TSTP Solution File: GRP190-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP190-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 11:13:27 EDT 2023
% Result : Unsatisfiable 3.39s 1.83s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 24
% Syntax : Number of formulae : 42 ( 35 unt; 7 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 194 ( 2 ~; 0 |; 0 &; 192 @)
% ( 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 : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(least_upper_bound_type,type,
least_upper_bound: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(greatest_lower_bound_type,type,
greatest_lower_bound: $i > $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(identity_type,type,
identity: $i ).
thf(6,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(29,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(41,plain,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
thf(49,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)],[16]) ).
thf(11,axiom,
( ( least_upper_bound @ a @ b )
= a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p39a_1) ).
thf(39,plain,
( ( least_upper_bound @ a @ b )
= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(35,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( least_upper_bound @ ( inverse @ a ) @ ( inverse @ b ) )
!= ( inverse @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p39a) ).
thf(18,plain,
( ( least_upper_bound @ ( inverse @ a ) @ ( inverse @ b ) )
!= ( inverse @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(31,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)],[7]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
thf(23,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)],[3]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
thf(51,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)],[17]) ).
thf(15,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/sandbox/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)],[15]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
thf(25,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)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(21,plain,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
thf(33,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)],[8]) ).
thf(61,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,49,39,35,18,31,43,23,51,47,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP190-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n005.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 : Fri May 19 01:42:39 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.93/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.39/1.05 % [INFO] Parsing done (133ms).
% 1.39/1.06 % [INFO] Running in sequential loop mode.
% 1.75/1.26 % [INFO] eprover registered as external prover.
% 1.75/1.26 % [INFO] cvc4 registered as external prover.
% 1.75/1.27 % [INFO] Scanning for conjecture ...
% 1.85/1.32 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 2.00/1.35 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.09/1.37 % [INFO] Problem is propositional (TPTP CNF).
% 2.09/1.37 % [INFO] Type checking passed.
% 2.09/1.38 % [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 ...
% 3.39/1.82 % External prover 'e' found a proof!
% 3.39/1.82 % [INFO] Killing All external provers ...
% 3.39/1.82 % Time passed: 1272ms (effective reasoning time: 760ms)
% 3.39/1.82 % 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)>
% 3.39/1.83 % Axioms used in derivation (16): associativity, monotony_lub1, idempotence_of_lub, monotony_glb1, left_inverse, symmetry_of_glb, monotony_glb2, glb_absorbtion, idempotence_of_gld, associativity_of_glb, p39a_1, symmetry_of_lub, monotony_lub2, left_identity, associativity_of_lub, lub_absorbtion
% 3.39/1.83 % No. of inferences in proof: 35
% 3.39/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1272 ms resp. 760 ms w/o parsing
% 3.48/1.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.48/1.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------