= sk2 ),
inference(lifteq,[status(thm)],[5]) ).
thf(12,plain,
! [A: $i > $i] :
( ~ ( ( sk1
& ( A = sk2 ) )
| ( ~ sk1
& ( A = sk2 ) ) )
| ( sk1
& ( ( epsii
@ ^ [B: $i > $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 ) )
| ( ~ sk1
& ( ( epsii
@ ^ [B: $i > $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 ) ) ),
inference(choice,[status(esa)],[11]) ).
thf(13,plain,
! [A: $i > $i] :
( ( ( epsii
@ ^ [B: $i > $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 )
| ( ( epsii
@ ^ [B: $i > $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 )
| ~ sk1
| ( A != sk2 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(22,plain,
! [A: $i > $i] :
( ( ( epsii
@ ^ [B: $i > $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 )
| ( ( epsii
@ ^ [B: $i > $i] :
( ( sk1
& ( B = sk2 ) )
| ( ~ sk1
& ( B = sk2 ) ) ) )
= sk2 )
| ( A != sk2 )
| ~ sk1 ),
inference(lifteq,[status(thm)],[13]) ).
thf(23,plain,
( ( ( epsii
@ ^ [A: $i > $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,
( ( epsii
@ ^ [A: $i > $i] :
( ( $false
& ( A = sk2 ) )
| ( ~ $false
& ( A = sk2 ) ) ) )
!= sk2 ),
inference(rewrite,[status(thm)],[6,34]) ).
thf(36,plain,
( ( epsii
@ ^ [A: $i > $i] : ( A = sk2 ) )
!= sk2 ),
inference(simp,[status(thm)],[35]) ).
thf(43,plain,
$false,
inference(simplifyReflect,[status(thm)],[42,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO543^1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Jun 23 06:55:40 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.97/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.96 % [INFO] Parsing done (101ms).
% 1.24/0.96 % [INFO] Running in sequential loop mode.
% 1.46/1.16 % [INFO] eprover registered as external prover.
% 1.46/1.17 % [INFO] Scanning for conjecture ...
% 1.80/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.80/1.24 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.90/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.90/1.24 % [INFO] Type checking passed.
% 1.90/1.25 % [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 ...
% 2.91/1.68 % [INFO] Killing All external provers ...
% 2.91/1.68 % Time passed: 1162ms (effective reasoning time: 713ms)
% 2.91/1.68 % 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)>
% 2.91/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1162 ms resp. 713 ms w/o parsing
% 3.18/1.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.18/1.72 % [INFO] Killing All external provers ...
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