TSTP Solution File: LAT318+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT318+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 11:27:45 EDT 2023
% Result : ContradictoryAxioms 63.15s 12.92s
% Output : Refutation 63.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 42 ( 11 unt; 9 typ; 0 def)
% Number of atoms : 116 ( 40 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 337 ( 44 ~; 14 |; 44 &; 214 @)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 0 ^; 80 !; 10 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(r2_tarski_type,type,
r2_tarski: $i > $i > $o ).
thf(sk7_type,type,
sk7: $i > $i > $i ).
thf(sk25_type,type,
sk25: $i > $i ).
thf(sk157_type,type,
sk157: $i > $i ).
thf(64,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(861,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)],[64]) ).
thf(862,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)],[861]) ).
thf(864,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[862]) ).
thf(868,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[864]) ).
thf(869,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[868]) ).
thf(16,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(683,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)],[16]) ).
thf(684,plain,
! [B: $i,A: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
!= ( k2_zfmisc_1 @ B @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[683]) ).
thf(685,plain,
! [B: $i,A: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
!= ( k2_zfmisc_1 @ B @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[684]) ).
thf(686,plain,
! [B: $i,A: $i] :
( ( sk7 @ A @ ( k2_zfmisc_1 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k2_zfmisc_1),[sk7])]) ).
thf(11793,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk7 @ B @ k1_xboole_0 )
= C )
| ( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
!= ( k2_zfmisc_1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[869,686]) ).
thf(11794,plain,
! [A: $i] :
( ( sk7 @ k1_xboole_0 @ k1_xboole_0 )
= A ),
inference(pattern_uni,[status(thm)],[11793:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(90,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(994,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(995,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ~ ? [C: $i] :
( ( r2_hidden @ C @ B )
& ~ ? [D: $i] :
( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ~ ? [C: $i] :
( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(miniscope,[status(thm)],[994]) ).
thf(998,plain,
! [A: $i] : ( r2_hidden @ A @ ( sk25 @ A ) ),
inference(cnf,[status(esa)],[995]) ).
thf(409,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(2479,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(2480,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ~ ? [C: $i] :
( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(miniscope,[status(thm)],[2479]) ).
thf(2484,plain,
! [A: $i] : ( r2_hidden @ A @ ( sk157 @ A ) ),
inference(cnf,[status(esa)],[2480]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(1751,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1752,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ~ ( r2_hidden @ B @ A ) ),
inference(cnf,[status(esa)],[1751]) ).
thf(10060,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r2_hidden @ C @ B )
| ( ( r2_hidden @ A @ ( sk157 @ A ) )
!= ( r2_hidden @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2484,1752]) ).
thf(10061,plain,
! [A: $i] :
~ ( r2_hidden @ ( sk157 @ A ) @ A ),
inference(pattern_uni,[status(thm)],[10060:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk157 @ D ))]]) ).
thf(10082,plain,
! [A: $i] :
~ ( r2_hidden @ ( sk157 @ A ) @ A ),
inference(simp,[status(thm)],[10061]) ).
thf(11003,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ A @ ( sk25 @ A ) )
!= ( r2_hidden @ ( sk157 @ B ) @ B ) ),
inference(paramod_ordered,[status(thm)],[998,10082]) ).
thf(11016,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk157 @ B ) )
| ( ( sk25 @ A )
!= B ) ),
inference(simp,[status(thm)],[11003]) ).
thf(11022,plain,
! [A: $i] :
( ( sk25 @ ( sk157 @ A ) )
!= A ),
inference(simp,[status(thm)],[11016]) ).
thf(12161,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ k1_xboole_0 @ k1_xboole_0 )
!= B )
| ( A
!= ( sk25 @ ( sk157 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[11794,11022]) ).
thf(12162,plain,
! [A: $i] :
( ( sk7 @ k1_xboole_0 @ k1_xboole_0 )
!= A ),
inference(pattern_uni,[status(thm)],[12161:[bind(A,$thf( sk25 @ ( sk157 @ D ) )),bind(B,$thf( D ))]]) ).
thf(12334,plain,
$false,
inference(simp,[status(thm)],[12162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LAT318+2 : TPTP v8.1.2. Released v3.4.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n017.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 13:47:32 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.97/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.66/1.31 % [INFO] Parsing done (457ms).
% 2.66/1.32 % [INFO] Running in sequential loop mode.
% 3.32/1.54 % [INFO] eprover registered as external prover.
% 3.32/1.55 % [INFO] cvc4 registered as external prover.
% 3.32/1.55 % [INFO] Scanning for conjecture ...
% 3.81/1.74 % [INFO] Found a conjecture and 2985 axioms. Running axiom selection ...
% 5.22/2.10 % [INFO] Axiom selection finished. Selected 621 axioms (removed 2364 axioms).
% 6.48/2.49 % [INFO] Problem is first-order (TPTP FOF).
% 6.62/2.52 % [INFO] Type checking passed.
% 6.62/2.53 % [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 ...
% 63.15/12.91 % [INFO] Killing All external provers ...
% 63.15/12.91 % Time passed: 12387ms (effective reasoning time: 11590ms)
% 63.15/12.92 % Axioms used in derivation (5): t113_zfmisc_1, t115_zfmisc_1, t136_zfmisc_1, t9_tarski, antisymmetry_r2_hidden
% 63.15/12.92 % No. of inferences in proof: 33
% 63.15/12.92 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 12387 ms resp. 11590 ms w/o parsing
% 63.15/12.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 63.15/12.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------