TSTP Solution File: SWV061^7 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SWV061^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n019.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 17:27:37 EDT 2024
% Result : Theorem 26.24s 7.36s
% Output : Refutation 26.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 25 ( 13 unt; 0 typ; 6 def)
% Number of atoms : 102 ( 7 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 159 ( 30 ~; 21 |; 0 &; 108 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 30 ( 8 ^ 22 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: $i > $o,B: $i] :
~ ( A @ B ) ) ) ).
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(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(mbox_s4_def,definition,
( mbox_s4
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(true_type,type,
true: $i > $o ).
thf(gt_type,type,
gt: mu > mu > $i > $o ).
thf(loopcounter_type,type,
loopcounter: mu ).
thf(n1_type,type,
n1: mu ).
thf(sk3_type,type,
sk3: $o ).
thf(sk6_type,type,
sk6: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(1,conjecture,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ true ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( gt @ loopcounter @ n1 ) ) ) ) @ ( mbox_s4 @ true ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( gt @ loopcounter @ n1 ) ) @ ( mbox_s4 @ true ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_array_0002) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ true ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( gt @ loopcounter @ n1 ) ) ) ) @ ( mbox_s4 @ true ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( gt @ loopcounter @ n1 ) ) @ ( mbox_s4 @ true ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(169,plain,
~ ! [A: $i,B: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( true @ C ) )
| ~ ( ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ~ ! [D: $i] :
( ~ ( rel_s4 @ C @ D )
| ~ ! [E: $i] :
( ~ ( rel_s4 @ D @ E )
| ( gt @ loopcounter @ n1 @ E ) ) )
| ! [D: $i] :
( ~ ( rel_s4 @ C @ D )
| ( true @ D ) ) )
| ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ~ ! [D: $i] :
( ~ ( rel_s4 @ C @ D )
| ( gt @ loopcounter @ n1 @ D ) )
| ! [D: $i] :
( ~ ( rel_s4 @ C @ D )
| ( true @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(177,plain,
( ~ ( true @ sk6 )
| sk3 ),
inference(cnf,[status(esa)],[169]) ).
thf(136,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(865,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(866,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(cnf,[status(esa)],[865]) ).
thf(121,axiom,
mvalid @ ( mbox_s4 @ true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ttrue) ).
thf(822,plain,
! [A: $i,B: $i] :
( ~ ( rel_s4 @ A @ B )
| ( true @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(823,plain,
! [B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ( true @ B ) ),
inference(cnf,[status(esa)],[822]) ).
thf(2507,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ C )
| ( ( rel_s4 @ A @ A )
!= ( rel_s4 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[866,823]) ).
thf(2508,plain,
! [A: $i] : ( true @ A ),
inference(pattern_uni,[status(thm)],[2507:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(2534,plain,
( ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[177,2508]) ).
thf(2535,plain,
sk3,
inference(simp,[status(thm)],[2534]) ).
thf(170,plain,
( ~ sk3
| ~ ( true @ sk8 ) ),
inference(cnf,[status(esa)],[169]) ).
thf(2531,plain,
( ~ sk3
| ~ $true ),
inference(rewrite,[status(thm)],[170,2508]) ).
thf(2532,plain,
~ sk3,
inference(simp,[status(thm)],[2531]) ).
thf(2578,plain,
$false,
inference(rewrite,[status(thm)],[2535,2532]) ).
thf(2579,plain,
$false,
inference(simp,[status(thm)],[2578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV061^7 : TPTP v8.2.0. Released v5.5.0.
% 0.04/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 17:23:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.96/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.05/1.18 % [INFO] Parsing done (260ms).
% 2.05/1.19 % [INFO] Running in sequential loop mode.
% 2.60/1.40 % [INFO] nitpick registered as external prover.
% 2.60/1.40 % [INFO] Scanning for conjecture ...
% 3.15/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 166 axioms. Running axiom selection ...
% 3.15/1.63 % [INFO] Axiom selection finished. Selected 166 axioms (removed 0 axioms).
% 3.71/1.74 % [INFO] Problem is higher-order (TPTP THF).
% 3.71/1.75 % [INFO] Type checking passed.
% 3.71/1.75 % [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 ...
% 26.23/7.35 % [INFO] Killing All external provers ...
% 26.23/7.35 % Time passed: 6805ms (effective reasoning time: 6160ms)
% 26.23/7.35 % 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)>
% 26.23/7.36 % Axioms used in derivation (2): a1, ttrue
% 26.24/7.36 % No. of inferences in proof: 19
% 26.24/7.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6805 ms resp. 6160 ms w/o parsing
% 26.35/7.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.35/7.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------