TSTP Solution File: LAT330+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT330+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 11:27:54 EDT 2023
% Result : ContradictoryAxioms 164.47s 32.53s
% Output : Refutation 164.47s
% 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(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(sk13_type,type,
sk13: $i > $i > $i ).
thf(167,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(1951,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)],[167]) ).
thf(1952,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
inference(cnf,[status(esa)],[1951]) ).
thf(1953,plain,
! [A: $i] :
( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
= ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
inference(lifteq,[status(thm)],[1952]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(1232,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)],[50]) ).
thf(1233,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1232]) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1233]) ).
thf(37944,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)],[1953,1234]) ).
thf(37945,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[37944:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(38041,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[37945]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(1187,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)],[39]) ).
thf(1188,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[1187]) ).
thf(1189,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[1188]) ).
thf(1190,plain,
! [B: $i,A: $i] :
( ( sk13 @ A @ ( k4_xboole_0 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k4_xboole_0),[sk13])]) ).
thf(39002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ 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)],[38041,1190]) ).
thf(39003,plain,
! [A: $i] :
( ( sk13 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[39002:[bind(A,$thf( F )),bind(B,$thf( k1_zfmisc_1 @ ( k1_tarski @ F ) )),bind(C,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(39166,plain,
! [A: $i] :
( ( sk13 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[39003]) ).
thf(132,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(1800,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1801,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1800]) ).
thf(1802,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1801]) ).
thf(36704,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ B @ k1_xboole_0 )
= C )
| ( ( k4_xboole_0 @ k1_xboole_0 @ A )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1802,1190]) ).
thf(36705,plain,
! [A: $i] :
( ( sk13 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[36704:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(45344,plain,
( ( k1_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[39166,36705]) ).
thf(330,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(2929,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)],[330]) ).
thf(2930,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)],[2929]) ).
thf(2931,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[2930]) ).
thf(2933,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[2931]) ).
thf(2934,plain,
v1_xboole_0 @ k1_xboole_0,
inference(simp,[status(thm)],[2933]) ).
thf(710,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(4828,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(4829,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(miniscope,[status(thm)],[4828]) ).
thf(4830,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[4829]) ).
thf(7518,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2934,4830]) ).
thf(7527,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[7518]) ).
thf(45345,plain,
$false,
inference(simplifyReflect,[status(thm)],[45344,7527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LAT330+2 : TPTP v8.1.2. Released v3.4.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 14:23:36 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.88/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.41/1.21 % [INFO] Parsing done (376ms).
% 2.41/1.22 % [INFO] Running in sequential loop mode.
% 2.85/1.42 % [INFO] eprover registered as external prover.
% 2.85/1.42 % [INFO] cvc4 registered as external prover.
% 2.85/1.42 % [INFO] Scanning for conjecture ...
% 3.71/1.62 % [INFO] Found a conjecture and 3003 axioms. Running axiom selection ...
% 4.97/2.05 % [INFO] Axiom selection finished. Selected 1018 axioms (removed 1985 axioms).
% 6.86/2.59 % [INFO] Problem is first-order (TPTP FOF).
% 6.86/2.63 % [INFO] Type checking passed.
% 6.86/2.63 % [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 ...
% 164.47/32.52 % [INFO] Killing All external provers ...
% 164.47/32.53 % Time passed: 32019ms (effective reasoning time: 31305ms)
% 164.47/32.53 % Axioms used in derivation (6): d5_xboole_0, fc2_subset_1, t22_zfmisc_1, t30_zfmisc_1, t4_boole, t32_xboole_1
% 164.47/32.53 % No. of inferences in proof: 39
% 164.47/32.53 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 32019 ms resp. 31305 ms w/o parsing
% 164.47/32.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 164.47/32.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------