TSTP Solution File: DAT056^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : DAT056^1 : TPTP v8.2.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 19:48:45 EDT 2024
% Result : Theorem 16.79s 4.00s
% Output : Refutation 16.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 50 ( 21 unt; 14 typ; 0 def)
% Number of atoms : 65 ( 64 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 578 ( 21 ~; 20 |; 0 &; 528 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 119 ( 0 ^ 119 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(lst_type,type,
lst: $tType ).
thf(a_type,type,
a: $tType ).
thf(ap_type,type,
ap: lst > lst > lst ).
thf(cns_type,type,
cns: a > lst > lst ).
thf(nl_type,type,
nl: lst ).
thf(xs_type,type,
xs: lst ).
thf(sk1_type,type,
sk1: lst ).
thf(sk2_type,type,
sk2: lst ).
thf(sk3_type,type,
sk3: lst ).
thf(sk4_type,type,
sk4: lst ).
thf(sk5_type,type,
sk5: a ).
thf(sk6_type,type,
sk6: lst ).
thf(sk7_type,type,
sk7: lst ).
thf(sk8_type,type,
sk8: lst ).
thf(1,conjecture,
! [A: lst,B: lst] :
( ( ap @ xs @ ( ap @ A @ B ) )
= ( ap @ ( ap @ xs @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: lst,B: lst] :
( ( ap @ xs @ ( ap @ A @ B ) )
= ( ap @ ( ap @ xs @ A ) @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: lst,B: lst] :
( ( ap @ xs @ ( ap @ A @ B ) )
= ( ap @ ( ap @ xs @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ( ap @ xs @ ( ap @ sk1 @ sk2 ) )
!= ( ap @ ( ap @ xs @ sk1 ) @ sk2 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
( ( ap @ ( ap @ xs @ sk1 ) @ sk2 )
!= ( ap @ xs @ ( ap @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(3,axiom,
! [A: lst] :
( ! [B: lst,C: lst] :
( ( ap @ nl @ ( ap @ B @ C ) )
= ( ap @ ( ap @ nl @ B ) @ C ) )
=> ( ! [B: a,C: lst] :
( ! [D: lst,E: lst] :
( ( ap @ C @ ( ap @ D @ E ) )
= ( ap @ ( ap @ C @ D ) @ E ) )
=> ! [D: lst,E: lst] :
( ( ap @ ( cns @ B @ C ) @ ( ap @ D @ E ) )
= ( ap @ ( ap @ ( cns @ B @ C ) @ D ) @ E ) ) )
=> ! [B: lst,C: lst] :
( ( ap @ A @ ( ap @ B @ C ) )
= ( ap @ ( ap @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093) ).
thf(9,plain,
! [A: lst] :
( ! [B: lst,C: lst] :
( ( ap @ nl @ ( ap @ B @ C ) )
= ( ap @ ( ap @ nl @ B ) @ C ) )
=> ( ! [B: a,C: lst] :
( ! [D: lst,E: lst] :
( ( ap @ C @ ( ap @ D @ E ) )
= ( ap @ ( ap @ C @ D ) @ E ) )
=> ! [D: lst,E: lst] :
( ( ap @ ( cns @ B @ C ) @ ( ap @ D @ E ) )
= ( ap @ ( ap @ ( cns @ B @ C ) @ D ) @ E ) ) )
=> ! [B: lst,C: lst] :
( ( ap @ A @ ( ap @ B @ C ) )
= ( ap @ ( ap @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
( ! [A: lst,B: lst] :
( ( ap @ nl @ ( ap @ A @ B ) )
= ( ap @ ( ap @ nl @ A ) @ B ) )
=> ( ! [A: a,B: lst] :
( ! [C: lst,D: lst] :
( ( ap @ B @ ( ap @ C @ D ) )
= ( ap @ ( ap @ B @ C ) @ D ) )
=> ! [C: lst,D: lst] :
( ( ap @ ( cns @ A @ B ) @ ( ap @ C @ D ) )
= ( ap @ ( ap @ ( cns @ A @ B ) @ C ) @ D ) ) )
=> ! [A: lst,B: lst,C: lst] :
( ( ap @ A @ ( ap @ B @ C ) )
= ( ap @ ( ap @ A @ B ) @ C ) ) ) ),
inference(miniscope,[status(thm)],[9]) ).
