TSTP Solution File: COL099-1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COL099-1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 07:29:34 EDT 2024
% Result : Unsatisfiable 2.82s 1.67s
% Output : Refutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 28
% Syntax : Number of formulae : 44 ( 15 unt; 13 typ; 0 def)
% Number of atoms : 61 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 262 ( 38 ~; 30 |; 0 &; 194 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 66 ( 0 ^ 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(pair_type,type,
pair: $i > $i > $i ).
thf(y_type,type,
y: $i ).
thf(yp_type,type,
yp: $i ).
thf(trancl_type,type,
trancl: $i > $i ).
thf(r_type,type,
r: $i ).
thf(ya_type,type,
ya: $i ).
thf(combK_type,type,
combK: $i ).
thf(combS_type,type,
combS: $i ).
thf(comb_app_type,type,
comb_app: $i > $i > $i ).
thf(trans_type,type,
trans: $i > $o ).
thf(diamond_type,type,
diamond: $i > $o ).
thf(diamond_strip_lemmaD_sk1_type,type,
diamond_strip_lemmaD_sk1: $i > $i > $i > $i > $i ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app1) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( combK
!= ( comb_app @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_app) ).
thf(22,plain,
! [B: $i,A: $i] :
( combK
!= ( comb_app @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
diamond @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1h1) ).
thf(49,plain,
diamond @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( trans @ A )
| ~ ( member @ ( pair @ B @ C ) @ A )
| ~ ( member @ ( pair @ C @ D ) @ A )
| ( member @ ( pair @ B @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transD) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( trans @ A )
| ~ ( member @ ( pair @ B @ C ) @ A )
| ~ ( member @ ( pair @ C @ D ) @ A )
| ( member @ ( pair @ B @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ( member @ ( pair @ A @ B ) @ ( trancl @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r_into_trancl) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ C )
| ( member @ ( pair @ A @ B ) @ ( trancl @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( diamond @ A )
| ~ ( member @ ( pair @ B @ C ) @ ( trancl @ A ) )
| ~ ( member @ ( pair @ B @ D ) @ A )
| ( member @ ( pair @ C @ ( diamond_strip_lemmaD_sk1 @ B @ C @ D @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD2) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( diamond @ A )
| ~ ( member @ ( pair @ B @ C ) @ ( trancl @ A ) )
| ~ ( member @ ( pair @ B @ D ) @ A )
| ( member @ ( pair @ C @ ( diamond_strip_lemmaD_sk1 @ B @ C @ D @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i] : ( trans @ ( trancl @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_trancl) ).
thf(42,plain,
! [A: $i] : ( trans @ ( trancl @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( combS
!= ( comb_app @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_app) ).
thf(25,plain,
! [B: $i,A: $i] :
( combS
!= ( comb_app @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app2) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( diamond @ A )
| ~ ( member @ ( pair @ B @ C ) @ ( trancl @ A ) )
| ~ ( member @ ( pair @ B @ D ) @ A )
| ( member @ ( pair @ D @ ( diamond_strip_lemmaD_sk1 @ B @ C @ D @ A ) ) @ ( trancl @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD1) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( diamond @ A )
| ~ ( member @ ( pair @ B @ C ) @ ( trancl @ A ) )
| ~ ( member @ ( pair @ B @ D ) @ A )
| ( member @ ( pair @ D @ ( diamond_strip_lemmaD_sk1 @ B @ C @ D @ A ) ) @ ( trancl @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( member @ ( pair @ ya @ A ) @ ( trancl @ r ) )
| ~ ( member @ ( pair @ yp @ A ) @ ( trancl @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1c2) ).
thf(17,plain,
! [A: $i] :
( ~ ( member @ ( pair @ ya @ A ) @ ( trancl @ r ) )
| ~ ( member @ ( pair @ yp @ A ) @ ( trancl @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
member @ ( pair @ y @ ya ) @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1h2) ).
thf(50,plain,
member @ ( pair @ y @ ya ) @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,negated_conjecture,
member @ ( pair @ y @ yp ) @ ( trancl @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1c1) ).
thf(16,plain,
member @ ( pair @ y @ yp ) @ ( trancl @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ( C != D )
| ( ( comb_app @ A @ C )
= ( comb_app @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app3) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ( C != D )
| ( ( comb_app @ A @ C )
= ( comb_app @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
combK != combS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_s) ).
thf(19,plain,
combK != combS,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(51,plain,
$false,
inference(e,[status(thm)],[28,22,49,43,40,47,42,25,32,45,17,50,16,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : COL099-1 : TPTP v8.1.2. Released v2.7.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n029.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 6 14:03:24 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.12/0.99 % [INFO] Parsing done (117ms).
% 1.12/1.00 % [INFO] Running in sequential loop mode.
% 1.68/1.20 % [INFO] eprover registered as external prover.
% 1.68/1.21 % [INFO] cvc4 registered as external prover.
% 1.68/1.21 % [INFO] Scanning for conjecture ...
% 1.82/1.27 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.82/1.29 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.82/1.31 % [INFO] Problem is propositional (TPTP CNF).
% 1.82/1.31 % [INFO] Type checking passed.
% 1.82/1.31 % [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 ...
% 2.82/1.67 % External prover 'e' found a proof!
% 2.82/1.67 % [INFO] Killing All external provers ...
% 2.82/1.67 % Time passed: 1135ms (effective reasoning time: 671ms)
% 2.82/1.67 % 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)>
% 2.82/1.67 % Axioms used in derivation (13): app_app3, r_into_trancl, diamond_strip_lemmaD2, trans_trancl, diamond_strip_lemmaD1, app_app1, diamond_trancl_1h2, k_app, app_app2, s_app, k_s, diamond_trancl_1h1, transD
% 2.82/1.67 % No. of inferences in proof: 31
% 2.82/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1135 ms resp. 671 ms w/o parsing
% 3.08/1.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.08/1.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------