TSTP Solution File: SWV489+3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV489+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Fri May 19 12:16:04 EDT 2023
% Result : Theorem 96.79s 17.10s
% Output : Refutation 96.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 37 ( 9 unt; 9 typ; 0 def)
% Number of atoms : 105 ( 30 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 294 ( 9 ~; 5 |; 42 &; 208 @)
% ( 3 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 61 ( 0 ^; 58 !; 3 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(int_leq_type,type,
int_leq: $i > $i > $o ).
thf(int_one_type,type,
int_one: $i ).
thf(n_type,type,
n: $i ).
thf(a_type,type,
a: $i > $i > $i ).
thf(real_zero_type,type,
real_zero: $i ).
thf(int_less_type,type,
int_less: $i > $i > $o ).
thf(int_zero_type,type,
int_zero: $i ).
thf(plus_type,type,
plus: $i > $i > $i ).
thf(real_one_type,type,
real_one: $i ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( int_less @ A @ B )
& ( int_less @ B @ C ) )
=> ( int_less @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_transitive) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( ( int_less @ A @ B )
& ( int_less @ B @ C ) )
=> ( int_less @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
int_less @ int_zero @ int_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_zero_one) ).
thf(41,plain,
int_less @ int_zero @ int_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i] :
( ( plus @ A @ int_zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
thf(45,plain,
! [A: $i] :
( ( plus @ A @ int_zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( int_less @ A @ B )
| ( int_leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_total) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( int_less @ A @ B )
| ( int_leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( int_leq @ int_one @ A )
& ( int_leq @ A @ n )
& ( int_leq @ int_one @ B )
& ( int_leq @ B @ n ) )
=> ( ! [C: $i] :
( ( ( int_less @ int_zero @ C )
& ( A
= ( plus @ B @ C ) ) )
=> ! [D: $i] :
( ( ( int_leq @ int_one @ D )
& ( int_leq @ D @ B ) )
=> ( ( a @ ( plus @ D @ C ) @ D )
= real_zero ) ) )
& ! [C: $i] :
( ( ( int_leq @ int_one @ C )
& ( int_leq @ C @ B ) )
=> ( ( a @ C @ C )
= real_one ) )
& ! [C: $i] :
( ( ( int_less @ int_zero @ C )
& ( B
= ( plus @ A @ C ) ) )
=> ! [D: $i] :
( ( ( int_leq @ int_one @ D )
& ( int_leq @ D @ A ) )
=> ( ( a @ D @ ( plus @ D @ C ) )
= real_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qii) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( int_leq @ int_one @ A )
& ( int_leq @ A @ n )
& ( int_leq @ int_one @ B )
& ( int_leq @ B @ n ) )
=> ( ! [C: $i] :
( ( ( int_less @ int_zero @ C )
& ( A
= ( plus @ B @ C ) ) )
=> ! [D: $i] :
( ( ( int_leq @ int_one @ D )
& ( int_leq @ D @ B ) )
=> ( ( a @ ( plus @ D @ C ) @ D )
= real_zero ) ) )
& ! [C: $i] :
( ( ( int_leq @ int_one @ C )
& ( int_leq @ C @ B ) )
=> ( ( a @ C @ C )
= real_one ) )
& ! [C: $i] :
( ( ( int_less @ int_zero @ C )
& ( B
= ( plus @ A @ C ) ) )
=> ! [D: $i] :
( ( ( int_leq @ int_one @ D )
& ( int_leq @ D @ A ) )
=> ( ( a @ D @ ( plus @ D @ C ) )
= real_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( int_less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_irreflexive) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( int_less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( int_less @ A @ B )
<=> ? [C: $i] :
( ( ( plus @ A @ C )
= B )
& ( int_less @ int_zero @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_inverse) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( ( int_less @ A @ B )
=> ? [C: $i] :
( ( ( plus @ A @ C )
= B )
& ( int_less @ int_zero @ C ) ) )
& ( ? [C: $i] :
( ( ( plus @ A @ C )
= B )
& ( int_less @ int_zero @ C ) )
=> ( int_less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: $i] :
( ( int_less @ int_zero @ A )
<=> ( int_leq @ int_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_successor_of_zero) ).
thf(58,plain,
! [A: $i] :
( ( ( int_less @ int_zero @ A )
=> ( int_leq @ int_one @ A ) )
& ( ( int_leq @ int_one @ A )
=> ( int_less @ int_zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( int_leq @ int_one @ A )
& ( int_leq @ A @ n )
& ( int_leq @ int_one @ B )
& ( int_leq @ B @ n )
& ( A != B ) )
=> ( ( a @ A @ B )
= real_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( int_leq @ int_one @ A )
& ( int_leq @ A @ n )
& ( int_leq @ int_one @ B )
& ( int_leq @ B @ n )
& ( A != B ) )
=> ( ( a @ A @ B )
= real_zero ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [A: $i,B: $i] :
( ( ( int_leq @ int_one @ A )
& ( int_leq @ A @ n )
& ( int_leq @ int_one @ B )
& ( int_leq @ B @ n )
& ( A != B ) )
=> ( ( a @ A @ B )
= real_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_commutative) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( int_leq @ A @ B )
<=> ( ( int_less @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( ( int_leq @ A @ B )
=> ( ( int_less @ A @ B )
| ( A = B ) ) )
& ( ( ( int_less @ A @ B )
| ( A = B ) )
=> ( int_leq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( int_less @ A @ B )
& ( int_leq @ C @ D ) )
=> ( int_leq @ ( plus @ A @ C ) @ ( plus @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_order1) ).
thf(48,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( int_less @ A @ B )
& ( int_leq @ C @ D ) )
=> ( int_leq @ ( plus @ A @ C ) @ ( plus @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).
thf(63,plain,
real_zero != real_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(57570,plain,
$false,
inference(cvc4,[status(thm)],[33,41,45,39,66,35,50,58,15,42,24,48,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV489+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 02:41:59 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.84/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (121ms).
% 1.21/0.97 % [INFO] Running in sequential loop mode.
% 1.51/1.16 % [INFO] eprover registered as external prover.
% 1.51/1.16 % [INFO] cvc4 registered as external prover.
% 1.51/1.17 % [INFO] Scanning for conjecture ...
% 1.76/1.23 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.86/1.25 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 1.86/1.28 % [INFO] Problem is first-order (TPTP FOF).
% 1.86/1.28 % [INFO] Type checking passed.
% 1.86/1.28 % [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 ...
% 96.79/17.10 % External prover 'cvc4' found a proof!
% 96.79/17.10 % [INFO] Killing All external provers ...
% 96.79/17.10 % Time passed: 16582ms (effective reasoning time: 16126ms)
% 96.79/17.10 % 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)>
% 96.79/17.10 % Axioms used in derivation (12): plus_and_order1, qii, int_less_total, int_leq, int_less_transitive, int_zero_one, plus_and_inverse, int_less_irreflexive, plus_commutative, real_constants, plus_zero, one_successor_of_zero
% 96.79/17.10 % No. of inferences in proof: 28
% 96.79/17.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16582 ms resp. 16126 ms w/o parsing
% 96.79/17.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 96.79/17.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------