thf(11,plain,
! [C: lst,B: lst,A: lst] :
( ( ( ap @ nl @ ( ap @ sk3 @ sk4 ) )
!= ( ap @ ( ap @ nl @ sk3 ) @ sk4 ) )
| ( ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) )
!= ( ap @ ( ap @ ( cns @ sk5 @ sk6 ) @ sk7 ) @ sk8 ) )
| ( ( ap @ A @ ( ap @ B @ C ) )
= ( ap @ ( ap @ A @ B ) @ C ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(13,plain,
! [C: lst,B: lst,A: lst] :
( ( ( ap @ ( ap @ nl @ sk3 ) @ sk4 )
!= ( ap @ nl @ ( ap @ sk3 @ sk4 ) ) )
| ( ( ap @ ( ap @ ( cns @ sk5 @ sk6 ) @ sk7 ) @ sk8 )
!= ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) ) )
| ( ( ap @ ( ap @ A @ B ) @ C )
= ( ap @ A @ ( ap @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(14,plain,
! [C: lst,B: lst,A: lst] :
( ( ( ap @ ( ap @ nl @ sk3 ) @ sk4 )
!= ( ap @ nl @ ( ap @ sk3 @ sk4 ) ) )
| ( ( ap @ ( ap @ ( cns @ sk5 @ sk6 ) @ sk7 ) @ sk8 )
!= ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) ) )
| ( ( ap @ ( ap @ A @ B ) @ C )
= ( ap @ A @ ( ap @ B @ C ) ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(5,axiom,
! [A: lst] :
( ( ap @ nl @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2p_Osimps_I1_J) ).
thf(19,plain,
! [A: lst] :
( ( ap @ nl @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
! [A: lst] :
( ( ap @ nl @ A )
= A ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [A: lst] :
( ( ap @ nl @ A )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(91,plain,
! [C: lst,B: lst,A: lst] :
( ( ( ap @ sk3 @ sk4 )
!= ( ap @ sk3 @ sk4 ) )
| ( ( ap @ ( ap @ ( cns @ sk5 @ sk6 ) @ sk7 ) @ sk8 )
!= ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) ) )
| ( ( ap @ ( ap @ A @ B ) @ C )
= ( ap @ A @ ( ap @ B @ C ) ) ) ),
inference(rewrite,[status(thm)],[14,21]) ).
thf(92,plain,
! [C: lst,B: lst,A: lst] :
( ( ( ap @ ( ap @ ( cns @ sk5 @ sk6 ) @ sk7 ) @ sk8 )
!= ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) ) )
| ( ( ap @ ( ap @ A @ B ) @ C )
= ( ap @ A @ ( ap @ B @ C ) ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(12,plain,
! [E: lst,D: lst,C: lst,B: lst,A: lst] :
( ( ( ap @ nl @ ( ap @ sk3 @ sk4 ) )
!= ( ap @ ( ap @ nl @ sk3 ) @ sk4 ) )
| ( ( ap @ sk6 @ ( ap @ A @ B ) )
= ( ap @ ( ap @ sk6 @ A ) @ B ) )
| ( ( ap @ C @ ( ap @ D @ E ) )
= ( ap @ ( ap @ C @ D ) @ E ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(15,plain,
! [E: lst,D: lst,C: lst,B: lst,A: lst] :
( ( ( ap @ ( ap @ nl @ sk3 ) @ sk4 )
!= ( ap @ nl @ ( ap @ sk3 @ sk4 ) ) )
| ( ( ap @ ( ap @ sk6 @ A ) @ B )
= ( ap @ sk6 @ ( ap @ A @ B ) ) )
| ( ( ap @ ( ap @ C @ D ) @ E )
= ( ap @ C @ ( ap @ D @ E ) ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(541,plain,
! [E: lst,D: lst,C: lst,B: lst,A: lst] :
( ( ( ap @ sk3 @ sk4 )
!= ( ap @ sk3 @ sk4 ) )
| ( ( ap @ ( ap @ sk6 @ A ) @ B )
= ( ap @ sk6 @ ( ap @ A @ B ) ) )
| ( ( ap @ ( ap @ C @ D ) @ E )
= ( ap @ C @ ( ap @ D @ E ) ) ) ),
inference(rewrite,[status(thm)],[15,21]) ).
thf(542,plain,
! [E: lst,D: lst,C: lst,B: lst,A: lst] :
( ( ( ap @ ( ap @ sk6 @ A ) @ B )
= ( ap @ sk6 @ ( ap @ A @ B ) ) )
| ( ( ap @ ( ap @ C @ D ) @ E )
= ( ap @ C @ ( ap @ D @ E ) ) ) ),
inference(simp,[status(thm)],[541]) ).
thf(634,plain,
! [E: lst,D: lst,C: lst,B: lst,A: lst] :
( ( ( ap @ ( ap @ sk6 @ A ) @ B )
= ( ap @ sk6 @ ( ap @ A @ B ) ) )
| ( ( ap @ ( ap @ C @ D ) @ E )
!= ( ap @ ( ap @ sk6 @ A ) @ B ) )
| ( ( ap @ C @ ( ap @ D @ E ) )
!= ( ap @ sk6 @ ( ap @ A @ B ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[542]) ).
