TSTP Solution File: SYO068^4.001 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO068^4.001 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 08:59:11 EDT 2024
% Result : Theorem 3.92s 2.26s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 33 ( 13 unt; 9 typ; 3 def)
% Number of atoms : 69 ( 5 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 116 ( 20 ~; 16 |; 0 &; 76 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 33 ( 3 ^ 30 !; 0 ?; 33 :)
% 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(p0_type,type,
p0: $i > $o ).
thf(p1_type,type,
p1: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(1,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i] : ( p0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
~ ( p0 @ sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(3,axiom,
! [A: $i] : ( irel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom) ).
thf(9,plain,
! [A: $i] : ( irel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [A: $i] : ( irel @ A @ A ),
inference(cnf,[status(esa)],[9]) ).
thf(6,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
thf(15,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p1 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p1 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p0 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( p1 @ ( sk2 @ A ) )
| ~ ( irel @ A @ B )
| ~ ( p1 @ ( sk3 @ B @ A ) )
| ~ ( irel @ B @ C )
| ( p0 @ C ) ),
inference(cnf,[status(esa)],[15]) ).
thf(5,axiom,
ivalid @ ( iatom @ p1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(13,plain,
! [A: $i] : ( p1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,plain,
! [A: $i] : ( p1 @ A ),
inference(cnf,[status(esa)],[13]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ ( irel @ A @ B )
| ~ $true
| ~ ( irel @ B @ C )
| ( p0 @ C ) ),
inference(rewrite,[status(thm)],[19,14]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( irel @ A @ B )
| ~ ( irel @ B @ C )
| ( p0 @ C ) ),
inference(simp,[status(thm)],[32]) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( irel @ B @ C )
| ( p0 @ D )
| ( ( irel @ A @ A )
!= ( irel @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,33]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( irel @ B @ A )
| ( p0 @ A ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( p0 @ B )
| ( ( irel @ A @ A )
!= ( irel @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,37]) ).
thf(48,plain,
! [A: $i] : ( p0 @ A ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(51,plain,
~ $true,
inference(rewrite,[status(thm)],[8,48]) ).
thf(52,plain,
$false,
inference(simp,[status(thm)],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SYO068^4.001 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.11 % Command : run_Leo-III %s %d
% 0.10/0.31 % Computer : n008.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 10:41:39 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.90/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/1.12 % [INFO] Parsing done (204ms).
% 1.32/1.13 % [INFO] Running in sequential loop mode.
% 2.00/1.48 % [INFO] nitpick registered as external prover.
% 2.00/1.48 % [INFO] Scanning for conjecture ...
% 2.15/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.33/1.63 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.33/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.33/1.64 % [INFO] Type checking passed.
% 2.33/1.65 % [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 ...
% 3.92/2.26 % [INFO] Killing All external provers ...
% 3.92/2.26 % Time passed: 1803ms (effective reasoning time: 1118ms)
% 3.92/2.26 % 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)>
% 3.92/2.26 % Axioms used in derivation (3): refl_axiom, axiom2, axiom1
% 3.92/2.26 % No. of inferences in proof: 21
% 3.92/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1803 ms resp. 1118 ms w/o parsing
% 3.92/2.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.92/2.32 % [INFO] Killing All external provers ...
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