TSTP Solution File: SYO035^1 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO035^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 08:55:30 EDT 2024
% Result : Theorem 3.16s 1.82s
% Output : Refutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 10 unt; 5 typ; 2 def)
% Number of atoms : 46 ( 35 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 44 ( 10 ~; 5 |; 0 &; 22 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 22 ^ 14 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(leibeq1_type,type,
leibeq1: $i > $i > $o ).
thf(leibeq1_def,definition,
( leibeq1
= ( ^ [A: $i,B: $i] :
! [C: $i > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(leibeq2_type,type,
leibeq2: ( $i > $o ) > ( $i > $o ) > $o ).
thf(leibeq2_def,definition,
( leibeq2
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: ( $i > $o ) > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( leibeq2
@ ^ [C: $i] : ( C = A )
@ ^ [C: $i] : ( C = B ) )
=> ( leibeq1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( leibeq2
@ ^ [C: $i] : ( C = A )
@ ^ [C: $i] : ( C = B ) )
=> ( leibeq1 @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i] :
( ! [C: ( $i > $o ) > $o] :
( ( C
@ ^ [D: $i] : ( D = A ) )
=> ( C
@ ^ [D: $i] : ( D = B ) ) )
=> ! [C: $i > $o] :
( ( C @ A )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [A: ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : ( B = sk1 ) )
| ( A
@ ^ [B: $i] : ( B = sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
( ( ( ^ [A: $i] : ( A = sk1 ) )
!= ( ^ [A: $i] : ( A = sk1 ) ) )
| ( ( ^ [A: $i] : ( A = sk1 ) )
= ( ^ [A: $i] : ( A = sk2 ) ) ) ),
inference(replace_leibeq,[status(thm)],[6:[bind(A,$thf( (=) @ ( $i > $o ) @ ^ [B: $i] : ( B = sk1 ) ))]]) ).
thf(8,plain,
( ( ( ^ [A: $i] : ( A = sk1 ) )
!= ( ^ [A: $i] : ( A = sk1 ) ) )
| ( ( ^ [A: $i] : ( A = sk2 ) )
= ( ^ [A: $i] : ( A = sk1 ) ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(9,plain,
( ( ^ [A: $i] : ( A = sk2 ) )
= ( ^ [A: $i] : ( A = sk1 ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(12,plain,
! [A: $i] :
( ( A = sk2 )
= ( A = sk1 ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(16,plain,
! [A: $i] :
( ( A != sk2 )
| ( A = sk1 ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(18,plain,
! [A: $i] :
( ( A != sk2 )
| ( A = sk1 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(20,plain,
sk2 = sk1,
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk2 ))]]) ).
thf(5,plain,
sk3 @ sk1,
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
~ ( sk3 @ sk2 ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
( ( sk3 @ sk2 )
!= ( sk3 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[5,4]) ).
thf(11,plain,
sk2 != sk1,
inference(simp,[status(thm)],[10]) ).
thf(22,plain,
$false,
inference(simplifyReflect,[status(thm)],[20,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SYO035^1 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.17 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n028.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 20 09:49:39 EDT 2024
% 0.16/0.39 % CPUTime :
% 1.05/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.05 % [INFO] Parsing done (111ms).
% 1.29/1.06 % [INFO] Running in sequential loop mode.
% 1.69/1.27 % [INFO] eprover registered as external prover.
% 1.69/1.27 % [INFO] cvc4 registered as external prover.
% 1.69/1.28 % [INFO] Scanning for conjecture ...
% 1.89/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.89/1.35 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.89/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 1.89/1.36 % [INFO] Type checking passed.
% 1.89/1.36 % [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 ...
% 3.16/1.81 % [INFO] Killing All external provers ...
% 3.16/1.82 % Time passed: 1256ms (effective reasoning time: 752ms)
% 3.16/1.82 % 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)>
% 3.16/1.82 % Axioms used in derivation (0):
% 3.16/1.82 % No. of inferences in proof: 16
% 3.16/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1256 ms resp. 752 ms w/o parsing
% 3.19/1.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.19/1.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------