TSTP Solution File: KLE044+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE044+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 11:24:56 EDT 2023
% Result : Theorem 77.12s 19.08s
% Output : Refutation 77.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of formulae : 42 ( 27 unt; 6 typ; 0 def)
% Number of atoms : 47 ( 25 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 241 ( 2 ~; 0 |; 4 &; 228 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 63 ( 0 ^; 63 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_type,type,
leq: $i > $i > $o ).
thf(star_type,type,
star: $i > $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B )
=> ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_left) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B )
=> ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(60,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)],[17]) ).
thf(11,axiom,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_left) ).
thf(45,plain,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(22,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(39,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)],[9]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(63,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)],[18]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
=> ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_right) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
=> ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).
thf(47,plain,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(42,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(25,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(5,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(28,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(33,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)],[7]) ).
thf(15,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(54,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(49,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(36,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i] :
( ( leq @ ( star @ ( addition @ one @ A ) ) @ ( star @ A ) )
& ( leq @ ( star @ A ) @ ( star @ ( addition @ one @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( leq @ ( star @ ( addition @ one @ A ) ) @ ( star @ A ) )
& ( leq @ ( star @ A ) @ ( star @ ( addition @ one @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i] :
( ( leq @ ( star @ ( addition @ one @ A ) ) @ ( star @ A ) )
& ( leq @ ( star @ A ) @ ( star @ ( addition @ one @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(73219,plain,
$false,
inference(cvc4,[status(thm)],[52,57,60,45,22,39,63,31,47,42,25,28,33,54,49,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE044+2 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 03:09:02 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.99/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.04 % [INFO] Parsing done (134ms).
% 1.29/1.05 % [INFO] Running in sequential loop mode.
% 1.71/1.24 % [INFO] eprover registered as external prover.
% 1.71/1.24 % [INFO] cvc4 registered as external prover.
% 1.71/1.25 % [INFO] Scanning for conjecture ...
% 1.71/1.30 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.99/1.34 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.99/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 1.99/1.37 % [INFO] Type checking passed.
% 1.99/1.37 % [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 ...
% 77.12/19.08 % External prover 'cvc4' found a proof!
% 77.12/19.08 % [INFO] Killing All external provers ...
% 77.12/19.08 % Time passed: 18564ms (effective reasoning time: 18031ms)
% 77.12/19.08 % 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)>
% 77.12/19.08 % Axioms used in derivation (16): additive_identity, star_induction_right, left_annihilation, star_induction_left, right_distributivity, star_unfold_left, right_annihilation, multiplicative_left_identity, additive_idempotence, additive_associativity, multiplicative_right_identity, star_unfold_right, order, additive_commutativity, multiplicative_associativity, left_distributivity
% 77.12/19.08 % No. of inferences in proof: 36
% 77.12/19.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18564 ms resp. 18031 ms w/o parsing
% 77.12/19.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.12/19.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------