TSTP Solution File: NUM686^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 : Tue May 7 08:00:30 EDT 2024
% Result : Theorem 2.68s 1.60s
% Output : Refutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 22 ( 3 unt; 8 typ; 0 def)
% Number of atoms : 37 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 87 ( 2 ~; 0 |; 0 &; 79 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 16 ( 0 ^ 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_type,type,
x: nat ).
thf(y_type,type,
y: nat ).
thf(z_type,type,
z: nat ).
thf(u_type,type,
u: nat ).
thf(some_type,type,
some: ( nat > $o ) > $o ).
thf(diffprop_type,type,
diffprop: nat > nat > nat > $o ).
thf(pl_type,type,
pl: nat > nat > nat ).
thf(4,axiom,
some @ ( diffprop @ z @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(10,plain,
some @ ( diffprop @ z @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ A @ B ) )
=> ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
thf(14,plain,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ A @ B ) )
=> ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
some @ ( diffprop @ x @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(9,plain,
some @ ( diffprop @ x @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
thf(17,plain,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ B @ A ) )
=> ( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
thf(11,plain,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ B @ A ) )
=> ( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz21) ).
thf(2,negated_conjecture,
~ ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[10,14,9,17,11,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.14 % Command : run_Leo-III %s %d
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 6 12:27:24 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.85/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.96 % [INFO] Parsing done (113ms).
% 1.24/0.96 % [INFO] Running in sequential loop mode.
% 1.71/1.17 % [INFO] eprover registered as external prover.
% 1.71/1.18 % [INFO] cvc4 registered as external prover.
% 1.71/1.18 % [INFO] Scanning for conjecture ...
% 1.87/1.23 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.87/1.26 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.87/1.27 % [INFO] Problem is higher-order (TPTP THF).
% 1.87/1.27 % [INFO] Type checking passed.
% 1.87/1.28 % [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 ...
% 2.68/1.60 % External prover 'e' found a proof!
% 2.68/1.60 % [INFO] Killing All external provers ...
% 2.68/1.60 % Time passed: 1087ms (effective reasoning time: 631ms)
% 2.68/1.60 % 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)>
% 2.68/1.60 % Axioms used in derivation (5): n, m, satz15, satz19a, satz6
% 2.68/1.60 % No. of inferences in proof: 14
% 2.68/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1087 ms resp. 631 ms w/o parsing
% 3.07/1.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.07/1.67 % [INFO] Killing All external provers ...
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