TSTP Solution File: SEU450+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU450+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 11:59:17 EDT 2023
% Result : ContradictoryAxioms 55.96s 12.17s
% Output : Refutation 55.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 45 ( 26 unt; 7 typ; 0 def)
% Number of atoms : 56 ( 41 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 148 ( 13 ~; 7 |; 2 &; 119 @)
% ( 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 : 47 ( 0 ^; 46 !; 1 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(79,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1247,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1248,plain,
( ( k1_tarski @ k1_xboole_0 )
= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1247]) ).
thf(23,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(980,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)],[23]) ).
thf(981,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[980]) ).
thf(982,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[981]) ).
thf(10855,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1248,982]) ).
thf(10856,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( k2_tarski @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[10855:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(10918,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( k2_tarski @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[10856]) ).
thf(18,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(958,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)],[18]) ).
thf(959,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[958]) ).
thf(960,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[959]) ).
thf(961,plain,
! [B: $i,A: $i] :
( ( sk6 @ A @ ( k4_xboole_0 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k4_xboole_0),[sk6])]) ).
thf(11760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ B @ k1_xboole_0 )
= C )
| ( ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( k2_tarski @ k1_xboole_0 @ A ) )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10918,961]) ).
thf(11761,plain,
! [A: $i] :
( ( sk6 @ ( k2_tarski @ k1_xboole_0 @ A ) @ k1_xboole_0 )
= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[11760:[bind(A,$thf( F )),bind(B,$thf( k2_tarski @ k1_xboole_0 @ F )),bind(C,$thf( k1_zfmisc_1 @ k1_xboole_0 ))]]) ).
thf(11852,plain,
! [A: $i] :
( ( sk6 @ ( k2_tarski @ k1_xboole_0 @ A ) @ k1_xboole_0 )
= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[11761]) ).
thf(58,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(1159,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1160,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1159]) ).
thf(1161,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1160]) ).
thf(6627,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ B @ k1_xboole_0 )
= C )
| ( ( k4_xboole_0 @ k1_xboole_0 @ A )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1161,961]) ).
thf(6628,plain,
! [A: $i] :
( ( sk6 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[6627:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(12378,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[11852,6628]) ).
thf(671,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(4200,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)],[671]) ).
thf(4201,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)],[4200]) ).
thf(4202,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[4201]) ).
thf(4204,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[4202]) ).
thf(4205,plain,
v1_xboole_0 @ k1_xboole_0,
inference(simp,[status(thm)],[4204]) ).
thf(471,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(3116,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(3117,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(miniscope,[status(thm)],[3116]) ).
thf(3118,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[3117]) ).
thf(5286,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4205,3118]) ).
thf(5288,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[5286]) ).
thf(12379,plain,
$false,
inference(simplifyReflect,[status(thm)],[12378,5288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SEU450+2 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.13 % Command : run_Leo-III %s %d
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu May 18 13:24:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.94/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.65/1.27 % [INFO] Parsing done (449ms).
% 2.65/1.28 % [INFO] Running in sequential loop mode.
% 3.16/1.48 % [INFO] eprover registered as external prover.
% 3.16/1.48 % [INFO] cvc4 registered as external prover.
% 3.16/1.48 % [INFO] Scanning for conjecture ...
% 3.95/1.72 % [INFO] Found a conjecture and 4535 axioms. Running axiom selection ...
% 5.94/2.27 % [INFO] Axiom selection finished. Selected 901 axioms (removed 3634 axioms).
% 7.61/2.73 % [INFO] Problem is first-order (TPTP FOF).
% 7.77/2.77 % [INFO] Type checking passed.
% 7.77/2.77 % [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 ...
% 55.96/12.16 % [INFO] Killing All external provers ...
% 55.96/12.17 % Time passed: 11653ms (effective reasoning time: 10873ms)
% 55.96/12.17 % Axioms used in derivation (6): d5_xboole_0, t1_zfmisc_1, fc1_subset_1, t22_zfmisc_1, t4_boole, t32_xboole_1
% 55.96/12.17 % No. of inferences in proof: 38
% 55.96/12.17 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11653 ms resp. 10873 ms w/o parsing
% 55.96/12.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 55.96/12.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------