TSTP Solution File: NUM741^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : NUM741^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 08:00:41 EDT 2024
% Result : Theorem 5.38s 2.22s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 25 ( 12 unt; 9 typ; 0 def)
% Number of atoms : 22 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 138 ( 2 ~; 0 |; 0 &; 130 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 ^ 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(x_type,type,
x: frac ).
thf(y_type,type,
y: frac ).
thf(z_type,type,
z: frac ).
thf(nat_type,type,
nat: $tType ).
thf(less_type,type,
less: nat > nat > $o ).
thf(ts_type,type,
ts: nat > nat > nat ).
thf(num_type,type,
num: frac > nat ).
thf(den_type,type,
den: frac > nat ).
thf(3,axiom,
less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(10,plain,
less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: nat,B: nat,C: nat] :
( ( ts @ ( ts @ A @ B ) @ C )
= ( ts @ A @ ( ts @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz31) ).
thf(21,plain,
! [A: nat,B: nat,C: nat] :
( ( ts @ ( ts @ A @ B ) @ C )
= ( ts @ A @ ( ts @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz50) ).
thf(2,negated_conjecture,
~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( less @ ( ts @ A @ C ) @ ( ts @ B @ C ) )
=> ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz33c) ).
thf(12,plain,
! [A: nat,B: nat,C: nat] :
( ( less @ ( ts @ A @ C ) @ ( ts @ B @ C ) )
=> ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).
thf(18,plain,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(11,plain,
less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( less @ A @ B )
=> ( ( less @ C @ D )
=> ( less @ ( ts @ A @ C ) @ ( ts @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz34a) ).
thf(15,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( less @ A @ B )
=> ( ( less @ C @ D )
=> ( less @ ( ts @ A @ C ) @ ( ts @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(345,plain,
$false,
inference(e,[status(thm)],[10,21,9,12,18,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM741^1 : TPTP v8.1.2. Released v3.7.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n010.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 12:31:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/0.98 % [INFO] Parsing done (121ms).
% 1.31/0.99 % [INFO] Running in sequential loop mode.
% 1.74/1.21 % [INFO] eprover registered as external prover.
% 1.74/1.21 % [INFO] cvc4 registered as external prover.
% 1.74/1.21 % [INFO] Scanning for conjecture ...
% 1.91/1.26 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.91/1.28 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.91/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.91/1.31 % [INFO] Type checking passed.
% 1.91/1.31 % [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 ...
% 5.38/2.22 % External prover 'e' found a proof!
% 5.38/2.22 % [INFO] Killing All external provers ...
% 5.38/2.22 % Time passed: 1689ms (effective reasoning time: 1225ms)
% 5.38/2.22 % 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)>
% 5.38/2.22 % Axioms used in derivation (6): satz29, satz33c, satz31, l, satz34a, k
% 5.38/2.22 % No. of inferences in proof: 16
% 5.38/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1689 ms resp. 1225 ms w/o parsing
% 5.38/2.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.38/2.25 % [INFO] Killing All external provers ...
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