TSTP Solution File: SET025-3 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET025-3 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 03:04:56 EDT 2024
% Result : Unsatisfiable 7.16s 2.49s
% Output : Refutation 7.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 13 unt; 6 typ; 0 def)
% Number of atoms : 17 ( 9 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 75 ( 9 ~; 1 |; 0 &; 65 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 ^ 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(little_set_type,type,
little_set: $i > $o ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(singleton_set_type,type,
singleton_set: $i > $i ).
thf(non_ordered_pair_type,type,
non_ordered_pair: $i > $i > $i ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( non_ordered_pair @ ( singleton_set @ A ) @ ( non_ordered_pair @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( non_ordered_pair @ ( singleton_set @ A ) @ ( non_ordered_pair @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(419,plain,
! [B: $i,A: $i] :
( ( non_ordered_pair @ ( singleton_set @ A ) @ ( non_ordered_pair @ A @ B ) )
= ( ordered_pair @ A @ B ) ),
inference(lifteq,[status(thm)],[418]) ).
thf(139,axiom,
! [B: $i,A: $i] : ( little_set @ ( non_ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair4) ).
thf(476,plain,
! [B: $i,A: $i] : ( little_set @ ( non_ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1,negated_conjecture,
~ ( little_set @ ( ordered_pair @ a @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pairs_are_small) ).
thf(148,plain,
~ ( little_set @ ( ordered_pair @ a @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(149,plain,
~ ( little_set @ ( ordered_pair @ a @ b ) ),
inference(polarity_switch,[status(thm)],[148]) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( little_set @ ( non_ordered_pair @ A @ B ) )
!= ( little_set @ ( ordered_pair @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[476,149]) ).
thf(504,plain,
! [B: $i,A: $i] :
( ( non_ordered_pair @ A @ B )
!= ( ordered_pair @ a @ b ) ),
inference(simp,[status(thm)],[503]) ).
thf(628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ a @ b ) )
| ( ( non_ordered_pair @ ( singleton_set @ A ) @ ( non_ordered_pair @ A @ B ) )
!= ( non_ordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[419,504]) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ a @ b ) ),
inference(pattern_uni,[status(thm)],[628:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( singleton_set @ F )),bind(D,$thf( non_ordered_pair @ F @ G ))]]) ).
thf(638,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ a @ b ) ),
inference(simp,[status(thm)],[629]) ).
thf(642,plain,
$false,
inference(pattern_uni,[status(thm)],[638:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET025-3 : TPTP v8.2.0. Released v1.0.0.
% 0.13/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n020.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 : Mon May 20 12:20:09 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.01 % [INFO] Parsing done (157ms).
% 1.53/1.02 % [INFO] Running in sequential loop mode.
% 1.88/1.21 % [INFO] nitpick registered as external prover.
% 1.88/1.22 % [INFO] Scanning for conjecture ...
% 1.98/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 150 axioms. Running axiom selection ...
% 2.15/1.35 % [INFO] Axiom selection finished. Selected 146 axioms (removed 4 axioms).
% 2.43/1.43 % [INFO] Problem is propositional (TPTP CNF).
% 2.43/1.44 % [INFO] Type checking passed.
% 2.43/1.45 % [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 ...
% 7.16/2.48 % [INFO] Killing All external provers ...
% 7.16/2.49 % Time passed: 1968ms (effective reasoning time: 1462ms)
% 7.16/2.49 % Axioms used in derivation (2): ordered_pair, non_ordered_pair4
% 7.16/2.49 % No. of inferences in proof: 14
% 7.16/2.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1968 ms resp. 1462 ms w/o parsing
% 7.16/2.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.16/2.50 % [INFO] Killing All external provers ...
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