TSTP Solution File: HAL002+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 11:16:45 EDT 2023
% Result : Theorem 4.34s 1.99s
% Output : Refutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 30
% Syntax : Number of formulae : 49 ( 3 unt; 13 typ; 0 def)
% Number of atoms : 171 ( 44 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 583 ( 2 ~; 0 |; 75 &; 446 @)
% ( 4 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 156 ( 0 ^; 146 !; 10 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(injection_type,type,
injection: $i > $o ).
thf(x_type,type,
x: $i ).
thf(injection_2_type,type,
injection_2: $i > $o ).
thf(morphism_type,type,
morphism: $i > $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(commute_type,type,
commute: $i > $i > $i > $i > $o ).
thf(surjection_type,type,
surjection: $i > $o ).
thf(subtract_type,type,
subtract: $i > $i > $i > $i ).
thf(zero_type,type,
zero: $i > $i ).
thf(exact_type,type,
exact: $i > $i > $o ).
thf(any1_type,type,
any1: $i ).
thf(any2_type,type,
any2: $i ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( morphism @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ C )
=> ? [E: $i] :
( ( element @ E @ B )
& ( ( apply @ A @ E )
= D ) ) ) )
=> ( surjection @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',properties_for_surjection) ).
thf(29,plain,
! [A: $i,B: $i,C: $i] :
( ( ( morphism @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ C )
=> ? [E: $i] :
( ( element @ E @ B )
& ( ( apply @ A @ E )
= D ) ) ) )
=> ( surjection @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( injection_2 @ A )
& ( morphism @ A @ B @ C ) )
=> ! [D: $i] :
( ( ( element @ D @ B )
& ( ( apply @ A @ D )
= ( zero @ C ) ) )
=> ( D
= ( zero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injection_properties_2) ).
thf(89,plain,
! [A: $i,B: $i,C: $i] :
( ( ( injection_2 @ A )
& ( morphism @ A @ B @ C ) )
=> ! [D: $i] :
( ( ( element @ D @ B )
& ( ( apply @ A @ D )
= ( zero @ C ) ) )
=> ( D
= ( zero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( surjection @ A )
& ( morphism @ A @ B @ C ) )
=> ! [D: $i] :
( ( element @ D @ C )
=> ? [E: $i] :
( ( element @ E @ B )
& ( ( apply @ A @ E )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjection_properties) ).
thf(60,plain,
! [A: $i,B: $i,C: $i] :
( ( ( surjection @ A )
& ( morphism @ A @ B @ C ) )
=> ! [D: $i] :
( ( element @ D @ C )
=> ? [E: $i] :
( ( element @ E @ B )
& ( ( apply @ A @ E )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( morphism @ A @ B @ C )
& ! [D: $i,E: $i] :
( ( ( element @ D @ B )
& ( element @ E @ B )
& ( ( apply @ A @ D )
= ( apply @ A @ E ) ) )
=> ( D = E ) ) )
=> ( injection @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',properties_for_injection) ).
thf(92,plain,
! [A: $i,B: $i,C: $i] :
( ( ( morphism @ A @ B @ C )
& ! [D: $i,E: $i] :
( ( ( element @ D @ B )
& ( element @ E @ B )
& ( ( apply @ A @ D )
= ( apply @ A @ E ) ) )
=> ( D = E ) ) )
=> ( injection @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( morphism @ A @ B @ C )
=> ( ! [D: $i] :
( ( element @ D @ B )
=> ( element @ ( apply @ A @ D ) @ C ) )
& ( ( apply @ A @ ( zero @ B ) )
= ( zero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',morphism) ).
thf(41,plain,
! [A: $i,B: $i,C: $i] :
( ( morphism @ A @ B @ C )
=> ( ! [D: $i] :
( ( element @ D @ B )
=> ( element @ ( apply @ A @ D ) @ C ) )
& ( ( apply @ A @ ( zero @ B ) )
= ( zero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( morphism @ A @ C @ D )
& ( morphism @ B @ D @ E )
& ! [F: $i] :
( ( ( element @ F @ D )
& ( ( apply @ B @ F )
= ( zero @ E ) ) )
<=> ? [G: $i] :
( ( element @ G @ C )
& ( ( apply @ A @ G )
= F ) ) ) )
=> ( exact @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',properties_for_exact) ).
