TSTP Solution File: KLE070+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE070+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 11:24:59 EDT 2023
% Result : Theorem 3.32s 1.82s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 24
% Syntax : Number of formulae : 44 ( 36 unt; 6 typ; 0 def)
% Number of atoms : 42 ( 38 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 198 ( 2 ~; 0 |; 1 &; 192 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(addition_type,type,
addition: $i > $i > $i ).
thf(domain_type,type,
domain: $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(one_type,type,
one: $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(56,plain,
! [A: $i,B: $i,C: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
! [A: $i] :
( ( addition @ A @ ( multiplication @ ( domain @ A ) @ A ) )
= ( multiplication @ ( domain @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
thf(74,plain,
! [A: $i] :
( ( addition @ A @ ( multiplication @ ( domain @ A ) @ A ) )
= ( multiplication @ ( domain @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
( ( domain @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
thf(38,plain,
( ( domain @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(65,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(32,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(59,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( domain @ ( multiplication @ A @ B ) )
= ( domain @ ( multiplication @ A @ ( domain @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( domain @ ( multiplication @ A @ B ) )
= ( domain @ ( multiplication @ A @ ( domain @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( addition @ ( domain @ A ) @ ( multiplication @ ( domain @ A ) @ ( domain @ B ) ) )
= ( domain @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( addition @ ( domain @ A ) @ ( multiplication @ ( domain @ A ) @ ( domain @ B ) ) )
= ( domain @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ! [A: $i,B: $i] :
( ( addition @ ( domain @ A ) @ ( multiplication @ ( domain @ A ) @ ( domain @ B ) ) )
= ( domain @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] :
( ( addition @ ( domain @ A ) @ one )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
thf(46,plain,
! [A: $i] :
( ( addition @ ( domain @ A ) @ one )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
thf(29,plain,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( domain @ ( addition @ A @ B ) )
= ( addition @ ( domain @ A ) @ ( domain @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain5) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( domain @ ( addition @ A @ B ) )
= ( addition @ ( domain @ A ) @ ( domain @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
=> ( ( addition @ A @ B )
= B ) )
& ( ( ( addition @ A @ B )
= B )
=> ( leq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
thf(40,plain,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(26,plain,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(23,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(68,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(62,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(77,plain,
$false,
inference(e,[status(thm)],[56,74,38,65,32,59,35,43,20,46,29,71,49,40,26,23,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE070+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n024.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 19 03:05:07 EDT 2023
% 0.16/0.36 % CPUTime :
% 1.00/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.05 % [INFO] Parsing done (138ms).
% 1.26/1.06 % [INFO] Running in sequential loop mode.
% 1.73/1.27 % [INFO] eprover registered as external prover.
% 1.73/1.27 % [INFO] cvc4 registered as external prover.
% 1.73/1.28 % [INFO] Scanning for conjecture ...
% 1.99/1.33 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 1.99/1.37 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.21/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.21/1.39 % [INFO] Type checking passed.
% 2.21/1.40 % [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 ...
% 3.32/1.82 % External prover 'e' found a proof!
% 3.32/1.82 % [INFO] Killing All external provers ...
% 3.32/1.82 % Time passed: 1300ms (effective reasoning time: 763ms)
% 3.32/1.82 % 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)>
% 3.32/1.82 % Axioms used in derivation (17): additive_identity, domain4, domain5, domain3, left_annihilation, multiplicative_right_identity, right_annihilation, multiplicative_left_identity, domain1, additive_idempotence, additive_associativity, right_distributivity, domain2, order, additive_commutativity, multiplicative_associativity, left_distributivity
% 3.32/1.82 % No. of inferences in proof: 38
% 3.32/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1300 ms resp. 763 ms w/o parsing
% 3.41/1.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.41/1.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------