TSTP Solution File: LCL710^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : LCL710^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n017.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 11:15:28 EDT 2024
% Result : Theorem 5.58s 2.33s
% Output : Refutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 16 unt; 0 typ; 6 def)
% Number of atoms : 57 ( 13 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 172 ( 36 ~; 19 |; 0 &; 112 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 44 ( 14 ^ 30 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mforall_prop_type,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(mforall_prop_def,definition,
( mforall_prop
= ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
! [C: $i > $o] : ( A @ C @ B ) ) ) ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
! [D: $i] :
( ~ ( A @ C @ D )
| ( B @ D ) ) ) ) ).
thf(mdia_type,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mdia_def,definition,
( mdia
= ( ^ [A: $i > $i > $o,B: $i > $o] : ( mnot @ ( mbox @ A @ ( mnot @ B ) ) ) ) ) ).
thf(msymmetric_type,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(msymmetric_def,definition,
( msymmetric
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ B ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $o ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] : ( mimplies @ B @ ( mbox @ A @ ( mdia @ A @ B ) ) ) ) )
=> ( msymmetric @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] : ( mimplies @ B @ ( mbox @ A @ ( mdia @ A @ B ) ) ) ) )
=> ( msymmetric @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ! [B: $i,C: $i > $o] :
( ~ ( C @ B )
| ! [D: $i] :
( ~ ( A @ B @ D )
| ~ ! [E: $i] :
( ~ ( A @ D @ E )
| ~ ( C @ E ) ) ) )
=> ! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
sk1 @ sk3 @ sk4,
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
~ ( sk1 @ sk4 @ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ sk3 @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[5,4]) ).
thf(9,plain,
( ( sk4 != sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[8]) ).
thf(10,plain,
sk4 != sk3,
inference(simp,[status(thm)],[9]) ).
thf(6,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ A )
| ~ ( sk1 @ A @ C )
| ( B @ ( sk2 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(17,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ A )
| ~ ( sk1 @ A @ C )
| ( ( B @ ( sk2 @ C @ B @ A ) )
!= ( ~ ( B @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6]) ).
thf(24,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ A )
| ~ ( sk1 @ A @ C )
| ( ( B @ ( sk2 @ C @ B @ A ) )
!= ( ~ ( B @ A ) ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(13,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ A )
| ( B @ ( sk2 @ C @ B @ A ) )
| ( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(14,plain,
! [A: $i > $o] :
( ~ ( A @ sk3 )
| ( A @ ( sk2 @ sk4 @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(34,plain,
! [A: $i > $o] :
( ~ ( A @ sk3 )
| ( A @ ( sk2 @ sk4 @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(100,plain,
! [A: $i > $o] :
( ~ ~ ( A @ sk3 )
| ~ ( A
@ ( sk2 @ sk4
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) ) ),
inference(prim_subst,[status(thm)],[34:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(120,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ sk4
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk3 ) ),
inference(cnf,[status(esa)],[100]) ).
thf(121,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ sk4
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk3 ) ),
inference(simp,[status(thm)],[120]) ).
thf(235,plain,
$false,
inference(e,[status(thm)],[5,10,24,121,6,34,3,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL710^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n017.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Jun 22 17:23:10 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.95/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/1.07 % [INFO] Parsing done (158ms).
% 1.42/1.08 % [INFO] Running in sequential loop mode.
% 1.90/1.29 % [INFO] eprover registered as external prover.
% 1.90/1.29 % [INFO] Scanning for conjecture ...
% 2.27/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.27/1.41 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.27/1.42 % [INFO] Problem is higher-order (TPTP THF).
% 2.27/1.42 % [INFO] Type checking passed.
% 2.27/1.42 % [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 ...
% 5.58/2.32 % External prover 'e' found a proof!
% 5.58/2.33 % [INFO] Killing All external provers ...
% 5.58/2.33 % Time passed: 1809ms (effective reasoning time: 1245ms)
% 5.58/2.33 % 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)>
% 5.58/2.33 % Axioms used in derivation (0):
% 5.58/2.33 % No. of inferences in proof: 18
% 5.58/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1809 ms resp. 1245 ms w/o parsing
% 5.58/2.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.58/2.35 % [INFO] Killing All external provers ...
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