TSTP Solution File: GEG011^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : GEG011^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 May 20 19:57:00 EDT 2024
% Result : Theorem 5.20s 2.88s
% Output : Refutation 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 34
% Syntax : Number of formulae : 45 ( 12 unt; 17 typ; 8 def)
% Number of atoms : 162 ( 8 equ; 0 cnn)
% Maximal formula atoms : 37 ( 5 avg)
% Number of connectives : 395 ( 37 ~; 14 |; 44 &; 265 @)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 10 con; 0-3 aty)
% Number of variables : 98 ( 22 ^ 61 !; 15 ?; 98 :)
% 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(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(reg_type,type,
reg: $tType ).
thf(c_type,type,
c: reg > reg > $o ).
thf(ec_type,type,
ec: reg > reg > $o ).
thf(ec_def,definition,
( ec
= ( ^ [A: reg,B: reg] :
( ( c @ A @ B )
& ~ ( o @ A @ B ) ) ) ) ).
thf(pp_type,type,
pp: reg > reg > $o ).
thf(pp_def,definition,
( pp
= ( ^ [A: reg,B: reg] :
( ( p @ A @ B )
& ~ ( p @ B @ A ) ) ) ) ).
thf(tpp_type,type,
tpp: reg > reg > $o ).
thf(tpp_def,definition,
( tpp
= ( ^ [A: reg,B: reg] :
( ( pp @ A @ B )
& ? [C: reg] :
( ( ec @ C @ A )
& ( ec @ C @ B ) ) ) ) ) ).
thf(ntpp_type,type,
ntpp: reg > reg > $o ).
thf(ntpp_def,definition,
( ntpp
= ( ^ [A: reg,B: reg] :
( ( pp @ A @ B )
& ~ ? [C: reg] :
( ( ec @ C @ A )
& ( ec @ C @ B ) ) ) ) ) ).
thf(catalunya_type,type,
catalunya: reg ).
thf(france_type,type,
france: reg ).
thf(spain_type,type,
spain: reg ).
thf(paris_type,type,
paris: reg ).
thf(a_type,type,
a: $i > $i > $o ).
thf(fool_type,type,
fool: $i > $i > $o ).
thf(10,axiom,
( mvalid
@ ( mbox @ a
@ ^ [A: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(88,plain,
! [A: $i,B: $i] :
( ~ ( a @ A @ B )
| ( ! [C: reg] :
( ( c @ C @ paris )
=> ( c @ C @ france ) )
& ~ ! [C: reg] :
( ( c @ C @ france )
=> ( c @ C @ paris ) )
& ~ ? [C: reg] :
( ( c @ C @ paris )
& ~ ? [D: reg] :
( ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ C ) )
& ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ paris ) ) )
& ( c @ C @ france )
& ~ ? [D: reg] :
( ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ C ) )
& ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ france ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ fool @ ( mbox @ fool @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_axiom_for_fool) ).
thf(52,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( fool @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( fool @ A @ C )
| ! [D: $i] :
( ~ ( fool @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: reg] : ( c @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_reflexive) ).
thf(45,plain,
! [A: reg] : ( c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_axiom_for_fool) ).
