TSTP Solution File: ROB021-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ROB021-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 11:49:57 EDT 2023
% Result : Unsatisfiable 2.77s 1.56s
% Output : Refutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 15 ( 9 unt; 4 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 76 ( 4 ~; 2 |; 0 &; 70 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(add_type,type,
add: $i > $i > $i ).
thf(negate_type,type,
negate: $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(1,negated_conjecture,
( ( add @ ( negate @ ( add @ a @ ( negate @ b ) ) ) @ ( negate @ ( add @ ( negate @ a ) @ ( negate @ b ) ) ) )
!= b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).
thf(6,plain,
( ( add @ ( negate @ ( add @ a @ ( negate @ b ) ) ) @ ( negate @ ( add @ ( negate @ a ) @ ( negate @ b ) ) ) )
!= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( negate @ ( add @ ( negate @ ( add @ A @ B ) ) @ ( negate @ ( add @ A @ ( negate @ B ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',robbins_axiom) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( negate @ ( add @ ( negate @ ( add @ A @ B ) ) @ ( negate @ ( add @ A @ ( negate @ B ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( add @ ( add @ A @ B ) @ C )
= ( add @ A @ ( add @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_add) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( add @ ( add @ A @ B ) @ C )
= ( add @ A @ ( add @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( ( negate @ A )
!= ( negate @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',negative_equality_implies_positive_equality) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( ( negate @ A )
!= ( negate @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[6,9,13,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ROB021-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n001.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
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 00:15:21 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.83/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.94 % [INFO] Parsing done (108ms).
% 1.19/0.95 % [INFO] Running in sequential loop mode.
% 1.50/1.14 % [INFO] eprover registered as external prover.
% 1.50/1.14 % [INFO] cvc4 registered as external prover.
% 1.50/1.15 % [INFO] Scanning for conjecture ...
% 1.71/1.19 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.80/1.21 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.80/1.21 % [INFO] Problem is propositional (TPTP CNF).
% 1.80/1.22 % [INFO] Type checking passed.
% 1.80/1.22 % [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 ...
% 2.77/1.55 % External prover 'e' found a proof!
% 2.77/1.55 % [INFO] Killing All external provers ...
% 2.77/1.55 % Time passed: 1042ms (effective reasoning time: 604ms)
% 2.77/1.55 % 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)>
% 2.77/1.55 % Axioms used in derivation (4): commutativity_of_add, robbins_axiom, associativity_of_add, negative_equality_implies_positive_equality
% 2.77/1.55 % No. of inferences in proof: 11
% 2.77/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1042 ms resp. 604 ms w/o parsing
% 3.04/1.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.04/1.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------