TSTP Solution File: ALG258^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : ALG258^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 : Mon May 20 18:16:23 EDT 2024
% Result : Theorem 18.93s 4.82s
% Output : Refutation 18.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 58 ( 26 unt; 14 typ; 1 def)
% Number of atoms : 82 ( 74 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 434 ( 42 ~; 26 |; 0 &; 356 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 92 ( 0 ^ 92 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(one_type,type,
one: term ).
thf(lam_type,type,
lam: term > term ).
thf(sub_type,type,
sub: term > subst > term ).
thf(sh_type,type,
sh: subst ).
thf(push_type,type,
push: term > subst > subst ).
thf(comp_type,type,
comp: subst > subst > subst ).
thf(hoaslaminj_lthm_type,type,
hoaslaminj_lthm: $o ).
thf(hoaslaminj_lthm_def,definition,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ) ).
thf(sk1_type,type,
sk1: subst > term > term ).
thf(sk2_type,type,
sk2: subst > term > term ).
thf(sk3_type,type,
sk3: subst ).
thf(sk4_type,type,
sk4: term ).
thf(sk5_type,type,
sk5: term > term ).
thf(1,conjecture,
hoaslaminj_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoaslaminj_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term,B: subst] :
( ( sub @ one @ ( push @ A @ B ) )
= A )
=> ( ! [A: term,B: subst] :
( ( comp @ sh @ ( push @ A @ B ) )
= B )
=> ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) )
=> ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ! [B: subst > term > term] :
( ! [C: subst,D: term,E: subst] :
( ( sub @ ( B @ C @ D ) @ E )
= ( B @ ( comp @ C @ E ) @ ( sub @ D @ E ) ) )
=> ( ( ( lam @ ( A @ sh @ one ) )
= ( lam @ ( B @ sh @ one ) ) )
=> ! [C: subst,D: term] :
( ( A @ C @ D )
= ( B @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [B: subst,A: term] :
( ( comp @ sh @ ( push @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
! [B: subst,A: term] :
( ( comp @ sh @ ( push @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[8]) ).
thf(19,plain,
! [B: subst,A: term] :
( ( comp @ sh @ ( push @ A @ B ) )
= B ),
inference(simp,[status(thm)],[18]) ).
thf(5,plain,
! [B: subst,A: term] :
( ( sub @ one @ ( push @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [B: subst,A: term] :
( ( sub @ one @ ( push @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[5]) ).
thf(6,plain,
! [C: subst,B: term,A: subst] :
( ( sub @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ ( comp @ A @ C ) @ ( sub @ B @ C ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [C: subst,B: term,A: subst] :
( ( sk1 @ ( comp @ A @ C ) @ ( sub @ B @ C ) )
= ( sub @ ( sk1 @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(14,plain,
! [C: subst,B: term,A: subst] :
( ( sk1 @ ( comp @ A @ C ) @ ( sub @ B @ C ) )
= ( sub @ ( sk1 @ A @ B ) @ C ) ),
inference(simp,[status(thm)],[13]) ).
thf(36,plain,
! [E: subst,D: term,C: subst,B: subst,A: term] :
( ( ( sk1 @ ( comp @ C @ E ) @ A )
= ( sub @ ( sk1 @ C @ D ) @ E ) )
| ( ( sub @ one @ ( push @ A @ B ) )
!= ( sub @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[11,14]) ).
thf(37,plain,
! [C: subst,B: term,A: subst] :
( ( sk1 @ ( comp @ A @ ( push @ B @ C ) ) @ B )
= ( sub @ ( sk1 @ A @ one ) @ ( push @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( one )),bind(E,$thf( push @ F @ G ))]]) ).
