TSTP Solution File: LAT338+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT338+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 11:27:59 EDT 2023
% Result : ContradictoryAxioms 160.68s 33.49s
% Output : Refutation 160.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 20 unt; 8 typ; 0 def)
% Number of atoms : 63 ( 51 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 155 ( 18 ~; 14 |; 4 &; 112 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 56 !; 2 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(sk420_type,type,
sk420: $i > $i > $i ).
thf(275,axiom,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(2720,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(2721,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
inference(cnf,[status(esa)],[2720]) ).
thf(2722,plain,
! [A: $i] :
( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
= ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
inference(lifteq,[status(thm)],[2721]) ).
thf(682,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(4872,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(4874,plain,
v1_xboole_0 @ k1_xboole_0,
inference(cnf,[status(esa)],[4872]) ).
thf(567,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(4279,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(4280,plain,
~ ? [A: $i,B: $i] : ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(miniscope,[status(thm)],[4279]) ).
thf(4281,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[4280]) ).
thf(14492,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4874,4281]) ).
thf(14501,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[14492]) ).
thf(16780,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 )
| ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
!= ( k2_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2722,14501]) ).
thf(16781,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[16780:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(16800,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[16781]) ).
thf(1226,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
<=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(7658,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)],[1226]) ).
thf(7659,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)],[7658]) ).
thf(7661,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[7659]) ).
thf(7665,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[7661]) ).
thf(7666,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[7665]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(5732,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)],[857]) ).
thf(5733,plain,
! [B: $i,A: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
!= ( k2_zfmisc_1 @ B @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[5732]) ).
thf(5734,plain,
! [B: $i,A: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
!= ( k2_zfmisc_1 @ B @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[5733]) ).
thf(5735,plain,
! [B: $i,A: $i] :
( ( sk420 @ A @ ( k2_zfmisc_1 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k2_zfmisc_1),[sk420])]) ).
thf(31306,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk420 @ B @ k1_xboole_0 )
= C )
| ( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
!= ( k2_zfmisc_1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7666,5735]) ).
thf(31307,plain,
! [A: $i] :
( ( sk420 @ k1_xboole_0 @ k1_xboole_0 )
= A ),
inference(pattern_uni,[status(thm)],[31306:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(7660,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[7659]) ).
thf(7663,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[7660]) ).
thf(7664,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[7663]) ).
thf(31304,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk420 @ B @ k1_xboole_0 )
= C )
| ( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
!= ( k2_zfmisc_1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7664,5735]) ).
thf(31305,plain,
! [A: $i] :
( ( sk420 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[31304:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(31346,plain,
! [A: $i] : k1_xboole_0 = A,
inference(rewrite,[status(thm)],[31307,31305]) ).
thf(31362,plain,
$false,
inference(simplifyReflect,[status(thm)],[16800,31346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT338+2 : TPTP v8.1.2. Released v3.4.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n024.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 14:30:23 EDT 2023
% 0.16/0.36 % CPUTime :
% 1.01/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.86/1.40 % [INFO] Parsing done (486ms).
% 2.86/1.41 % [INFO] Running in sequential loop mode.
% 3.15/1.60 % [INFO] eprover registered as external prover.
% 3.15/1.60 % [INFO] cvc4 registered as external prover.
% 3.15/1.61 % [INFO] Scanning for conjecture ...
% 4.25/1.89 % [INFO] Found a conjecture and 5469 axioms. Running axiom selection ...
% 6.70/2.86 % [INFO] Axiom selection finished. Selected 1447 axioms (removed 4022 axioms).
% 8.75/3.52 % [INFO] Problem is first-order (TPTP FOF).
% 8.75/3.57 % [INFO] Type checking passed.
% 8.75/3.57 % [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 ...
% 160.68/33.48 % [INFO] Killing All external provers ...
% 160.68/33.48 % Time passed: 32970ms (effective reasoning time: 32070ms)
% 160.68/33.49 % Axioms used in derivation (5): t115_zfmisc_1, fc3_subset_1, t30_zfmisc_1, t113_zfmisc_1, fc4_relat_1
% 160.68/33.49 % No. of inferences in proof: 36
% 160.68/33.49 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 32970 ms resp. 32070 ms w/o parsing
% 160.68/33.50 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 160.68/33.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------