TSTP Solution File: LAT290+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT290+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 11:27:24 EDT 2023
% Result : ContradictoryAxioms 103.40s 21.26s
% Output : Refutation 103.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 49 ( 19 unt; 9 typ; 0 def)
% Number of atoms : 95 ( 48 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 273 ( 34 ~; 15 |; 23 &; 188 @)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 0 ^; 72 !; 6 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(r2_tarski_type,type,
r2_tarski: $i > $i > $o ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk307_type,type,
sk307: $i > $i ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
<=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(1970,plain,
! [A: $i,B: $i] :
( ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) )
& ( ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1971,plain,
( ! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) )
& ! [A: $i,B: $i] :
( ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[1970]) ).
thf(1973,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1971]) ).
thf(1977,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1973]) ).
thf(1978,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1977]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(1333,plain,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1334,plain,
! [B: $i,A: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
!= ( k2_zfmisc_1 @ B @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[1333]) ).
thf(1335,plain,
! [B: $i,A: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
!= ( k2_zfmisc_1 @ B @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[1334]) ).
thf(1336,plain,
! [B: $i,A: $i] :
( ( sk6 @ A @ ( k2_zfmisc_1 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k2_zfmisc_1),[sk6])]) ).
thf(25078,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ B @ k1_xboole_0 )
= C )
| ( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
!= ( k2_zfmisc_1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1978,1336]) ).
thf(25079,plain,
! [A: $i] :
( ( sk6 @ k1_xboole_0 @ k1_xboole_0 )
= A ),
inference(pattern_uni,[status(thm)],[25078:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(910,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(4820,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(4821,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(cnf,[status(esa)],[4820]) ).
thf(4822,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[4821]) ).
thf(988,axiom,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(5221,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(5222,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(cnf,[status(esa)],[5221]) ).
thf(1076,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(5585,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(5586,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ~ ? [C: $i] :
( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(miniscope,[status(thm)],[5585]) ).
thf(5590,plain,
! [A: $i] : ( r2_hidden @ A @ ( sk307 @ A ) ),
inference(cnf,[status(esa)],[5586]) ).
thf(864,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(4615,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(4616,plain,
~ ? [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(miniscope,[status(thm)],[4615]) ).
thf(4617,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ~ ( r1_tarski @ B @ A ) ),
inference(cnf,[status(esa)],[4616]) ).
thf(8422,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ C @ B )
| ( ( r2_hidden @ A @ ( sk307 @ A ) )
!= ( r2_hidden @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5590,4617]) ).
thf(8423,plain,
! [A: $i] :
~ ( r1_tarski @ ( sk307 @ A ) @ A ),
inference(pattern_uni,[status(thm)],[8422:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk307 @ D ))]]) ).
thf(8447,plain,
! [A: $i] :
~ ( r1_tarski @ ( sk307 @ A ) @ A ),
inference(simp,[status(thm)],[8423]) ).
thf(13070,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) )
!= ( r1_tarski @ ( sk307 @ B ) @ B ) ),
inference(paramod_ordered,[status(thm)],[5222,8447]) ).
thf(13084,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk307 @ B ) )
| ( ( k1_zfmisc_1 @ ( k3_tarski @ A ) )
!= B ) ),
inference(simp,[status(thm)],[13070]) ).
thf(13091,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k3_tarski @ ( sk307 @ A ) ) )
!= A ),
inference(simp,[status(thm)],[13084]) ).
thf(13711,plain,
! [B: $i,A: $i] :
( ( ( k1_zfmisc_1 @ A )
!= B )
| ( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
!= ( k3_tarski @ ( sk307 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4822,13091]) ).
thf(13715,plain,
! [A: $i] :
( ( k3_tarski @ ( sk307 @ ( k1_zfmisc_1 @ A ) ) )
!= ( k3_tarski @ ( k1_zfmisc_1 @ A ) ) ),
inference(simp,[status(thm)],[13711]) ).
thf(24581,plain,
! [A: $i] :
( ( k3_tarski @ ( sk307 @ ( k1_zfmisc_1 @ A ) ) )
!= A ),
inference(rewrite,[status(thm)],[13715,4822]) ).
thf(25246,plain,
! [B: $i,A: $i] :
( ( ( k3_tarski @ ( sk307 @ ( sk6 @ k1_xboole_0 @ k1_xboole_0 ) ) )
!= B )
| ( A
!= ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25079,24581]) ).
thf(25247,plain,
! [A: $i] :
( ( k3_tarski @ ( sk307 @ ( sk6 @ k1_xboole_0 @ k1_xboole_0 ) ) )
!= A ),
inference(pattern_uni,[status(thm)],[25246:[bind(A,$thf( k1_zfmisc_1 @ C )),bind(B,$thf( C ))]]) ).
thf(26699,plain,
$false,
inference(simp,[status(thm)],[25247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT290+2 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n009.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Thu May 18 14:03:04 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.07/1.41 % [INFO] Parsing done (531ms).
% 3.07/1.42 % [INFO] Running in sequential loop mode.
% 3.38/1.62 % [INFO] eprover registered as external prover.
% 3.38/1.62 % [INFO] cvc4 registered as external prover.
% 3.38/1.62 % [INFO] Scanning for conjecture ...
% 4.66/1.92 % [INFO] Found a conjecture and 6453 axioms. Running axiom selection ...
% 6.41/2.65 % [INFO] Axiom selection finished. Selected 1217 axioms (removed 5236 axioms).
% 8.21/3.16 % [INFO] Problem is first-order (TPTP FOF).
% 8.40/3.20 % [INFO] Type checking passed.
% 8.40/3.20 % [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 ...
% 103.40/21.25 % [INFO] Killing All external provers ...
% 103.40/21.26 % Time passed: 20709ms (effective reasoning time: 19831ms)
% 103.40/21.26 % Axioms used in derivation (6): t113_zfmisc_1, t99_zfmisc_1, t115_zfmisc_1, t7_ordinal1, t100_zfmisc_1, t136_zfmisc_1
% 103.40/21.26 % No. of inferences in proof: 40
% 103.40/21.26 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20709 ms resp. 19831 ms w/o parsing
% 103.40/21.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 103.40/21.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------