TSTP Solution File: SEU156+1 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SEU156+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 08:08:58 EDT 2024
% Result : Theorem 2.82s 1.92s
% Output : Refutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 37 ( 21 unt; 5 typ; 0 def)
% Number of atoms : 48 ( 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 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 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(4,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(25,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(6,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(29,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(28,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(41,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)],[12]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(39,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(31,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(34,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(45,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
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/sandbox/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(17,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(10,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(36,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(30,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(51,plain,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(64,plain,
$false,
inference(cvc4,[status(thm)],[25,29,28,41,22,39,48,31,55,34,45,17,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SEU156+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 6 10:37:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.89/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/1.02 % [INFO] Parsing done (150ms).
% 1.11/1.03 % [INFO] Running in sequential loop mode.
% 1.67/1.33 % [INFO] eprover registered as external prover.
% 1.67/1.34 % [INFO] cvc4 registered as external prover.
% 1.67/1.34 % [INFO] Scanning for conjecture ...
% 1.76/1.42 % [INFO] Found a conjecture and 14 axioms. Running axiom selection ...
% 1.86/1.45 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.94/1.48 % [INFO] Problem is first-order (TPTP FOF).
% 1.94/1.48 % [INFO] Type checking passed.
% 1.94/1.48 % [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 ...
% 2.82/1.92 % External prover 'cvc4' found a proof!
% 2.82/1.92 % [INFO] Killing All external provers ...
% 2.82/1.92 % Time passed: 1464ms (effective reasoning time: 883ms)
% 2.82/1.92 % 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)>
% 2.82/1.92 % Axioms used in derivation (14): fc1_zfmisc_1, dt_k4_tarski, dt_k2_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, dt_k1_tarski, d5_tarski
% 2.82/1.92 % No. of inferences in proof: 32
% 2.82/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1464 ms resp. 883 ms w/o parsing
% 3.17/1.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.17/1.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------