TSTP Solution File: SEU156+3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU156+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 : Fri May 19 11:57:16 EDT 2023
% Result : Theorem 2.67s 1.61s
% Output : Refutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 31 ( 15 unt; 5 typ; 0 def)
% Number of atoms : 42 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 110 ( 12 ~; 0 |; 7 &; 82 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 57 ( 0 ^; 53 !; 4 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(45,plain,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(49,plain,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(39,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(35,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(25,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(28,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(33,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(30,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(54,plain,
$false,
inference(e,[status(thm)],[14,45,22,49,39,35,42,25,28,33,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU156+3 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 12:51:49 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.86/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.95 % [INFO] Parsing done (118ms).
% 1.21/0.96 % [INFO] Running in sequential loop mode.
% 1.52/1.15 % [INFO] eprover registered as external prover.
% 1.52/1.16 % [INFO] cvc4 registered as external prover.
% 1.52/1.16 % [INFO] Scanning for conjecture ...
% 1.81/1.21 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.88/1.24 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.88/1.25 % [INFO] Problem is first-order (TPTP FOF).
% 1.88/1.26 % [INFO] Type checking passed.
% 1.88/1.26 % [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 ...
% 2.67/1.60 % External prover 'e' found a proof!
% 2.67/1.60 % [INFO] Killing All external provers ...
% 2.67/1.61 % Time passed: 1092ms (effective reasoning time: 642ms)
% 2.67/1.61 % 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)>
% 2.67/1.61 % Axioms used in derivation (11): fc1_zfmisc_1, d5_tarski, t8_zfmisc_1, t9_zfmisc_1, commutativity_k2_tarski, t69_enumset1, reflexivity_r1_tarski, t6_zfmisc_1, rc1_xboole_0, t10_zfmisc_1, rc2_xboole_0
% 2.67/1.61 % No. of inferences in proof: 26
% 2.67/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1092 ms resp. 642 ms w/o parsing
% 3.03/1.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.03/1.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------