TSTP Solution File: PUZ150^18 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : PUZ150^18 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n027.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 13:48:21 EDT 2024
% Result : Theorem 4.10s 2.26s
% Output : Refutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 31 ( 13 unt; 0 typ; 5 def)
% Number of atoms : 176 ( 5 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 359 ( 5 ~; 15 |; 3 &; 298 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 5 con; 0-3 aty)
% Number of variables : 65 ( 12 ^ 50 !; 3 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mindex_type,type,
mindex: $tType ).
thf(mrel_type,type,
mrel: mindex > mworld > mworld > $o ).
thf('\'#c\'_type',type,
'\'#c\'': mindex ).
thf('\'#b\'_type',type,
'\'#b\'': mindex ).
thf('\'#a\'_type',type,
'\'#a\'': mindex ).
thf(mactual_type,type,
mactual: mworld ).
thf(mlocal_type,type,
mlocal: ( mworld > $o ) > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mnot_type,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
thf(mor_type,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mor_def,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mbox_type,type,
mbox: mindex > ( mworld > $o ) > mworld > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mindex,B: mworld > $o,C: mworld] :
! [D: mworld] :
( ( mrel @ A @ C @ D )
=> ( B @ D ) ) ) ) ).
thf(mdia_type,type,
mdia: mindex > ( mworld > $o ) > mworld > $o ).
thf(mdia_def,definition,
( mdia
= ( ^ [A: mindex,B: mworld > $o,C: mworld] :
? [D: mworld] :
( ( mrel @ A @ C @ D )
& ( B @ D ) ) ) ) ).
thf(c0_type,type,
c0: mworld > $o ).
thf(c1_type,type,
c1: mworld > $o ).
thf(b0_type,type,
b0: mworld > $o ).
thf(c2_type,type,
c2: mworld > $o ).
thf(b1_type,type,
b1: mworld > $o ).
thf(a0_type,type,
a0: mworld > $o ).
thf(b2_type,type,
b2: mworld > $o ).
thf(a1_type,type,
a1: mworld > $o ).
thf(a2_type,type,
a2: mworld > $o ).
thf(cb_type,type,
cb: mworld > $o ).
thf(1,conjecture,
mlocal @ ( mbox @ '\'#b\'' @ ( mnot @ ( mdia @ '\'#a\'' @ ( mdia @ '\'#b\'' @ ( mbox @ '\'#c\'' @ ( mnot @ a0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mbox @ '\'#b\'' @ ( mnot @ ( mdia @ '\'#a\'' @ ( mdia @ '\'#b\'' @ ( mbox @ '\'#c\'' @ ( mnot @ a0 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: mworld] :
( ( mrel @ '\'#b\'' @ mactual @ A )
=> ~ ? [B: mworld] :
( ( mrel @ '\'#a\'' @ A @ B )
& ? [C: mworld] :
( ( mrel @ '\'#b\'' @ B @ C )
& ! [D: mworld] :
( ( mrel @ '\'#c\'' @ C @ D )
=> ~ ( a0 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
mlocal @ ( mbox @ '\'#a\'' @ ( mbox @ '\'#b\'' @ ( mor @ ( mbox @ '\'#c\'' @ c0 ) @ ( mor @ ( mbox @ '\'#c\'' @ c1 ) @ ( mbox @ '\'#c\'' @ c2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_knows_a_b_c_0) ).
thf(29,plain,
! [A: mworld] :
( ( mrel @ '\'#a\'' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '\'#b\'' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '\'#c\'' @ B @ C )
=> ( c0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#c\'' @ B @ C )
=> ( c1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#c\'' @ B @ C )
=> ( c2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
mlocal @ ( mbox @ '\'#b\'' @ ( mbox @ '\'#a\'' @ ( mor @ ( mbox @ '\'#c\'' @ c0 ) @ ( mor @ ( mbox @ '\'#c\'' @ c1 ) @ ( mbox @ '\'#c\'' @ c2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_knows_b_a_c) ).
thf(27,plain,
! [A: mworld] :
( ( mrel @ '\'#b\'' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '\'#a\'' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '\'#c\'' @ B @ C )
=> ( c0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#c\'' @ B @ C )
=> ( c1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#c\'' @ B @ C )
=> ( c2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
mlocal @ a0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a0) ).
thf(39,plain,
a0 @ mactual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
mlocal @ ( mbox @ '\'#c\'' @ ( mbox @ '\'#b\'' @ ( mor @ ( mbox @ '\'#a\'' @ a0 ) @ ( mor @ ( mbox @ '\'#a\'' @ a1 ) @ ( mbox @ '\'#a\'' @ a2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_knows_c_b_a) ).
