TSTP Solution File: LAT313+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT313+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 11:27:42 EDT 2023
% Result : ContradictoryAxioms 90.80s 19.65s
% Output : Refutation 90.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 11 unt; 6 typ; 0 def)
% Number of atoms : 66 ( 50 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 121 ( 15 ~; 15 |; 6 &; 73 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 43 !; 2 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(sk56_type,type,
sk56: $i > $i > $i ).
thf(sk291_type,type,
sk291: $i ).
thf(78,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(1088,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)],[78]) ).
thf(1089,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)],[1088]) ).
thf(1090,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[1089]) ).
thf(1092,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[1090]) ).
thf(1093,plain,
v1_xboole_0 @ k1_xboole_0,
inference(simp,[status(thm)],[1092]) ).
thf(537,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(3382,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(3384,plain,
~ ( v1_xboole_0 @ sk291 ),
inference(cnf,[status(esa)],[3382]) ).
thf(4556,plain,
( ( v1_xboole_0 @ sk291 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1093,3384]) ).
thf(4560,plain,
sk291 != k1_xboole_0,
inference(simp,[status(thm)],[4556]) ).
thf(95,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(1173,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)],[95]) ).
thf(1174,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)],[1173]) ).
thf(1176,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1174]) ).
thf(1180,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1176]) ).
thf(1181,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1180]) ).
thf(133,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(1363,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)],[133]) ).
thf(1364,plain,
! [B: $i,A: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
!= ( k2_zfmisc_1 @ B @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[1363]) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
!= ( k2_zfmisc_1 @ B @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[1364]) ).
thf(1366,plain,
! [B: $i,A: $i] :
( ( sk56 @ A @ ( k2_zfmisc_1 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k2_zfmisc_1),[sk56])]) ).
thf(25208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk56 @ B @ k1_xboole_0 )
= C )
| ( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
!= ( k2_zfmisc_1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1181,1366]) ).
thf(25209,plain,
! [A: $i] :
( ( sk56 @ k1_xboole_0 @ k1_xboole_0 )
= A ),
inference(pattern_uni,[status(thm)],[25208:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(1175,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1174]) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1175]) ).
thf(1179,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1178]) ).
thf(25186,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk56 @ B @ k1_xboole_0 )
= C )
| ( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
!= ( k2_zfmisc_1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1179,1366]) ).
thf(25187,plain,
! [A: $i] :
( ( sk56 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[25186:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(25579,plain,
! [A: $i] : k1_xboole_0 = A,
inference(rewrite,[status(thm)],[25209,25187]) ).
thf(25580,plain,
$false,
inference(simplifyReflect,[status(thm)],[4560,25579]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT313+2 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n028.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 14:24:04 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.82/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.43/1.29 % [INFO] Parsing done (447ms).
% 2.43/1.31 % [INFO] Running in sequential loop mode.
% 3.39/1.54 % [INFO] eprover registered as external prover.
% 3.39/1.54 % [INFO] cvc4 registered as external prover.
% 3.39/1.55 % [INFO] Scanning for conjecture ...
% 4.00/1.75 % [INFO] Found a conjecture and 2971 axioms. Running axiom selection ...
% 5.47/2.20 % [INFO] Axiom selection finished. Selected 770 axioms (removed 2201 axioms).
% 7.26/2.71 % [INFO] Problem is first-order (TPTP FOF).
% 7.26/2.74 % [INFO] Type checking passed.
% 7.26/2.75 % [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 ...
% 90.80/19.65 % [INFO] Killing All external provers ...
% 90.80/19.65 % Time passed: 19139ms (effective reasoning time: 18339ms)
% 90.80/19.65 % Axioms used in derivation (4): d5_xboole_0, rc2_relat_1, t113_zfmisc_1, t115_zfmisc_1
% 90.80/19.65 % No. of inferences in proof: 31
% 90.80/19.65 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 19139 ms resp. 18339 ms w/o parsing
% 90.80/19.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 90.80/19.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------