TSTP Solution File: GRP183-4 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP183-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 11:13:26 EDT 2023
% Result : Unsatisfiable 14.86s 3.45s
% Output : Refutation 14.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 25
% Syntax : Number of formulae : 45 ( 39 unt; 6 typ; 0 def)
% Number of atoms : 39 ( 38 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 214 ( 2 ~; 0 |; 0 &; 212 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 0 ^; 72 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(greatest_lower_bound_type,type,
greatest_lower_bound: $i > $i > $i ).
thf(least_upper_bound_type,type,
least_upper_bound: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(identity_type,type,
identity: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(7,axiom,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(33,plain,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( least_upper_bound @ B @ C ) )
= ( least_upper_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( least_upper_bound @ B @ C ) )
= ( least_upper_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20x_2) ).
thf(45,plain,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
( ( inverse @ identity )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20x_1) ).
thf(39,plain,
( ( inverse @ identity )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( greatest_lower_bound @ A @ B ) @ C )
= ( greatest_lower_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( greatest_lower_bound @ A @ B ) @ C )
= ( greatest_lower_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( greatest_lower_bound @ B @ C ) )
= ( greatest_lower_bound @ ( greatest_lower_bound @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( greatest_lower_bound @ B @ C ) )
= ( greatest_lower_bound @ ( greatest_lower_bound @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(51,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( least_upper_bound @ A @ ( least_upper_bound @ B @ C ) )
= ( least_upper_bound @ ( least_upper_bound @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( least_upper_bound @ A @ ( least_upper_bound @ B @ C ) )
= ( least_upper_bound @ ( least_upper_bound @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( inverse @ ( multiply @ A @ B ) )
= ( multiply @ ( inverse @ B ) @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20x_3) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( inverse @ ( multiply @ A @ B ) )
= ( multiply @ ( inverse @ B ) @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(25,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( greatest_lower_bound @ ( least_upper_bound @ a @ identity ) @ ( least_upper_bound @ ( inverse @ a ) @ identity ) )
!= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_20x) ).
thf(20,plain,
( ( greatest_lower_bound @ ( least_upper_bound @ a @ identity ) @ ( least_upper_bound @ ( inverse @ a ) @ identity ) )
!= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( least_upper_bound @ A @ B ) @ C )
= ( least_upper_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( least_upper_bound @ A @ B ) @ C )
= ( least_upper_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(29,plain,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( greatest_lower_bound @ B @ C ) )
= ( greatest_lower_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( greatest_lower_bound @ B @ C ) )
= ( greatest_lower_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3657,plain,
$false,
inference(e,[status(thm)],[33,53,41,45,27,49,39,35,31,43,51,47,37,25,20,57,29,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP183-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % 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 : Fri May 19 02:17:45 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (119ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.55/1.15 % [INFO] eprover registered as external prover.
% 1.55/1.15 % [INFO] cvc4 registered as external prover.
% 1.55/1.16 % [INFO] Scanning for conjecture ...
% 1.79/1.20 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.95/1.24 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.95/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 1.95/1.26 % [INFO] Type checking passed.
% 1.95/1.26 % [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 ...
% 14.86/3.44 % External prover 'e' found a proof!
% 14.86/3.44 % [INFO] Killing All external provers ...
% 14.86/3.45 % Time passed: 2928ms (effective reasoning time: 2473ms)
% 14.86/3.45 % 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)>
% 14.86/3.45 % Axioms used in derivation (18): monotony_lub1, idempotence_of_lub, monotony_glb1, p20x_3, left_inverse, symmetry_of_glb, monotony_glb2, glb_absorbtion, idempotence_of_gld, associativity_of_glb, p20x_2, associativity, monotony_lub2, left_identity, associativity_of_lub, lub_absorbtion, p20x_1, symmetry_of_lub
% 14.86/3.45 % No. of inferences in proof: 39
% 14.86/3.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2928 ms resp. 2473 ms w/o parsing
% 14.86/3.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.86/3.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------