thf(35,plain,
! [A: mworld] :
( ( mrel @ '\'#c\'' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '\'#b\'' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '\'#a\'' @ B @ C )
=> ( a0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#a\'' @ B @ C )
=> ( a1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#a\'' @ B @ C )
=> ( a2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
mlocal @ ( mbox @ '\'#a\'' @ ( mbox @ '\'#c\'' @ ( mor @ ( mbox @ '\'#b\'' @ b0 ) @ ( mor @ ( mbox @ '\'#b\'' @ b1 ) @ ( mbox @ '\'#b\'' @ b2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_knows_a_c_b) ).
thf(31,plain,
! [A: mworld] :
( ( mrel @ '\'#a\'' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '\'#c\'' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '\'#b\'' @ B @ C )
=> ( b0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#b\'' @ B @ C )
=> ( b1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#b\'' @ B @ C )
=> ( b2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: mworld,B: mworld] : ( mrel @ '\'#a\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#a_universal') ).
thf(23,plain,
! [A: mworld,B: mworld] : ( mrel @ '\'#a\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: mworld,B: mworld] : ( mrel @ '\'#c\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#c_universal') ).
thf(19,plain,
! [A: mworld,B: mworld] : ( mrel @ '\'#c\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
mlocal @ ( mbox @ '\'#b\'' @ ( mbox @ '\'#c\'' @ ( mor @ ( mbox @ '\'#a\'' @ a0 ) @ ( mor @ ( mbox @ '\'#a\'' @ a1 ) @ ( mbox @ '\'#a\'' @ a2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_knows_b_c_a) ).
thf(37,plain,
! [A: mworld] :
( ( mrel @ '\'#b\'' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '\'#c\'' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '\'#a\'' @ B @ C )
=> ( a0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#a\'' @ B @ C )
=> ( a1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#a\'' @ B @ C )
=> ( a2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
mlocal @ ( mbox @ '\'#a\'' @ ( mbox @ '\'#b\'' @ ( mor @ ( mbox @ '\'#c\'' @ c0 ) @ ( mor @ ( mbox @ '\'#c\'' @ c1 ) @ ( mbox @ '\'#c\'' @ c2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_knows_a_b_c) ).
thf(25,plain,
! [A: mworld] :
( ( mrel @ '\'#a\'' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '\'#b\'' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '\'#c\'' @ B @ C )
=> ( c0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#c\'' @ B @ C )
=> ( c1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#c\'' @ B @ C )
=> ( c2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: mworld,B: mworld] : ( mrel @ '\'#b\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#b_universal') ).
thf(21,plain,
! [A: mworld,B: mworld] : ( mrel @ '\'#b\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
mlocal @ ( mbox @ '\'#c\'' @ ( mbox @ '\'#a\'' @ ( mor @ ( mbox @ '\'#b\'' @ cb ) @ ( mor @ ( mbox @ '\'#b\'' @ b1 ) @ ( mbox @ '\'#b\'' @ b2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_knows_c_a_b) ).
thf(33,plain,
! [A: mworld] :
( ( mrel @ '\'#c\'' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '\'#a\'' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '\'#b\'' @ B @ C )
=> ( cb @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#b\'' @ B @ C )
=> ( b1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '\'#b\'' @ B @ C )
=> ( b2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(51,plain,
$false,
inference(e,[status(thm)],[14,29,27,39,35,31,23,19,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : PUZ150^18 : TPTP v8.2.0. Released v8.1.0.
% 0.12/0.13 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n027.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 : Tue Jun 18 09:56:26 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.08/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.39/1.11 % [INFO] Parsing done (153ms).
% 1.39/1.12 % [INFO] Running in sequential loop mode.
% 2.09/1.50 % [INFO] eprover registered as external prover.
% 2.15/1.50 % [INFO] Scanning for conjecture ...
% 2.21/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.45/1.63 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.45/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.45/1.65 % [INFO] Type checking passed.
% 2.45/1.65 % [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 ...
% 4.10/2.26 % External prover 'e' found a proof!
% 4.10/2.26 % [INFO] Killing All external provers ...
% 4.10/2.26 % Time passed: 1722ms (effective reasoning time: 1135ms)
% 4.10/2.26 % 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)>
% 4.10/2.26 % Axioms used in derivation (11): mrel_#b_universal, axiom_knows_a_b_c, axiom_a0, axiom_knows_b_c_a, axiom_knows_a_c_b, mrel_#a_universal, axiom_knows_c_a_b, axiom_knows_c_b_a, mrel_#c_universal, axiom_knows_a_b_c_0, axiom_knows_b_a_c
% 4.10/2.26 % No. of inferences in proof: 26
% 4.10/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1722 ms resp. 1135 ms w/o parsing
% 4.27/2.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.27/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------