TSTP Solution File: LAT337+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT337+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 11:27:58 EDT 2023
% Result : ContradictoryAxioms 159.96s 35.52s
% Output : Refutation 159.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 51 ( 31 unt; 7 typ; 0 def)
% Number of atoms : 63 ( 48 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 179 ( 16 ~; 8 |; 2 &; 146 @)
% ( 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 : 53 ( 0 ^; 52 !; 1 ?; 53 :)
% 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(sk14_type,type,
sk14: $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/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(1967,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(1968,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
inference(cnf,[status(esa)],[1967]) ).
thf(1969,plain,
! [A: $i] :
( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
= ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
inference(lifteq,[status(thm)],[1968]) ).
thf(50,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(1256,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(1257,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1256]) ).
thf(1258,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1257]) ).
thf(57273,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)],[1969,1258]) ).
thf(57274,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[57273:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(57476,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[57274]) ).
thf(39,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(1211,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(1212,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[1211]) ).
thf(1213,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[1212]) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ( sk14 @ A @ ( k4_xboole_0 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k4_xboole_0),[sk14])]) ).
thf(57587,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ 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)],[57476,1214]) ).
thf(57588,plain,
! [A: $i] :
( ( sk14 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[57587:[bind(A,$thf( F )),bind(B,$thf( k1_zfmisc_1 @ ( k1_tarski @ F ) )),bind(C,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(57845,plain,
! [A: $i] :
( ( sk14 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[57588]) ).
thf(132,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(1824,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1825,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1824]) ).
thf(1826,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1825]) ).
thf(36330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ B @ k1_xboole_0 )
= C )
| ( ( k4_xboole_0 @ k1_xboole_0 @ A )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1826,1214]) ).
thf(36331,plain,
! [A: $i] :
( ( sk14 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[36330:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(58225,plain,
( ( k1_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[57845,36331]) ).
thf(145,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1882,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1883,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1882]) ).
thf(323,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(2864,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)],[323]) ).
thf(2865,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)],[2864]) ).
thf(2866,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[2865]) ).
thf(2868,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[2866]) ).
thf(2869,plain,
v1_xboole_0 @ k1_xboole_0,
inference(simp,[status(thm)],[2868]) ).
thf(491,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(3690,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(3691,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(miniscope,[status(thm)],[3690]) ).
thf(3692,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[3691]) ).
thf(7864,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2869,3692]) ).
thf(7873,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[7864]) ).
thf(11187,plain,
! [A: $i] :
( ( ( k1_tarski @ k1_xboole_0 )
!= k1_xboole_0 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1883,7873]) ).
thf(11188,plain,
( ( k1_tarski @ k1_xboole_0 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[11187:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(58226,plain,
$false,
inference(simplifyReflect,[status(thm)],[58225,11188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT337+2 : TPTP v8.1.2. Released v3.4.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n015.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 14:56:38 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.53/1.25 % [INFO] Parsing done (382ms).
% 2.53/1.26 % [INFO] Running in sequential loop mode.
% 3.03/1.46 % [INFO] eprover registered as external prover.
% 3.03/1.47 % [INFO] cvc4 registered as external prover.
% 3.03/1.47 % [INFO] Scanning for conjecture ...
% 3.90/1.69 % [INFO] Found a conjecture and 3025 axioms. Running axiom selection ...
% 5.25/2.12 % [INFO] Axiom selection finished. Selected 1040 axioms (removed 1985 axioms).
% 6.80/2.66 % [INFO] Problem is first-order (TPTP FOF).
% 7.01/2.70 % [INFO] Type checking passed.
% 7.01/2.70 % [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 ...
% 159.96/35.51 % [INFO] Killing All external provers ...
% 159.96/35.52 % Time passed: 34984ms (effective reasoning time: 34250ms)
% 159.96/35.52 % Axioms used in derivation (7): d5_xboole_0, t1_zfmisc_1, fc1_subset_1, t22_zfmisc_1, t30_zfmisc_1, t4_boole, t32_xboole_1
% 159.96/35.52 % No. of inferences in proof: 44
% 159.96/35.52 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 34984 ms resp. 34250 ms w/o parsing
% 159.96/35.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 159.96/35.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------