TSTP Solution File: ROB004-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ROB004-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 11:49:55 EDT 2023
% Result : Unsatisfiable 2.52s 1.68s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 21 ( 15 unt; 6 typ; 0 def)
% Number of atoms : 15 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 78 ( 2 ~; 0 |; 0 &; 76 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% 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(d_type,type,
d: $i ).
thf(c_type,type,
c: $i ).
thf(7,axiom,
( ( add @ c @ c )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_plus_c_is_c) ).
thf(21,plain,
( ( add @ c @ c )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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(13,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,
( ( negate @ d )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',negate_d_is_c) ).
thf(17,plain,
( ( negate @ d )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(8,plain,
( ( add @ ( negate @ ( add @ a @ ( negate @ b ) ) ) @ ( negate @ ( add @ ( negate @ a ) @ ( negate @ b ) ) ) )
!= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
( ( add @ c @ d )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_plus_d_is_d) ).
thf(19,plain,
( ( add @ c @ d )
= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
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(15,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(29,plain,
$false,
inference(e,[status(thm)],[21,13,17,11,8,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ROB004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n029.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 19 00:00:14 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.95/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.04/1.00 % [INFO] Parsing done (118ms).
% 1.29/1.01 % [INFO] Running in sequential loop mode.
% 1.69/1.23 % [INFO] eprover registered as external prover.
% 1.69/1.23 % [INFO] cvc4 registered as external prover.
% 1.69/1.24 % [INFO] Scanning for conjecture ...
% 1.69/1.29 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.69/1.31 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.69/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 1.69/1.32 % [INFO] Type checking passed.
% 1.69/1.32 % [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 ...
% 2.52/1.67 % External prover 'e' found a proof!
% 2.52/1.67 % [INFO] Killing All external provers ...
% 2.52/1.67 % Time passed: 1156ms (effective reasoning time: 666ms)
% 2.52/1.67 % 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)>
% 2.52/1.68 % Axioms used in derivation (6): c_plus_c_is_c, c_plus_d_is_d, negate_d_is_c, robbins_axiom, associativity_of_add, commutativity_of_add
% 2.52/1.68 % No. of inferences in proof: 15
% 2.52/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1156 ms resp. 666 ms w/o parsing
% 2.78/1.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.78/1.70 % [INFO] Killing All external provers ...
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