TSTP Solution File: KLE151-10 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE151-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 11:25:11 EDT 2023
% Result : Unsatisfiable 3.28s 1.74s
% Output : Refutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 36
% Syntax : Number of formulae : 60 ( 47 unt; 13 typ; 0 def)
% Number of atoms : 47 ( 46 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 322 ( 2 ~; 0 |; 0 &; 320 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 90 ( 0 ^; 90 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_type,type,
leq: $i > $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(sK2_goals_X0_type,type,
sK2_goals_X0: $i ).
thf(strong_iteration_type,type,
strong_iteration: $i > $i ).
thf(sK1_goals_X1_type,type,
sK1_goals_X1: $i ).
thf(true_type,type,
true: $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(ifeq2_type,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(ifeq3_type,type,
ifeq3: $i > $i > $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(star_type,type,
star: $i > $i ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B ) @ true @ ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction1) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B ) @ true @ ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A ) @ true @ ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction2) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A ) @ true @ ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( leq @ A @ ( addition @ ( multiplication @ B @ A ) @ C ) ) @ true @ ( leq @ A @ ( multiplication @ ( strong_iteration @ B ) @ C ) ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( leq @ A @ ( addition @ ( multiplication @ B @ A ) @ C ) ) @ true @ ( leq @ A @ ( multiplication @ ( strong_iteration @ B ) @ C ) ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( ifeq3 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ifeq3 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).
thf(49,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(35,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
thf(63,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(43,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(55,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
thf(51,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(47,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
( ( leq @ ( multiplication @ sK2_goals_X0 @ ( strong_iteration @ ( multiplication @ sK1_goals_X1 @ sK2_goals_X0 ) ) ) @ ( multiplication @ ( strong_iteration @ ( multiplication @ sK2_goals_X0 @ sK1_goals_X1 ) ) @ sK2_goals_X0 ) )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(24,plain,
( ( leq @ ( multiplication @ sK2_goals_X0 @ ( strong_iteration @ ( multiplication @ sK1_goals_X1 @ sK2_goals_X0 ) ) ) @ ( multiplication @ ( strong_iteration @ ( multiplication @ sK2_goals_X0 @ sK1_goals_X1 ) ) @ sK2_goals_X0 ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
thf(37,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).
thf(57,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( ifeq2 @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order_1) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ifeq2 @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(75,plain,
$false,
inference(cvc4,[status(thm)],[69,61,33,65,53,41,45,49,39,35,63,43,55,51,47,24,37,57,29,59,27,67,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : KLE151-10 : TPTP v8.1.2. Released v7.3.0.
% 0.09/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 03:09:19 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.88/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.94 % [INFO] Parsing done (121ms).
% 1.23/0.95 % [INFO] Running in sequential loop mode.
% 1.53/1.14 % [INFO] eprover registered as external prover.
% 1.53/1.14 % [INFO] cvc4 registered as external prover.
% 1.53/1.15 % [INFO] Scanning for conjecture ...
% 1.77/1.21 % [INFO] Found a conjecture and 22 axioms. Running axiom selection ...
% 1.88/1.24 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 1.88/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.88/1.27 % [INFO] Type checking passed.
% 1.88/1.27 % [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 ...
% 3.28/1.73 % External prover 'cvc4' found a proof!
% 3.28/1.73 % [INFO] Killing All external provers ...
% 3.28/1.73 % Time passed: 1231ms (effective reasoning time: 780ms)
% 3.28/1.73 % 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)>
% 3.28/1.74 % Axioms used in derivation (22): additive_identity, ifeq_axiom_001, ifeq_axiom, isolation, additive_associativity, multiplicative_right_identity, star_unfold2, order_1, multiplicative_left_identity, idempotence, ifeq_axiom_002, multiplicative_associativity, infty_unfold1, star_induction2, distributivity2, star_induction1, star_unfold1, left_annihilation, infty_coinduction, order, additive_commutativity, distributivity1
% 3.28/1.74 % No. of inferences in proof: 47
% 3.28/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1231 ms resp. 780 ms w/o parsing
% 3.28/1.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.28/1.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------