thf(40,plain,
! [C: subst,B: term,A: subst] :
( ( sk1 @ ( comp @ A @ ( push @ B @ C ) ) @ B )
= ( sub @ ( sk1 @ A @ one ) @ ( push @ B @ C ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(56,plain,
! [E: subst,D: term,C: subst,B: subst,A: term] :
( ( ( sk1 @ B @ D )
= ( sub @ ( sk1 @ C @ one ) @ ( push @ D @ E ) ) )
| ( ( comp @ sh @ ( push @ A @ B ) )
!= ( comp @ C @ ( push @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,40]) ).
thf(57,plain,
! [B: subst,A: term] :
( ( sk1 @ B @ A )
= ( sub @ ( sk1 @ sh @ one ) @ ( push @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sh )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(10,plain,
( ( lam @ ( sk1 @ sh @ one ) )
= ( lam @ ( sk2 @ sh @ one ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
( ( lam @ ( sk2 @ sh @ one ) )
= ( lam @ ( sk1 @ sh @ one ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(4,plain,
! [B: term,A: term] :
( ( ( lam @ A )
!= ( lam @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(20,plain,
! [B: term,A: term] :
( ( ( lam @ A )
!= ( lam @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(21,plain,
! [B: term,A: term] :
( ( ( lam @ A )
!= ( lam @ B ) )
| ( A = B ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
! [A: term] :
( ( sk5 @ ( lam @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(lam),[sk5])]) ).
thf(23,plain,
! [A: term] :
( ( ( sk5 @ ( lam @ ( sk1 @ sh @ one ) ) )
= A )
| ( ( lam @ ( sk2 @ sh @ one ) )
!= ( lam @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,22]) ).
thf(24,plain,
( ( sk2 @ sh @ one )
= ( sk5 @ ( lam @ ( sk1 @ sh @ one ) ) ) ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk2 @ sh @ one ))]]) ).
thf(25,plain,
( ( sk2 @ sh @ one )
= ( sk1 @ sh @ one ) ),
inference(rewrite,[status(thm)],[24,22]) ).
thf(7,plain,
! [C: subst,B: term,A: subst] :
( ( sub @ ( sk2 @ A @ B ) @ C )
= ( sk2 @ ( comp @ A @ C ) @ ( sub @ B @ C ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
! [C: subst,B: term,A: subst] :
( ( sk2 @ ( comp @ A @ C ) @ ( sub @ B @ C ) )
= ( sub @ ( sk2 @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(17,plain,
! [C: subst,B: term,A: subst] :
( ( sk2 @ ( comp @ A @ C ) @ ( sub @ B @ C ) )
= ( sub @ ( sk2 @ A @ B ) @ C ) ),
inference(simp,[status(thm)],[16]) ).
thf(9,plain,
( ( sk1 @ sk3 @ sk4 )
!= ( sk2 @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
( ( sk2 @ sk3 @ sk4 )
!= ( sk1 @ sk3 @ sk4 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(48,plain,
! [C: subst,B: term,A: subst] :
( ( ( sub @ ( sk2 @ A @ B ) @ C )
!= ( sk1 @ sk3 @ sk4 ) )
| ( ( sk2 @ ( comp @ A @ C ) @ ( sub @ B @ C ) )
!= ( sk2 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17,15]) ).
thf(50,plain,
! [C: subst,B: term,A: subst] :
( ( ( sub @ ( sk2 @ A @ B ) @ C )
!= ( sk1 @ sk3 @ sk4 ) )
| ( ( comp @ A @ C )
!= sk3 )
| ( ( sub @ B @ C )
!= sk4 ) ),
inference(simp,[status(thm)],[48]) ).
thf(145,plain,
! [C: subst,B: term,A: subst] :
( ( ( sub @ ( sk1 @ sh @ one ) @ C )
!= ( sk1 @ sk3 @ sk4 ) )
| ( ( comp @ A @ C )
!= sk3 )
| ( ( sub @ B @ C )
!= sk4 )
| ( ( sk2 @ sh @ one )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25,50]) ).