thf(48,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( morphism @ A @ C @ D )
& ( morphism @ B @ D @ E )
& ! [F: $i] :
( ( ( ( element @ F @ D )
& ( ( apply @ B @ F )
= ( zero @ E ) ) )
=> ? [G: $i] :
( ( element @ G @ C )
& ( ( apply @ A @ G )
= F ) ) )
& ( ? [G: $i] :
( ( element @ G @ C )
& ( ( apply @ A @ G )
= F ) )
=> ( ( element @ F @ D )
& ( ( apply @ B @ F )
= ( zero @ E ) ) ) ) ) )
=> ( exact @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( morphism @ A @ B @ C )
& ! [D: $i] :
( ( ( element @ D @ B )
& ( ( apply @ A @ D )
= ( zero @ C ) ) )
=> ( D
= ( zero @ B ) ) ) )
=> ( injection_2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',properties_for_injection_2) ).
thf(82,plain,
! [A: $i,B: $i,C: $i] :
( ( ( morphism @ A @ B @ C )
& ! [D: $i] :
( ( ( element @ D @ B )
& ( ( apply @ A @ D )
= ( zero @ C ) ) )
=> ( D
= ( zero @ B ) ) ) )
=> ( injection_2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
( ( injection @ x )
<=> ( injection_2 @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',my) ).
thf(2,negated_conjecture,
~ ( ( injection @ x )
<=> ( injection_2 @ x ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ( ( ( injection @ x )
=> ( injection_2 @ x ) )
& ( ( injection_2 @ x )
=> ( injection @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ A )
& ( element @ C @ A ) )
=> ( element @ ( subtract @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subtract_in_domain) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ A )
& ( element @ C @ A ) )
=> ( element @ ( subtract @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( injection @ A )
& ( morphism @ A @ B @ C ) )
=> ! [D: $i,E: $i] :
( ( ( element @ D @ B )
& ( element @ E @ B )
& ( ( apply @ A @ D )
= ( apply @ A @ E ) ) )
=> ( D = E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injection_properties) ).
thf(100,plain,
! [A: $i,B: $i,C: $i] :
( ( ( injection @ A )
& ( morphism @ A @ B @ C ) )
=> ! [D: $i,E: $i] :
( ( ( element @ D @ B )
& ( element @ E @ B )
& ( ( apply @ A @ D )
= ( apply @ A @ E ) ) )
=> ( D = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( morphism @ A @ E @ F )
& ( morphism @ B @ F @ H )
& ( morphism @ C @ E @ G )
& ( morphism @ D @ G @ H )
& ! [I: $i] :
( ( element @ I @ E )
=> ( ( apply @ B @ ( apply @ A @ I ) )
= ( apply @ D @ ( apply @ C @ I ) ) ) ) )
=> ( commute @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',properties_for_commute) ).
thf(24,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( morphism @ A @ E @ F )
& ( morphism @ B @ F @ H )
& ( morphism @ C @ E @ G )
& ( morphism @ D @ G @ H )
& ! [I: $i] :
( ( element @ I @ E )
=> ( ( apply @ B @ ( apply @ A @ I ) )
= ( apply @ D @ ( apply @ C @ I ) ) ) ) )
=> ( commute @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( commute @ A @ B @ C @ D )
& ( morphism @ A @ E @ F )
& ( morphism @ B @ F @ H )
& ( morphism @ C @ E @ G )
& ( morphism @ D @ G @ H ) )
=> ! [I: $i] :
( ( element @ I @ E )
=> ( ( apply @ B @ ( apply @ A @ I ) )
= ( apply @ D @ ( apply @ C @ I ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commute_properties) ).
