TSTP Solution File: SET907+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET907+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 11:54:48 EDT 2023
% Result : Theorem 2.68s 1.75s
% Output : Refutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 31 ( 13 unt; 5 typ; 0 def)
% Number of atoms : 47 ( 11 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 143 ( 14 ~; 0 |; 7 &; 108 @)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 49 ( 0 ^; 45 !; 4 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( in @ C @ B ) )
=> ( ( set_union2 @ ( unordered_pair @ A @ C ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( in @ C @ B ) )
=> ( ( set_union2 @ ( unordered_pair @ A @ C ) @ B )
= B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( in @ C @ B ) )
=> ( ( set_union2 @ ( unordered_pair @ A @ C ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ ( unordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ C )
& ( in @ B @ C ) ) )
& ( ( ( in @ A @ C )
& ( in @ B @ C ) )
=> ( subset @ ( unordered_pair @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(41,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(27,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(38,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(33,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(36,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(30,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(54,plain,
$false,
inference(e,[status(thm)],[24,14,46,41,27,43,38,21,33,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET907+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n004.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Thu May 18 18:46:55 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.92/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.08/0.98 % [INFO] Parsing done (123ms).
% 1.08/0.99 % [INFO] Running in sequential loop mode.
% 1.57/1.22 % [INFO] eprover registered as external prover.
% 1.57/1.22 % [INFO] cvc4 registered as external prover.
% 1.57/1.22 % [INFO] Scanning for conjecture ...
% 1.66/1.28 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.66/1.31 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.66/1.32 % [INFO] Problem is first-order (TPTP FOF).
% 1.66/1.33 % [INFO] Type checking passed.
% 1.66/1.33 % [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 ...
% 2.68/1.75 % External prover 'e' found a proof!
% 2.68/1.75 % [INFO] Killing All external provers ...
% 2.68/1.75 % Time passed: 1219ms (effective reasoning time: 750ms)
% 2.68/1.75 % 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)>
% 2.68/1.75 % Axioms used in derivation (11): fc2_xboole_0, commutativity_k2_xboole_0, fc3_xboole_0, commutativity_k2_tarski, t38_zfmisc_1, reflexivity_r1_tarski, rc1_xboole_0, t12_xboole_1, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden
% 2.68/1.75 % No. of inferences in proof: 26
% 2.68/1.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1219 ms resp. 750 ms w/o parsing
% 2.92/1.78 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.92/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------