TSTP Solution File: ROB016-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ROB016-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 3.06s 1.70s
% Output : Refutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 32 ( 17 unt; 9 typ; 0 def)
% Number of atoms : 31 ( 18 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 166 ( 10 ~; 8 |; 0 &; 148 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(negate_type,type,
negate: $i > $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(e_type,type,
e: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(k_type,type,
k: $i ).
thf(d_type,type,
d: $i ).
thf(one_type,type,
one: $i ).
thf(positive_integer_type,type,
positive_integer: $i > $o ).
thf(successor_type,type,
successor: $i > $i ).
thf(9,axiom,
( ( negate @ ( add @ d @ e ) )
= ( negate @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
thf(29,plain,
( ( negate @ ( add @ d @ e ) )
= ( negate @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i] :
( ( multiply @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_times_x) ).
thf(21,plain,
! [A: $i] :
( ( multiply @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( positive_integer @ A )
| ( positive_integer @ ( successor @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',next_integer) ).
thf(27,plain,
! [A: $i] :
( ~ ( positive_integer @ A )
| ( positive_integer @ ( successor @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( negate @ ( add @ e @ ( multiply @ k @ ( add @ d @ ( negate @ ( add @ d @ ( negate @ e ) ) ) ) ) ) )
!= ( negate @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_result) ).
thf(12,plain,
( ( negate @ ( add @ e @ ( multiply @ k @ ( add @ d @ ( negate @ ( add @ d @ ( negate @ e ) ) ) ) ) ) )
!= ( negate @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
positive_integer @ k,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_positive) ).
thf(31,plain,
positive_integer @ k,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(19,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(2,axiom,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( negate @ ( add @ ( negate @ A ) @ ( negate @ ( add @ B @ ( negate @ A ) ) ) ) )
!= B )
| ~ ( positive_integer @ C )
| ( ( negate @ ( add @ A @ ( multiply @ C @ ( add @ B @ ( negate @ ( add @ B @ ( negate @ A ) ) ) ) ) ) )
= ( negate @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_6) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( ( negate @ ( add @ ( negate @ A ) @ ( negate @ ( add @ B @ ( negate @ A ) ) ) ) )
!= B )
| ~ ( positive_integer @ C )
| ( ( negate @ ( add @ A @ ( multiply @ C @ ( add @ B @ ( negate @ ( add @ B @ ( negate @ A ) ) ) ) ) ) )
= ( negate @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(17,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(7,axiom,
positive_integer @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one) ).
thf(26,plain,
positive_integer @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( positive_integer @ A )
| ( ( multiply @ ( successor @ B ) @ A )
= ( add @ A @ ( multiply @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_by_adding) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( positive_integer @ A )
| ( ( multiply @ ( successor @ B ) @ A )
= ( add @ A @ ( multiply @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(52,plain,
$false,
inference(e,[status(thm)],[29,21,27,12,31,19,15,32,17,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ROB016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n019.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 : Thu May 18 23:46:58 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.03 % [INFO] Parsing done (129ms).
% 1.22/1.04 % [INFO] Running in sequential loop mode.
% 1.73/1.23 % [INFO] eprover registered as external prover.
% 1.73/1.23 % [INFO] cvc4 registered as external prover.
% 1.73/1.24 % [INFO] Scanning for conjecture ...
% 1.85/1.28 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.85/1.30 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.85/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 1.85/1.32 % [INFO] Type checking passed.
% 1.85/1.32 % [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 ...
% 3.06/1.70 % External prover 'e' found a proof!
% 3.06/1.70 % [INFO] Killing All external provers ...
% 3.06/1.70 % Time passed: 1155ms (effective reasoning time: 661ms)
% 3.06/1.70 % 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)>
% 3.06/1.70 % Axioms used in derivation (10): k_positive, one_times_x, next_integer, times_by_adding, condition, one, robbins_axiom, lemma_3_6, associativity_of_add, commutativity_of_add
% 3.06/1.70 % No. of inferences in proof: 23
% 3.06/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1155 ms resp. 661 ms w/o parsing
% 3.28/1.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.28/1.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------