thf(37,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( commute @ A @ B @ C @ D )
& ( morphism @ A @ E @ F )
& ( morphism @ B @ F @ H )
& ( morphism @ C @ E @ G )
& ( morphism @ D @ G @ H ) )
=> ! [I: $i] :
( ( element @ I @ E )
=> ( ( apply @ B @ ( apply @ A @ I ) )
= ( apply @ D @ ( apply @ C @ I ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( subtract @ A @ B @ B )
= ( zero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subtract_to_0) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( subtract @ A @ B @ B )
= ( zero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( morphism @ A @ B @ C )
=> ! [D: $i,E: $i] :
( ( ( element @ D @ B )
& ( element @ E @ B ) )
=> ( ( apply @ A @ ( subtract @ B @ D @ E ) )
= ( subtract @ C @ ( apply @ A @ D ) @ ( apply @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subtract_distribution) ).
thf(45,plain,
! [A: $i,B: $i,C: $i] :
( ( morphism @ A @ B @ C )
=> ! [D: $i,E: $i] :
( ( ( element @ D @ B )
& ( element @ E @ B ) )
=> ( ( apply @ A @ ( subtract @ B @ D @ E ) )
= ( subtract @ C @ ( apply @ A @ D ) @ ( apply @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( exact @ A @ B )
& ( morphism @ A @ C @ D )
& ( morphism @ B @ D @ E ) )
=> ! [F: $i] :
( ( ( element @ F @ D )
& ( ( apply @ B @ F )
= ( zero @ E ) ) )
<=> ? [G: $i] :
( ( element @ G @ C )
& ( ( apply @ A @ G )
= F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exact_properties) ).
thf(64,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( exact @ A @ B )
& ( morphism @ A @ C @ D )
& ( morphism @ B @ D @ E ) )
=> ! [F: $i] :
( ( ( ( element @ F @ D )
& ( ( apply @ B @ F )
= ( zero @ E ) ) )
=> ? [G: $i] :
( ( element @ G @ C )
& ( ( apply @ A @ G )
= F ) ) )
& ( ? [G: $i] :
( ( element @ G @ C )
& ( ( apply @ A @ G )
= F ) )
=> ( ( element @ F @ D )
& ( ( apply @ B @ F )
= ( zero @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
morphism @ x @ any1 @ any2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_morphism) ).
thf(81,plain,
morphism @ x @ any1 @ any2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ A )
& ( element @ C @ A ) )
=> ( ( subtract @ A @ B @ ( subtract @ A @ B @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subtract_cancellation) ).
thf(76,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ A )
& ( element @ C @ A ) )
=> ( ( subtract @ A @ B @ ( subtract @ A @ B @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(104,plain,
$false,
inference(e,[status(thm)],[29,89,60,92,41,48,82,19,79,100,24,37,34,45,64,81,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 23:24:38 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.97 % [INFO] Parsing done (130ms).
% 1.21/0.98 % [INFO] Running in sequential loop mode.
% 1.80/1.18 % [INFO] eprover registered as external prover.
% 1.80/1.19 % [INFO] cvc4 registered as external prover.
% 1.80/1.19 % [INFO] Scanning for conjecture ...
% 1.92/1.24 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.92/1.28 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.16/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 2.16/1.35 % [INFO] Type checking passed.
% 2.16/1.35 % [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 ...
% 4.04/1.98 % External prover 'e' found a proof!
% 4.04/1.98 % [INFO] Killing All external provers ...
% 4.34/1.98 % Time passed: 1475ms (effective reasoning time: 1001ms)
% 4.34/1.98 % 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)>
% 4.34/1.99 % Axioms used in derivation (16): surjection_properties, subtract_cancellation, x_morphism, properties_for_injection, properties_for_commute, exact_properties, properties_for_surjection, morphism, properties_for_injection_2, subtract_in_domain, subtract_to_0, injection_properties, properties_for_exact, subtract_distribution, injection_properties_2, commute_properties
% 4.34/1.99 % No. of inferences in proof: 36
% 4.34/1.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1475 ms resp. 1001 ms w/o parsing
% 4.34/2.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.34/2.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------