thf(637,plain,
! [B: lst,A: lst] :
( ( ap @ ( ap @ sk6 @ A ) @ B )
= ( ap @ sk6 @ ( ap @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[634:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( sk6 ))]]) ).
thf(773,plain,
! [B: lst,A: lst] :
( ( ap @ ( ap @ sk6 @ A ) @ B )
= ( ap @ sk6 @ ( ap @ A @ B ) ) ),
inference(simp,[status(thm)],[637]) ).
thf(4,axiom,
! [A: lst,B: lst,C: a] :
( ( ap @ ( cns @ C @ B ) @ A )
= ( cns @ C @ ( ap @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1p_Osimps_I2_J) ).
thf(16,plain,
! [A: lst,B: lst,C: a] :
( ( ap @ ( cns @ C @ B ) @ A )
= ( cns @ C @ ( ap @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [C: a,B: lst,A: lst] :
( ( ap @ ( cns @ C @ B ) @ A )
= ( cns @ C @ ( ap @ B @ A ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
! [C: a,B: lst,A: lst] :
( ( cns @ C @ ( ap @ B @ A ) )
= ( ap @ ( cns @ C @ B ) @ A ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(795,plain,
! [E: a,D: lst,C: lst,B: lst,A: lst] :
( ( ( cns @ E @ ( ap @ sk6 @ ( ap @ A @ B ) ) )
= ( ap @ ( cns @ E @ D ) @ C ) )
| ( ( ap @ ( ap @ sk6 @ A ) @ B )
!= ( ap @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[773,18]) ).
thf(796,plain,
! [C: lst,B: a,A: lst] :
( ( cns @ B @ ( ap @ sk6 @ ( ap @ C @ A ) ) )
= ( ap @ ( cns @ B @ ( ap @ sk6 @ C ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[795:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( ap @ sk6 @ G )),bind(E,$thf( E ))]]) ).
thf(871,plain,
! [C: lst,B: a,A: lst] :
( ( cns @ B @ ( ap @ sk6 @ ( ap @ C @ A ) ) )
= ( ap @ ( cns @ B @ ( ap @ sk6 @ C ) ) @ A ) ),
inference(simp,[status(thm)],[796]) ).
thf(3265,plain,
! [C: lst,B: a,A: lst] :
( ( ap @ ( ap @ ( cns @ B @ sk6 ) @ C ) @ A )
= ( ap @ ( cns @ B @ sk6 ) @ ( ap @ C @ A ) ) ),
inference(rewrite,[status(thm)],[871,18]) ).
thf(3266,plain,
! [C: lst,B: lst,A: lst] :
( ( ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) )
!= ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) ) )
| ( ( ap @ ( ap @ A @ B ) @ C )
= ( ap @ A @ ( ap @ B @ C ) ) ) ),
inference(rewrite,[status(thm)],[92,3265]) ).
thf(3267,plain,
! [C: lst,B: lst,A: lst] :
( ( ap @ ( ap @ A @ B ) @ C )
= ( ap @ A @ ( ap @ B @ C ) ) ),
inference(simp,[status(thm)],[3266]) ).
thf(3499,plain,
( ( ap @ xs @ ( ap @ sk1 @ sk2 ) )
!= ( ap @ xs @ ( ap @ sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[8,3267]) ).
thf(3500,plain,
$false,
inference(simp,[status(thm)],[3499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : DAT056^1 : TPTP v8.2.0. Released v5.4.0.
% 0.16/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n003.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 : Sun May 19 23:39:53 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.99/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.01 % [INFO] Parsing done (117ms).
% 1.25/1.02 % [INFO] Running in sequential loop mode.
% 1.76/1.24 % [INFO] nitpick registered as external prover.
% 1.76/1.25 % [INFO] Scanning for conjecture ...
% 1.83/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.96/1.33 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.96/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 1.96/1.35 % [INFO] Type checking passed.
% 1.96/1.35 % [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 ...
% 16.79/4.00 % [INFO] Killing All external provers ...
% 16.79/4.00 % Time passed: 3457ms (effective reasoning time: 2977ms)
% 16.79/4.00 % 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)>
% 16.79/4.00 % Axioms used in derivation (3): fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093, fact_2p_Osimps_I1_J, fact_1p_Osimps_I2_J
% 16.79/4.00 % No. of inferences in proof: 36
% 16.79/4.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3457 ms resp. 2977 ms w/o parsing
% 16.86/4.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.86/4.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------