TSTP Solution File: GRP136-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP136-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 11:13:18 EDT 2023
% Result : Unsatisfiable 2.73s 1.58s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 38 ( 33 unt; 5 typ; 0 def)
% Number of atoms : 33 ( 32 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 178 ( 2 ~; 0 |; 0 &; 176 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
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(least_upper_bound_type,type,
least_upper_bound: $i > $i > $i ).
thf(16,axiom,
( ( least_upper_bound @ a @ b )
= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_antisyma_2) ).
thf(48,plain,
( ( least_upper_bound @ a @ b )
= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,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(42,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)],[13]) ).
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/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(20,plain,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
( ( least_upper_bound @ a @ b )
= b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_antisyma_1) ).
thf(46,plain,
( ( least_upper_bound @ a @ b )
= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,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(28,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)],[6]) ).
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(38,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(1,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ax_antisyma) ).
thf(17,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,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(32,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(34,plain,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
thf(22,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(14,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(44,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)],[14]) ).
thf(12,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(40,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)],[12]) ).
thf(5,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(26,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(10,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(36,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,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(30,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)],[7]) ).
thf(50,plain,
$false,
inference(e,[status(thm)],[48,42,24,20,46,28,38,17,32,34,22,44,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : GRP136-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.04/0.14 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n016.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri May 19 02:38:58 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.94/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.95 % [INFO] Parsing done (118ms).
% 1.22/0.95 % [INFO] Running in sequential loop mode.
% 1.65/1.16 % [INFO] eprover registered as external prover.
% 1.65/1.16 % [INFO] cvc4 registered as external prover.
% 1.65/1.16 % [INFO] Scanning for conjecture ...
% 1.73/1.21 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 1.87/1.24 % [INFO] Axiom selection finished. Selected 15 axioms (removed 2 axioms).
% 1.99/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.99/1.26 % [INFO] Type checking passed.
% 1.99/1.27 % [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 ...
% 2.73/1.58 % External prover 'e' found a proof!
% 2.73/1.58 % [INFO] Killing All external provers ...
% 2.73/1.58 % Time passed: 1072ms (effective reasoning time: 622ms)
% 2.73/1.58 % 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)>
% 2.73/1.58 % Axioms used in derivation (15): associativity, monotony_lub1, monotony_lub2, idempotence_of_lub, ax_antisyma_2, monotony_glb1, ax_antisyma_1, symmetry_of_glb, monotony_glb2, glb_absorbtion, idempotence_of_gld, associativity_of_glb, symmetry_of_lub, associativity_of_lub, lub_absorbtion
% 2.73/1.58 % No. of inferences in proof: 33
% 2.73/1.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1072 ms resp. 622 ms w/o parsing
% 2.73/1.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.73/1.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------