thf(146,plain,
! [A: subst] :
( ( ( sub @ ( sk1 @ sh @ one ) @ A )
!= ( sk1 @ sk3 @ sk4 ) )
| ( ( comp @ sh @ A )
!= sk3 )
| ( ( sub @ one @ A )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( sh )),bind(B,$thf( one ))]]) ).
thf(182,plain,
! [A: subst] :
( ( ( sub @ ( sk1 @ sh @ one ) @ A )
!= ( sk1 @ sk3 @ sk4 ) )
| ( ( comp @ sh @ A )
!= sk3 )
| ( ( sub @ one @ A )
!= sk4 ) ),
inference(simp,[status(thm)],[146]) ).
thf(998,plain,
! [C: subst,B: subst,A: term] :
( ( ( sub @ ( sk1 @ sh @ one ) @ C )
!= ( sk1 @ sk3 @ sk4 ) )
| ( ( comp @ sh @ C )
!= sk3 )
| ( A != sk4 )
| ( ( sub @ one @ ( push @ A @ B ) )
!= ( sub @ one @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11,182]) ).
thf(999,plain,
! [B: subst,A: term] :
( ( ( sub @ ( sk1 @ sh @ one ) @ ( push @ A @ B ) )
!= ( sk1 @ sk3 @ sk4 ) )
| ( ( comp @ sh @ ( push @ A @ B ) )
!= sk3 )
| ( A != sk4 ) ),
inference(pattern_uni,[status(thm)],[998:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( push @ D @ E ))]]) ).
thf(1093,plain,
! [A: subst] :
( ( ( sub @ ( sk1 @ sh @ one ) @ ( push @ sk4 @ A ) )
!= ( sk1 @ sk3 @ sk4 ) )
| ( ( comp @ sh @ ( push @ sk4 @ A ) )
!= sk3 ) ),
inference(simp,[status(thm)],[999]) ).
thf(1107,plain,
! [A: subst] :
( ( ( sub @ ( sk1 @ sh @ one ) @ ( push @ sk4 @ A ) )
!= ( sk1 @ sk3 @ sk4 ) )
| ( A != sk3 ) ),
inference(rewrite,[status(thm)],[1093,19]) ).
thf(1114,plain,
! [C: subst,B: subst,A: term] :
( ( ( sk1 @ B @ A )
!= ( sk1 @ sk3 @ sk4 ) )
| ( C != sk3 )
| ( ( sub @ ( sk1 @ sh @ one ) @ ( push @ A @ B ) )
!= ( sub @ ( sk1 @ sh @ one ) @ ( push @ sk4 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,1107]) ).
thf(1115,plain,
! [A: subst] :
( ( ( sk1 @ A @ sk4 )
!= ( sk1 @ sk3 @ sk4 ) )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[1114:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1224,plain,
( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[1115]) ).
thf(1500,plain,
$false,
inference(simp,[status(thm)],[1224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : ALG258^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.06/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat May 18 22:54:54 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.98/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.86/1.29 % [INFO] Parsing done (328ms).
% 1.86/1.30 % [INFO] Running in sequential loop mode.
% 2.83/1.66 % [INFO] nitpick registered as external prover.
% 2.83/1.67 % [INFO] Scanning for conjecture ...
% 4.26/2.16 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 4.26/2.19 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 4.26/2.19 % [INFO] Problem is higher-order (TPTP THF).
% 4.26/2.19 % [INFO] Type checking passed.
% 4.26/2.19 % [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 ...
% 18.93/4.82 % [INFO] Killing All external provers ...
% 18.93/4.82 % Time passed: 4337ms (effective reasoning time: 3507ms)
% 18.93/4.82 % Solved by 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)>
% 18.93/4.82 % Axioms used in derivation (0):
% 18.93/4.82 % No. of inferences in proof: 43
% 18.93/4.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4337 ms resp. 3507 ms w/o parsing
% 18.93/4.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.93/4.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------