TSTP Solution File: SYO497^6 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO497^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% 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 : Tue May 21 08:57:09 EDT 2024
% Result : Theorem 3.55s 2.12s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 27
% Syntax : Number of formulae : 33 ( 12 unt; 13 typ; 10 def)
% Number of atoms : 85 ( 10 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 121 ( 12 ~; 8 |; 2 &; 95 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 37 ( 15 ^ 22 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
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_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(mforall_ind_def,definition,
( mforall_ind
= ( ^ [A: mu > $i > $o,B: $i] :
! [C: mu] : ( A @ C @ B ) ) ) ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mexists_ind_def,definition,
( mexists_ind
= ( ^ [A: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [B: mu] : ( mnot @ ( A @ B ) ) ) ) ) ) ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ 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(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(mtransitive_def,definition,
( mtransitive
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s5_type,type,
rel_s5: $i > $i > $o ).
thf(mbox_s5_type,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(mbox_s5_def,definition,
( mbox_s5
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(mdia_s5_type,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(mdia_s5_def,definition,
( mdia_s5
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ A ) ) ) ) ) ).
thf(f_type,type,
f: mu > $i > $o ).
thf(1,conjecture,
( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [A: mu] : ( mimplies @ ( f @ A ) @ ( mbox_s5 @ ( f @ A ) ) ) ) )
@ ( mdia_s5 @ ( mexists_ind @ f ) ) )
@ ( mbox_s5 @ ( mexists_ind @ f ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [A: mu] : ( mimplies @ ( f @ A ) @ ( mbox_s5 @ ( f @ A ) ) ) ) )
@ ( mdia_s5 @ ( mexists_ind @ f ) ) )
@ ( mbox_s5 @ ( mexists_ind @ f ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: mu] :
( ~ ( f @ C @ B )
| ! [D: $i] :
( ~ ( rel_s5 @ B @ D )
| ( f @ C @ D ) ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: mu] :
~ ( f @ C @ B ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ! [C: mu] :
~ ( f @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(14,plain,
! [A: $i] : ( rel_s5 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(16,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rel_s5 @ A @ B )
& ( rel_s5 @ B @ C ) )
=> ( rel_s5 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( rel_s5 @ A @ B )
=> ( rel_s5 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
$false,
inference(cvc4,[status(thm)],[6,14,16,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYO497^6 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.13 % Command : run_Leo-III %s %d
% 0.12/0.34 % Computer : n019.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 : Mon May 20 09:40:39 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.08/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.59/1.25 % [INFO] Parsing done (221ms).
% 1.59/1.27 % [INFO] Running in sequential loop mode.
% 2.08/1.50 % [INFO] eprover registered as external prover.
% 2.08/1.51 % [INFO] cvc4 registered as external prover.
% 2.08/1.51 % [INFO] Scanning for conjecture ...
% 2.41/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.41/1.69 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.41/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 2.41/1.70 % [INFO] Type checking passed.
% 2.41/1.70 % [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 ...
% 3.49/2.11 % External prover 'cvc4' found a proof!
% 3.49/2.11 % [INFO] Killing All external provers ...
% 3.49/2.11 % Time passed: 1616ms (effective reasoning time: 844ms)
% 3.49/2.11 % 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)>
% 3.55/2.12 % Axioms used in derivation (3): a1, a2, a3
% 3.55/2.12 % No. of inferences in proof: 10
% 3.55/2.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1616 ms resp. 844 ms w/o parsing
% 3.55/2.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.55/2.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------