thf(49,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( fool @ A @ C )
| ( B @ C ) )
| ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [A: $i] : ( ec @ spain @ france ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(81,plain,
! [A: $i,B: $i] :
( ~ ( fool @ A @ B )
| ( ( c @ spain @ france )
& ~ ? [C: reg] :
( ! [D: reg] :
( ( c @ D @ C )
=> ( c @ D @ spain ) )
& ! [D: reg] :
( ( c @ D @ C )
=> ( c @ D @ france ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [A: $i] :
! [B: reg] :
( ( ( ntpp @ france @ B )
& ( ntpp @ spain @ B ) )
=> ( ( pp @ paris @ B )
& ( pp @ catalunya @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [A: $i] :
! [B: reg] :
( ( ( ntpp @ france @ B )
& ( ntpp @ spain @ B ) )
=> ( ( pp @ paris @ B )
& ( pp @ catalunya @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i] :
( ~ ( a @ A @ B )
| ! [C: reg] :
( ( ! [D: reg] :
( ( c @ D @ france )
=> ( c @ D @ C ) )
& ~ ! [D: reg] :
( ( c @ D @ C )
=> ( c @ D @ france ) )
& ~ ? [D: reg] :
( ( c @ D @ france )
& ~ ? [E: reg] :
( ! [F: reg] :
( ( c @ F @ E )
=> ( c @ F @ D ) )
& ! [F: reg] :
( ( c @ F @ E )
=> ( c @ F @ france ) ) )
& ( c @ D @ C )
& ~ ? [E: reg] :
( ! [F: reg] :
( ( c @ F @ E )
=> ( c @ F @ D ) )
& ! [F: reg] :
( ( c @ F @ E )
=> ( c @ F @ C ) ) ) )
& ! [D: reg] :
( ( c @ D @ spain )
=> ( c @ D @ C ) )
& ~ ! [D: reg] :
( ( c @ D @ C )
=> ( c @ D @ spain ) )
& ~ ? [D: reg] :
( ( c @ D @ spain )
& ~ ? [E: reg] :
( ! [F: reg] :
( ( c @ F @ E )
=> ( c @ F @ D ) )
& ! [F: reg] :
( ( c @ F @ E )
=> ( c @ F @ spain ) ) )
& ( c @ D @ C )
& ~ ? [E: reg] :
( ! [F: reg] :
( ( c @ F @ E )
=> ( c @ F @ D ) )
& ! [F: reg] :
( ( c @ F @ E )
=> ( c @ F @ C ) ) ) ) )
=> ( ! [D: reg] :
( ( c @ D @ paris )
=> ( c @ D @ C ) )
& ~ ! [D: reg] :
( ( c @ D @ C )
=> ( c @ D @ paris ) )
& ! [D: reg] :
( ( c @ D @ catalunya )
=> ( c @ D @ C ) )
& ~ ! [D: reg] :
( ( c @ D @ C )
=> ( c @ D @ catalunya ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_a) ).
thf(55,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( fool @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( a @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
( mvalid
@ ( mbox @ a
@ ^ [A: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(58,plain,
! [A: $i,B: $i] :
( ~ ( a @ A @ B )
| ( ! [C: reg] :
( ( c @ C @ catalunya )
=> ( c @ C @ spain ) )
& ~ ! [C: reg] :
( ( c @ C @ spain )
=> ( c @ C @ catalunya ) )
& ? [C: reg] :
( ( c @ C @ catalunya )
& ~ ? [D: reg] :
( ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ C ) )
& ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ catalunya ) ) )
& ( c @ C @ spain )
& ~ ? [D: reg] :
( ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ C ) )
& ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ spain ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: reg,B: reg] :
( ( c @ A @ B )
=> ( c @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_symmetric) ).
thf(47,plain,
! [A: reg,B: reg] :
( ( c @ A @ B )
=> ( c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(101,plain,
$false,
inference(e,[status(thm)],[88,52,45,49,81,11,55,58,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEG011^1 : TPTP v8.2.0. Released v4.1.0.
% 0.03/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat May 18 21:55:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 1.03/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/1.28 % [INFO] Parsing done (263ms).
% 1.64/1.29 % [INFO] Running in sequential loop mode.
% 2.27/1.67 % [INFO] eprover registered as external prover.
% 2.27/1.67 % [INFO] cvc4 registered as external prover.
% 2.40/1.68 % [INFO] Scanning for conjecture ...
% 2.75/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.96/1.92 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.96/1.93 % [INFO] Problem is higher-order (TPTP THF).
% 2.96/1.93 % [INFO] Type checking passed.
% 2.96/1.93 % [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 ...
% 5.20/2.88 % External prover 'e' found a proof!
% 5.20/2.88 % [INFO] Killing All external provers ...
% 5.20/2.88 % Time passed: 2380ms (effective reasoning time: 1581ms)
% 5.20/2.88 % 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)>
% 5.20/2.88 % Axioms used in derivation (8): k_axiom_for_fool, ax2, c_symmetric, i_axiom_for_fool_a, ax1, t_axiom_for_fool, ax3, c_reflexive
% 5.20/2.88 % No. of inferences in proof: 20
% 5.20/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2380 ms resp. 1581 ms w/o parsing
% 5.62/2.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.62/2.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------