TSTP Solution File: SET874+1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET874+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 03:07:14 EDT 2024
% Result : Theorem 69.45s 11.21s
% Output : Refutation 69.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 9 unt; 6 typ; 0 def)
% Number of atoms : 60 ( 39 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 176 ( 17 ~; 18 |; 6 &; 119 @)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 ^ 45 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
inference(cnf,[status(esa)],[59]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( ( set_union2 @ ( singleton @ A ) @ B )
= B )
| ~ ( in @ A @ B ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( set_union2 @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
= ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( set_union2 @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
= ( unordered_pair @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( set_union2 @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
= ( unordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
( ( set_union2 @ ( singleton @ sk1 ) @ ( unordered_pair @ sk1 @ sk2 ) )
!= ( unordered_pair @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
( ( set_union2 @ ( singleton @ sk1 ) @ ( unordered_pair @ sk1 @ sk2 ) )
!= ( unordered_pair @ sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(10297,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( B
!= ( unordered_pair @ sk1 @ sk2 ) )
| ( ( set_union2 @ ( singleton @ A ) @ B )
!= ( set_union2 @ ( singleton @ sk1 ) @ ( unordered_pair @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,15]) ).
thf(10298,plain,
( ~ ( in @ sk1 @ ( unordered_pair @ sk1 @ sk2 ) )
| ( ( unordered_pair @ sk1 @ sk2 )
!= ( unordered_pair @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[10297:[bind(A,$thf( sk1 )),bind(B,$thf( unordered_pair @ sk1 @ sk2 ))]]) ).
thf(10333,plain,
~ ( in @ sk1 @ ( unordered_pair @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[10298]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(24,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( unordered_pair @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( unordered_pair @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,plain,
( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
=> ( ! [D: $i] :
( ( in @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ! [D: $i] :
( ( ( D = A )
| ( D = B ) )
=> ( in @ D @ C ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( in @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ! [D: $i] :
( ( ( D = A )
| ( D = B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( unordered_pair @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[24]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( D != A )
| ( in @ D @ C ) ),
inference(cnf,[status(esa)],[25]) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( D != A )
| ( in @ D @ C ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(47,plain,
! [B: $i,A: $i] : ( in @ A @ ( unordered_pair @ A @ B ) ),
inference(simp,[status(thm)],[46]) ).
thf(10336,plain,
~ $true,
inference(rewrite,[status(thm)],[10333,47]) ).
thf(10337,plain,
$false,
inference(simp,[status(thm)],[10336]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET874+1 : TPTP v8.2.0. Released v3.2.0.
% 0.09/0.11 % Command : run_Leo-III %s %d
% 0.11/0.30 % Computer : n026.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.30 % CPULimit : 300
% 0.15/0.30 % WCLimit : 300
% 0.15/0.30 % DateTime : Mon May 20 13:22:54 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.84/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.02 % [INFO] Parsing done (173ms).
% 1.22/1.03 % [INFO] Running in sequential loop mode.
% 1.75/1.33 % [INFO] nitpick registered as external prover.
% 1.75/1.34 % [INFO] Scanning for conjecture ...
% 1.89/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.02/1.47 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.06/1.50 % [INFO] Problem is first-order (TPTP FOF).
% 2.06/1.51 % [INFO] Type checking passed.
% 2.16/1.51 % [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 ...
% 69.45/11.20 % [INFO] Killing All external provers ...
% 69.45/11.21 % Time passed: 10787ms (effective reasoning time: 10162ms)
% 69.45/11.21 % 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)>
% 69.45/11.21 % Axioms used in derivation (2): l23_zfmisc_1, d2_tarski
% 69.45/11.21 % No. of inferences in proof: 20
% 69.45/11.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10787 ms resp. 10162 ms w/o parsing
% 69.45/11.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 69.45/11.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------