TSTP Solution File: KLE106+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE106+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 11:25:04 EDT 2023
% Result : Theorem 56.78s 9.39s
% Output : Refutation 56.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 42
% Syntax : Number of formulae : 71 ( 51 unt; 15 typ; 0 def)
% Number of atoms : 63 ( 59 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 344 ( 3 ~; 1 |; 1 &; 334 @)
% ( 1 <=>; 2 =>; 2 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 0 ^; 95 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(addition_type,type,
addition: $i > $i > $i ).
thf(forward_diamond_type,type,
forward_diamond: $i > $i > $i ).
thf(domain_type,type,
domain: $i > $i ).
thf(backward_box_type,type,
backward_box: $i > $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(codomain_type,type,
codomain: $i > $i ).
thf(coantidomain_type,type,
coantidomain: $i > $i ).
thf(antidomain_type,type,
antidomain: $i > $i ).
thf(one_type,type,
one: $i ).
thf(backward_diamond_type,type,
backward_diamond: $i > $i > $i ).
thf(forward_box_type,type,
forward_box: $i > $i > $i ).
thf(c_type,type,
c: $i > $i ).
thf(domain_difference_type,type,
domain_difference: $i > $i > $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( addition @ ( coantidomain @ ( multiplication @ A @ B ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain2) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( addition @ ( coantidomain @ ( multiplication @ A @ B ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
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(37,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(9,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(52,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(27,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(106,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)],[27]) ).
thf(12,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(61,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( domain_difference @ A @ B )
= ( multiplication @ ( domain @ A ) @ ( antidomain @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_difference) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( domain_difference @ A @ B )
= ( multiplication @ ( domain @ A ) @ ( antidomain @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
! [A: $i] :
( ( addition @ ( antidomain @ ( antidomain @ A ) ) @ ( antidomain @ A ) )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
thf(70,plain,
! [A: $i] :
( ( addition @ ( antidomain @ ( antidomain @ A ) ) @ ( antidomain @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [A: $i] :
( ( c @ A )
= ( antidomain @ ( domain @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
thf(97,plain,
! [A: $i] :
( ( c @ A )
= ( antidomain @ ( domain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(109,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)],[28]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( addition @ ( antidomain @ ( multiplication @ A @ B ) ) @ ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) )
= ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( addition @ ( antidomain @ ( multiplication @ A @ B ) ) @ ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) )
= ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(49,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,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(76,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)],[17]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( forward_diamond @ A @ B )
= ( domain @ ( multiplication @ A @ ( domain @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_diamond) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( forward_diamond @ A @ B )
= ( domain @ ( multiplication @ A @ ( domain @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [A: $i] :
( ( codomain @ A )
= ( coantidomain @ ( coantidomain @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain4) ).
thf(43,plain,
! [A: $i] :
( ( codomain @ A )
= ( coantidomain @ ( coantidomain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(100,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
thf(46,plain,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( addition @ ( forward_diamond @ A @ ( domain @ B ) ) @ ( domain @ C ) )
= ( domain @ C ) )
<= ( ( addition @ ( domain @ B ) @ ( backward_box @ A @ ( domain @ C ) ) )
= ( backward_box @ A @ ( domain @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( addition @ ( forward_diamond @ A @ ( domain @ B ) ) @ ( domain @ C ) )
= ( domain @ C ) )
<= ( ( addition @ ( domain @ B ) @ ( backward_box @ A @ ( domain @ C ) ) )
= ( backward_box @ A @ ( domain @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( addition @ ( forward_diamond @ A @ ( domain @ B ) ) @ ( domain @ C ) )
= ( domain @ C ) )
| ( ( addition @ ( domain @ B ) @ ( backward_box @ A @ ( domain @ C ) ) )
!= ( backward_box @ A @ ( domain @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(34,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( forward_box @ A @ B )
= ( c @ ( forward_diamond @ A @ ( c @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_box) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( forward_box @ A @ B )
= ( c @ ( forward_diamond @ A @ ( c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( backward_box @ A @ B )
= ( c @ ( backward_diamond @ A @ ( c @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',backward_box) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( backward_box @ A @ B )
= ( c @ ( backward_diamond @ A @ ( c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(40,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).
thf(55,plain,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( backward_diamond @ A @ B )
= ( codomain @ ( multiplication @ ( codomain @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',backward_diamond) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( backward_diamond @ A @ B )
= ( codomain @ ( multiplication @ ( codomain @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ A ) ) @ ( coantidomain @ A ) )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain3) ).
thf(82,plain,
! [A: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ A ) ) @ ( coantidomain @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(18,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(79,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)],[18]) ).
thf(23,axiom,
! [A: $i] :
( ( domain @ A )
= ( antidomain @ ( antidomain @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
thf(94,plain,
! [A: $i] :
( ( domain @ A )
= ( antidomain @ ( antidomain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25443,plain,
$false,
inference(e,[status(thm)],[88,37,52,106,61,85,70,97,109,73,49,76,67,43,100,46,29,34,64,103,91,40,55,58,82,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE106+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n021.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 : Fri May 19 02:55:13 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.94/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.03 % [INFO] Parsing done (139ms).
% 1.26/1.04 % [INFO] Running in sequential loop mode.
% 1.84/1.24 % [INFO] eprover registered as external prover.
% 1.84/1.24 % [INFO] cvc4 registered as external prover.
% 1.84/1.24 % [INFO] Scanning for conjecture ...
% 1.94/1.30 % [INFO] Found a conjecture and 26 axioms. Running axiom selection ...
% 2.16/1.34 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 2.16/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.32/1.37 % [INFO] Type checking passed.
% 2.32/1.37 % [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 ...
% 56.78/9.39 % External prover 'e' found a proof!
% 56.78/9.39 % [INFO] Killing All external provers ...
% 56.78/9.39 % Time passed: 8856ms (effective reasoning time: 8348ms)
% 56.78/9.39 % 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)>
% 56.78/9.39 % Axioms used in derivation (26): forward_box, additive_identity, domain4, backward_box, domain3, multiplicative_right_identity, codomain2, complement, right_annihilation, domain1, backward_diamond, forward_diamond, codomain4, left_annihilation, codomain1, additive_idempotence, additive_associativity, right_distributivity, domain2, order, additive_commutativity, domain_difference, multiplicative_left_identity, codomain3, multiplicative_associativity, left_distributivity
% 56.78/9.39 % No. of inferences in proof: 56
% 56.78/9.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8856 ms resp. 8348 ms w/o parsing
% 56.78/9.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 56.78/9.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------