%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT056^1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:00 AM UTC 2026
% Result : Theorem 3.89s 2.27s
% Output : Refutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 8 unt; 0 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 : 0 ( 0 >; 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_decl,type,
ap: lst > lst > lst ).
thf(cns_decl,type,
cns: a > lst > lst ).
thf(nl_decl,type,
nl: lst ).
thf(xs_decl,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(17,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(20,plain,
! [A: lst] :
( ( ap @ nl @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,plain,
$false,
inference(e,[status(thm)],[6,9,17,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT056^1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n006.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 17:57:54 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.00 % [INFO] Parsing done (196ms).
% 1.25/1.01 % [INFO] Running in sequential loop mode.
% 2.04/1.42 % [INFO] eprover registered as external prover.
% 2.04/1.43 % [INFO] Scanning for conjecture ...
% 2.24/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.24/1.56 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.24/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.59 % [INFO] Type checking passed.
% 2.24/1.59 % [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 ...
% 3.89/2.27 % External prover 'e' found a proof!
% 3.89/2.27 % [INFO] Killing All external provers ...
% 3.89/2.27 % Time passed: 1914ms (effective reasoning time: 1251ms)
% 3.89/2.27 % 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)>
% 3.89/2.27 % 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
% 3.89/2.27 % No. of inferences in proof: 10
% 3.89/2.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1914 ms resp. 1251 ms w/o parsing
% 4.12/2.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.12/2.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------