TSTP Solution File: AGT037^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : AGT037^2 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 7 07:25:33 EDT 2024
% Result : Theorem 3.81s 1.87s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 43
% Syntax : Number of formulae : 64 ( 8 unt; 18 typ; 6 def)
% Number of atoms : 200 ( 6 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 398 ( 41 ~; 35 |; 0 &; 322 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 9 con; 0-3 aty)
% Number of variables : 85 ( 26 ^ 59 !; 0 ?; 85 :)
% 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(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(mdia_type,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mdia_def,definition,
( mdia
= ( ^ [A: $i > $i > $o,B: $i > $o] : ( mnot @ ( mbox @ A @ ( mnot @ B ) ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(a1_type,type,
a1: $i > $i > $o ).
thf(a2_type,type,
a2: $i > $i > $o ).
thf(a3_type,type,
a3: $i > $i > $o ).
thf(jan_type,type,
jan: mu ).
thf(piotr_type,type,
piotr: mu ).
thf(cola_type,type,
cola: mu ).
thf(pepsi_type,type,
pepsi: mu ).
thf(beer_type,type,
beer: mu ).
thf(likes_type,type,
likes: mu > mu > $i > $o ).
thf(very_much_likes_type,type,
very_much_likes: mu > mu > $i > $o ).
thf(possibly_likes_type,type,
possibly_likes: mu > mu > $i > $o ).
thf(17,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mbox @ a3 @ ( mimplies @ ( mand @ ( likes @ A @ B ) @ ( mand @ ( mbox @ a1 @ ( likes @ A @ B ) ) @ ( mbox @ a2 @ ( likes @ A @ B ) ) ) ) @ ( very_much_likes @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_4) ).
thf(56,plain,
! [A: $i,B: mu,C: mu,D: $i] :
( ~ ( a3 @ A @ D )
| ~ ( likes @ B @ C @ D )
| ~ ! [E: $i] :
( ~ ( a1 @ D @ E )
| ( likes @ B @ C @ E ) )
| ~ ! [E: $i] :
( ~ ( a2 @ D @ E )
| ( likes @ B @ C @ E ) )
| ( very_much_likes @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ piotr @ beer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_3) ).
thf(42,plain,
! [A: $i,B: $i] :
( ~ ( a1 @ A @ B )
| ( likes @ piotr @ beer @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ a1 @ ( mimplies @ ( mdia @ a1 @ ( likes @ A @ cola ) ) @ ( likes @ A @ pepsi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_4) ).
thf(52,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( a1 @ A @ C )
| ! [D: $i] :
( ~ ( a1 @ C @ D )
| ~ ( likes @ B @ cola @ D ) )
| ( likes @ B @ pepsi @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ a2 @ ( mimplies @ ( likes @ A @ pepsi ) @ ( likes @ A @ cola ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_4) ).
thf(46,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( a2 @ A @ C )
| ~ ( likes @ B @ pepsi @ C )
| ( likes @ B @ cola @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
mvalid @ ( mbox @ a3 @ ( likes @ jan @ cola ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_1) ).
thf(61,plain,
! [A: $i,B: $i] :
( ~ ( a3 @ A @ B )
| ( likes @ jan @ cola @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mdia @ a2 @ ( likes @ A @ B ) ) @ ( possibly_likes @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_4) ).
thf(65,plain,
! [A: $i,B: mu,C: mu] :
( ! [D: $i] :
( ~ ( a2 @ A @ D )
| ~ ( likes @ B @ C @ D ) )
| ( possibly_likes @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ a1 @ ( mimplies @ ( mdia @ a1 @ ( likes @ A @ pepsi ) ) @ ( likes @ A @ cola ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_3) ).
thf(44,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( a1 @ A @ C )
| ! [D: $i] :
( ~ ( a1 @ C @ D )
| ~ ( likes @ B @ pepsi @ D ) )
| ( likes @ B @ cola @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ piotr @ pepsi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_2) ).
thf(54,plain,
! [A: $i,B: $i] :
( ~ ( a1 @ A @ B )
| ( likes @ piotr @ pepsi @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mdia @ a3 @ ( likes @ A @ B ) ) @ ( possibly_likes @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_5) ).
