TSTP Solution File: NUM753^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : NUM753^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 08:00:44 EDT 2024
% Result : Theorem 2.52s 1.66s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 24 ( 10 unt; 8 typ; 0 def)
% Number of atoms : 28 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 96 ( 2 ~; 0 |; 0 &; 82 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 5 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(u_type,type,
u: frac ).
thf(eq_type,type,
eq: frac > frac > $o ).
thf(moref_type,type,
moref: frac > frac > $o ).
thf(pf_type,type,
pf: frac > frac > frac ).
thf(3,axiom,
eq @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(10,plain,
eq @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56) ).
thf(20,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
moref @ ( pf @ x @ z ) @ ( pf @ y @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62g) ).
thf(2,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44) ).
thf(12,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: frac] : ( eq @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).
thf(18,plain,
! [A: frac] : ( eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
moref @ z @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(11,plain,
moref @ z @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac] :
( ( moref @ A @ B )
=> ( moref @ ( pf @ C @ A ) @ ( pf @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62d) ).
thf(15,plain,
! [A: frac,B: frac,C: frac] :
( ( moref @ A @ B )
=> ( moref @ ( pf @ C @ A ) @ ( pf @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
$false,
inference(e,[status(thm)],[10,20,9,12,18,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM753^1 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.12 % Command : run_Leo-III %s %d
% 0.12/0.31 % Computer : n011.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon May 6 12:08:39 EDT 2024
% 0.12/0.31 % CPUTime :
% 0.84/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.95 % [INFO] Parsing done (126ms).
% 1.20/0.95 % [INFO] Running in sequential loop mode.
% 1.46/1.14 % [INFO] eprover registered as external prover.
% 1.46/1.15 % [INFO] cvc4 registered as external prover.
% 1.46/1.15 % [INFO] Scanning for conjecture ...
% 1.72/1.19 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.72/1.21 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.81/1.23 % [INFO] Problem is higher-order (TPTP THF).
% 1.87/1.23 % [INFO] Type checking passed.
% 1.87/1.23 % [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 ...
% 2.52/1.66 % External prover 'e' found a proof!
% 2.52/1.66 % [INFO] Killing All external provers ...
% 2.52/1.66 % Time passed: 1194ms (effective reasoning time: 701ms)
% 2.52/1.66 % 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)>
% 2.52/1.66 % Axioms used in derivation (6): e, satz62d, m, satz37, satz44, satz56
% 2.52/1.66 % No. of inferences in proof: 16
% 2.52/1.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1194 ms resp. 701 ms w/o parsing
% 2.52/1.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.52/1.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------