TSTP Solution File: DAT056^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---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 : n032.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 19:47:56 EDT 2024
% Result : Theorem 2.70s 1.88s
% Output : Refutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 16 ( 8 unt; 6 typ; 0 def)
% Number of atoms : 16 ( 15 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 124 ( 2 ~; 0 |; 0 &; 116 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 ^ 36 !; 0 ?; 36 :)
% 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(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(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(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(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(22,plain,
$false,
inference(e,[status(thm)],[6,9,16,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : DAT056^1 : TPTP v8.2.0. Released v5.4.0.
% 0.02/0.11 % Command : run_Leo-III %s %d
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sun May 19 23:39:54 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.80/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.10/0.97 % [INFO] Parsing done (135ms).
% 1.10/0.98 % [INFO] Running in sequential loop mode.
% 1.50/1.29 % [INFO] eprover registered as external prover.
% 1.50/1.29 % [INFO] cvc4 registered as external prover.
% 1.50/1.29 % [INFO] Scanning for conjecture ...
% 1.68/1.35 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.79/1.38 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.79/1.42 % [INFO] Problem is higher-order (TPTP THF).
% 1.79/1.42 % [INFO] Type checking passed.
% 1.79/1.42 % [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 ...
% 2.70/1.83 % External prover 'e' found a proof!
% 2.70/1.83 % [INFO] Killing All external provers ...
% 2.70/1.84 % Time passed: 1414ms (effective reasoning time: 847ms)
% 2.70/1.84 % 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)>
% 2.70/1.84 % 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_1p_Osimps_I2_J, fact_2p_Osimps_I1_J
% 2.70/1.84 % No. of inferences in proof: 10
% 2.70/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1414 ms resp. 847 ms w/o parsing
% 2.97/1.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.97/1.92 % [INFO] Killing All external provers ...
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