thf(50,plain,
! [A: $i,B: mu,C: mu] :
( ! [D: $i] :
( ~ ( a3 @ A @ D )
| ~ ( likes @ B @ C @ D ) )
| ( possibly_likes @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_3) ).
thf(36,plain,
! [A: $i] :
~ ! [B: $i] :
( ~ ( a1 @ A @ B )
| ~ ( likes @ piotr @ beer @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_2) ).
thf(28,plain,
! [A: $i] :
~ ! [B: $i] :
( ~ ( a3 @ A @ B )
| ~ ( likes @ piotr @ pepsi @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
mvalid @ ( possibly_likes @ jan @ cola ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( possibly_likes @ jan @ cola ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] : ( possibly_likes @ jan @ cola @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ jan @ cola ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_1) ).
thf(32,plain,
! [A: $i,B: $i] :
( ~ ( a1 @ A @ B )
| ( likes @ jan @ cola @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mdia @ a3 @ ( very_much_likes @ A @ B ) ) @ ( likes @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_2) ).
thf(34,plain,
! [A: $i,B: mu,C: mu] :
( ! [D: $i] :
( ~ ( a3 @ A @ D )
| ~ ( very_much_likes @ B @ C @ D ) )
| ( likes @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_1) ).
thf(48,plain,
! [A: $i,B: $i] :
( ~ ( a2 @ A @ B )
| ( likes @ jan @ pepsi @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ a2 @ ( mimplies @ ( likes @ A @ cola ) @ ( likes @ A @ pepsi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_5) ).
thf(63,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( a2 @ A @ C )
| ~ ( likes @ B @ cola @ C )
| ( likes @ B @ pepsi @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mdia @ a1 @ ( likes @ A @ B ) ) @ ( possibly_likes @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_3) ).
thf(40,plain,
! [A: $i,B: mu,C: mu] :
( ! [D: $i] :
( ~ ( a1 @ A @ D )
| ~ ( likes @ B @ C @ D ) )
| ( possibly_likes @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ piotr @ cola ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_2) ).
thf(26,plain,
! [A: $i,B: $i] :
( ~ ( a1 @ A @ B )
| ( likes @ piotr @ cola @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mbox @ a3 @ ( very_much_likes @ A @ B ) ) @ ( very_much_likes @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_1) ).
thf(23,plain,
! [A: $i,B: mu,C: mu] :
( ~ ! [D: $i] :
( ~ ( a3 @ A @ D )
| ( very_much_likes @ B @ C @ D ) )
| ( very_much_likes @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(67,plain,
$false,
inference(e,[status(thm)],[56,42,52,46,61,65,44,54,50,36,28,21,32,34,48,63,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : AGT037^2 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:51:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.01 % [INFO] Parsing done (160ms).
% 1.25/1.02 % [INFO] Running in sequential loop mode.
% 1.88/1.22 % [INFO] eprover registered as external prover.
% 1.88/1.23 % [INFO] cvc4 registered as external prover.
% 1.88/1.23 % [INFO] Scanning for conjecture ...
% 2.02/1.34 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 2.39/1.38 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.39/1.39 % [INFO] Problem is higher-order (TPTP THF).
% 2.39/1.39 % [INFO] Type checking passed.
% 2.39/1.40 % [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 ...
% 3.81/1.87 % External prover 'e' found a proof!
% 3.81/1.87 % [INFO] Killing All external provers ...
% 3.81/1.87 % Time passed: 1345ms (effective reasoning time: 842ms)
% 3.81/1.87 % 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)>
% 3.81/1.87 % Axioms used in derivation (18): axiom_a1_4, axiom_a3_3, axiom_user_communication_3, axiom_a2_2, axiom_a3_4, axiom_a1_1, axiom_user_communication_4, axiom_a2_3, axiom_a1_2, axiom_a2_5, axiom_user_communication_2, axiom_a1_3, axiom_a3_2, axiom_a2_1, axiom_user_communication_1, axiom_a2_4, axiom_user_communication_5, axiom_a3_1
% 3.81/1.87 % No. of inferences in proof: 40
% 3.81/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1345 ms resp. 842 ms w/o parsing
% 3.97/1.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.97/1.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------