TSTP Solution File: LCL707^1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : LCL707^1 : TPTP v8.2.0. Bugfixed v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n026.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 11:19:10 EDT 2024
% Result : Theorem 6.26s 2.43s
% Output : Refutation 6.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 19 unt; 0 typ; 7 def)
% Number of atoms : 119 ( 22 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 269 ( 30 ~; 48 |; 2 &; 184 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 52 ( 16 ^ 36 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mor_def,definition,
( mor
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).
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(mweakly_connected_type,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(mweakly_connected_def,definition,
( mweakly_connected
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( ( A @ C @ D )
| ( C = D )
| ( A @ D @ C ) ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $o ).
thf(sk4_type,type,
sk4: $i > $o ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( mweakly_connected @ A )
=> ( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] :
( mforall_prop
@ ^ [C: $i > $o] : ( mor @ ( mbox @ A @ ( mimplies @ ( mand @ B @ ( mbox @ A @ B ) ) @ C ) ) @ ( mbox @ A @ ( mimplies @ ( mand @ C @ ( mbox @ A @ C ) ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( mweakly_connected @ A )
=> ( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] :
( mforall_prop
@ ^ [C: $i > $o] : ( mor @ ( mbox @ A @ ( mimplies @ ( mand @ B @ ( mbox @ A @ B ) ) @ C ) ) @ ( mbox @ A @ ( mimplies @ ( mand @ C @ ( mbox @ A @ C ) ) @ B ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( ( A @ C @ D )
| ( C = D )
| ( A @ D @ C ) ) )
=> ! [B: $i,C: $i > $o,D: $i > $o] :
( ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( C @ E )
| ~ ! [F: $i] :
( ~ ( A @ E @ F )
| ( C @ F ) )
| ( D @ E ) )
| ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( D @ E )
| ~ ! [F: $i] :
( ~ ( A @ E @ F )
| ( D @ F ) )
| ( C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
sk1 @ sk2 @ sk5,
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
sk1 @ sk2 @ sk6,
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B = C )
| ( sk1 @ C @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( sk1 @ C @ B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( sk1 @ C @ B )
| ( ( sk1 @ sk2 @ sk6 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7,13]) ).
thf(75,plain,
! [A: $i] :
( ( sk6 = A )
| ~ ( sk1 @ sk2 @ A )
| ( sk1 @ sk6 @ A )
| ( sk1 @ A @ sk6 ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( sk2 )),bind(B,$thf( sk6 ))]]) ).
thf(93,plain,
! [A: $i] :
( ( sk6 = A )
| ~ ( sk1 @ sk2 @ A )
| ( sk1 @ sk6 @ A )
| ( sk1 @ A @ sk6 ) ),
inference(simp,[status(thm)],[75]) ).
thf(290,plain,
! [A: $i] :
( ( sk6 = A )
| ( sk1 @ sk6 @ A )
| ( sk1 @ A @ sk6 )
| ( ( sk1 @ sk2 @ sk5 )
!= ( sk1 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5,93]) ).
thf(291,plain,
( ( sk6 = sk5 )
| ( sk1 @ sk6 @ sk5 )
| ( sk1 @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( sk5 ))]]) ).
thf(6,plain,
sk3 @ sk5,
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
~ ( sk3 @ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(17,plain,
sk6 != sk5,
inference(simp,[status(thm)],[16]) ).
thf(488,plain,
( ( sk1 @ sk6 @ sk5 )
| ( sk1 @ sk5 @ sk6 ) ),
inference(simplifyReflect,[status(thm)],[291,17]) ).
thf(4,plain,
! [A: $i] :
( ~ ( sk1 @ sk6 @ A )
| ( sk4 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [A: $i] :
( ~ ( sk1 @ sk6 @ A )
| ( sk4 @ A ) ),
inference(simp,[status(thm)],[4]) ).
thf(511,plain,
! [A: $i] :
( ( sk1 @ sk5 @ sk6 )
| ( sk4 @ A )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[488,15]) ).
thf(512,plain,
( ( sk1 @ sk5 @ sk6 )
| ( sk4 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[511:[bind(A,$thf( sk5 ))]]) ).
thf(8,plain,
~ ( sk4 @ sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(534,plain,
( ( sk1 @ sk5 @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[512,8]) ).
thf(535,plain,
sk1 @ sk5 @ sk6,
inference(simp,[status(thm)],[534]) ).
thf(12,plain,
! [A: $i] :
( ~ ( sk1 @ sk5 @ A )
| ( sk3 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [A: $i] :
( ~ ( sk1 @ sk5 @ A )
| ( sk3 @ A ) ),
inference(simp,[status(thm)],[12]) ).
thf(536,plain,
! [A: $i] :
( ( sk3 @ A )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[535,14]) ).
thf(537,plain,
sk3 @ sk6,
inference(pattern_uni,[status(thm)],[536:[bind(A,$thf( sk6 ))]]) ).
thf(577,plain,
$false,
inference(rewrite,[status(thm)],[537,9]) ).
thf(578,plain,
$false,
inference(simp,[status(thm)],[577]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL707^1 : TPTP v8.2.0. Bugfixed v5.1.0.
% 0.03/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Jun 22 16:51:25 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.95/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.10 % [INFO] Parsing done (170ms).
% 1.53/1.11 % [INFO] Running in sequential loop mode.
% 1.92/1.32 % [INFO] nitpick registered as external prover.
% 2.06/1.33 % [INFO] Scanning for conjecture ...
% 2.18/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.41/1.46 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.41/1.46 % [INFO] Problem is higher-order (TPTP THF).
% 2.41/1.46 % [INFO] Type checking passed.
% 2.41/1.46 % [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 ...
% 6.26/2.42 % [INFO] Killing All external provers ...
% 6.26/2.43 % Time passed: 1884ms (effective reasoning time: 1315ms)
% 6.26/2.43 % 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)>
% 6.26/2.43 % Axioms used in derivation (0):
% 6.26/2.43 % No. of inferences in proof: 30
% 6.26/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1884 ms resp. 1315 ms w/o parsing
% 6.26/2.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.26/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------