TSTP Solution File: LAT296+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT296+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 11:27:33 EDT 2023
% Result : ContradictoryAxioms 122.78s 23.86s
% Output : Refutation 122.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 46 ( 27 unt; 7 typ; 0 def)
% Number of atoms : 57 ( 42 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 165 ( 13 ~; 7 |; 2 &; 136 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 51 !; 1 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $i ).
thf(156,axiom,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(1850,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)],[156]) ).
thf(1851,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
inference(cnf,[status(esa)],[1850]) ).
thf(1852,plain,
! [A: $i] :
( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
= ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
inference(lifteq,[status(thm)],[1851]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(1203,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1204,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1203]) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1204]) ).
thf(42024,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ B ) @ ( 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)],[1852,1205]) ).
thf(42025,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[42024:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(42192,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[42025]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(1156,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1157,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[1156]) ).
thf(1158,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[1157]) ).
thf(1159,plain,
! [B: $i,A: $i] :
( ( sk10 @ A @ ( k4_xboole_0 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k4_xboole_0),[sk10])]) ).
thf(42305,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk10 @ B @ k1_xboole_0 )
= C )
| ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[42192,1159]) ).
thf(42306,plain,
! [A: $i] :
( ( sk10 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[42305:[bind(A,$thf( F )),bind(B,$thf( k1_zfmisc_1 @ ( k1_tarski @ F ) )),bind(C,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(42497,plain,
! [A: $i] :
( ( sk10 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[42306]) ).
thf(124,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(1724,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1725,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1724]) ).
thf(1726,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1725]) ).
thf(23694,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk10 @ B @ k1_xboole_0 )
= C )
| ( ( k4_xboole_0 @ k1_xboole_0 @ A )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1726,1159]) ).
thf(23695,plain,
! [A: $i] :
( ( sk10 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[23694:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(42668,plain,
( ( k1_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[42497,23695]) ).
thf(319,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(2726,plain,
! [A: $i] :
( ( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(2727,plain,
( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(miniscope,[status(thm)],[2726]) ).
thf(2728,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[2727]) ).
thf(2730,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[2728]) ).
thf(2731,plain,
v1_xboole_0 @ k1_xboole_0,
inference(simp,[status(thm)],[2730]) ).
thf(698,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(4638,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(4639,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(miniscope,[status(thm)],[4638]) ).
thf(4640,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[4639]) ).
thf(8260,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2731,4640]) ).
thf(8265,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8260]) ).
thf(42669,plain,
$false,
inference(simplifyReflect,[status(thm)],[42668,8265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT296+2 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n012.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu May 18 13:54:33 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.92/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.33/1.21 % [INFO] Parsing done (373ms).
% 2.33/1.22 % [INFO] Running in sequential loop mode.
% 2.90/1.41 % [INFO] eprover registered as external prover.
% 2.90/1.41 % [INFO] cvc4 registered as external prover.
% 2.90/1.42 % [INFO] Scanning for conjecture ...
% 3.59/1.59 % [INFO] Found a conjecture and 2927 axioms. Running axiom selection ...
% 4.92/1.99 % [INFO] Axiom selection finished. Selected 999 axioms (removed 1928 axioms).
% 6.53/2.46 % [INFO] Problem is first-order (TPTP FOF).
% 6.53/2.50 % [INFO] Type checking passed.
% 6.53/2.50 % [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 ...
% 122.78/23.85 % [INFO] Killing All external provers ...
% 122.78/23.85 % Time passed: 23332ms (effective reasoning time: 22623ms)
% 122.78/23.86 % Axioms used in derivation (6): d5_xboole_0, fc2_subset_1, t22_zfmisc_1, t30_zfmisc_1, t4_boole, t32_xboole_1
% 122.78/23.86 % No. of inferences in proof: 39
% 122.78/23.86 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23332 ms resp. 22623 ms w/o parsing
% 122.78/23.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 122.78/23.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------