TSTP Solution File: SET961+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 11:54:56 EDT 2023
% Result : Theorem 2.98s 1.69s
% Output : Refutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 18
% Syntax : Number of formulae : 31 ( 13 unt; 7 typ; 0 def)
% Number of atoms : 52 ( 21 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 141 ( 11 ~; 6 |; 6 &; 102 @)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 41 !; 4 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(7,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(38,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(53,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( in @ C @ A )
=> ( in @ C @ B ) )
& ( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ B @ A ) )
=> ( ( A = empty_set )
| ( B = empty_set )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ B @ A ) )
=> ( ( A = empty_set )
| ( B = empty_set )
| ( A = B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ B @ A ) )
=> ( ( A = empty_set )
| ( B = empty_set )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(39,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,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(35,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)],[6]) ).
thf(10,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(48,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(50,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(42,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( in @ A @ C )
& ( in @ B @ D ) ) )
& ( ( ( in @ A @ C )
& ( in @ B @ D ) )
=> ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(27,plain,
! [A: $i] :
( ( ( A = empty_set )
=> ! [B: $i] :
~ ( in @ B @ A ) )
& ( ! [B: $i] :
~ ( in @ B @ A )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(65,plain,
$false,
inference(e,[status(thm)],[38,53,13,39,35,48,50,42,24,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n003.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 19:16:01 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.83/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.93 % [INFO] Parsing done (109ms).
% 1.22/0.94 % [INFO] Running in sequential loop mode.
% 1.48/1.13 % [INFO] eprover registered as external prover.
% 1.48/1.14 % [INFO] cvc4 registered as external prover.
% 1.48/1.14 % [INFO] Scanning for conjecture ...
% 1.68/1.19 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.76/1.21 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.76/1.23 % [INFO] Problem is first-order (TPTP FOF).
% 1.88/1.23 % [INFO] Type checking passed.
% 1.88/1.23 % [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 ...
% 2.98/1.68 % External prover 'e' found a proof!
% 2.98/1.68 % [INFO] Killing All external provers ...
% 2.98/1.69 % Time passed: 1180ms (effective reasoning time: 743ms)
% 2.98/1.69 % 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)>
% 2.98/1.69 % Axioms used in derivation (10): fc1_zfmisc_1, d1_xboole_0, t2_tarski, commutativity_k2_tarski, l55_zfmisc_1, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, d5_tarski
% 2.98/1.69 % No. of inferences in proof: 24
% 2.98/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1180 ms resp. 743 ms w/o parsing
% 3.18/1.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.18/1.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------