TSTP Solution File: NUM768^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : NUM768^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 08:00:48 EDT 2024
% Result : Theorem 3.92s 1.95s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 38 ( 11 unt; 14 typ; 0 def)
% Number of atoms : 41 ( 9 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 225 ( 6 ~; 0 |; 0 &; 207 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 7 ^ 40 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(x_type,type,
x: frac ).
thf(y_type,type,
y: frac ).
thf(nat_type,type,
nat: $tType ).
thf(some_type,type,
some: ( nat > $o ) > $o ).
thf(ts_type,type,
ts: nat > nat > nat ).
thf(num_type,type,
num: frac > nat ).
thf(den_type,type,
den: frac > nat ).
thf(pl_type,type,
pl: nat > nat > nat ).
thf(eq_type,type,
eq: frac > frac > $o ).
thf(pf_type,type,
pf: frac > frac > frac ).
thf(fr_type,type,
fr: nat > nat > frac ).
thf(ind_type,type,
ind: ( nat > $o ) > nat ).
thf(amone_type,type,
amone: ( nat > $o ) > $o ).
thf(8,axiom,
! [A: frac] : ( eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(25,plain,
! [A: frac] : ( eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
( some
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(14,plain,
( some
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,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/sandbox/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)],[6]) ).
thf(1,conjecture,
( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz67c) ).
thf(2,negated_conjecture,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29) ).
thf(27,plain,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: frac,B: nat] : ( eq @ A @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40) ).
thf(23,plain,
! [A: frac,B: nat] : ( eq @ A @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat] : ( eq @ ( pf @ ( fr @ A @ C ) @ ( fr @ B @ C ) ) @ ( fr @ ( pl @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz57) ).
thf(30,plain,
! [A: nat,B: nat,C: nat] : ( eq @ ( pf @ ( fr @ A @ C ) @ ( fr @ B @ C ) ) @ ( fr @ ( pl @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( amone
@ ^ [C: nat] :
( A
= ( pl @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8b) ).
thf(15,plain,
! [A: nat,B: nat] :
( amone
@ ^ [C: nat] :
( A
= ( pl @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
thf(17,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: nat > $o] :
( ~ ( ( amone @ A )
=> ~ ( some @ A ) )
=> ( A @ ( ind @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneax) ).
thf(32,plain,
! [A: nat > $o] :
( ~ ( ( amone @ A )
=> ~ ( some @ A ) )
=> ( A @ ( ind @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: frac,B: nat] : ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40a) ).
thf(34,plain,
! [A: frac,B: nat] : ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55,plain,
$false,
inference(cvc4,[status(thm)],[25,14,20,13,27,23,30,15,17,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM768^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n028.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 12:09:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.82/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.96 % [INFO] Parsing done (123ms).
% 1.23/0.97 % [INFO] Running in sequential loop mode.
% 1.69/1.19 % [INFO] eprover registered as external prover.
% 1.69/1.19 % [INFO] cvc4 registered as external prover.
% 1.69/1.19 % [INFO] Scanning for conjecture ...
% 1.69/1.26 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.96/1.28 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.96/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.96/1.31 % [INFO] Type checking passed.
% 1.96/1.31 % [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 ...
% 3.92/1.94 % External prover 'cvc4' found a proof!
% 3.92/1.94 % [INFO] Killing All external provers ...
% 3.92/1.94 % Time passed: 1417ms (effective reasoning time: 973ms)
% 3.92/1.94 % 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)>
% 3.92/1.95 % Axioms used in derivation (10): satz29, satz40a, satz39, m, oneax, satz56, satz40, satz57, satz8b, satz37
% 3.92/1.95 % No. of inferences in proof: 24
% 3.92/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1417 ms resp. 973 ms w/o parsing
% 3.96/1.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.96/1.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------