TSTP Solution File: BOO013-3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : BOO013-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 10:11:55 EDT 2023
% Result : Unsatisfiable 3.88s 2.00s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 38
% Syntax : Number of formulae : 67 ( 33 unt; 10 typ; 0 def)
% Number of atoms : 133 ( 8 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 546 ( 78 ~; 76 |; 0 &; 392 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 166 ( 0 ^; 166 !; 0 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(sum_type,type,
sum: $i > $i > $i > $o ).
thf(x_type,type,
x: $i ).
thf(y_type,type,
y: $i ).
thf(multiplicative_identity_type,type,
multiplicative_identity: $i ).
thf(z_type,type,
z: $i ).
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(25,axiom,
! [A: $i] : ( product @ multiplicative_identity @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
thf(69,plain,
! [A: $i] : ( product @ multiplicative_identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: $i] : ( sum @ A @ ( inverse @ A ) @ multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
thf(61,plain,
! [A: $i] : ( sum @ A @ ( inverse @ A ) @ multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(19,axiom,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
thf(60,plain,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
! [A: $i] : ( product @ A @ ( inverse @ A ) @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse2) ).
thf(53,plain,
! [A: $i] : ( product @ A @ ( inverse @ A ) @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ D @ B @ E )
| ~ ( product @ A @ D @ F )
| ~ ( product @ C @ E @ G )
| ( sum @ F @ B @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity8) ).
thf(41,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ D @ B @ E )
| ~ ( product @ A @ D @ F )
| ~ ( product @ C @ E @ G )
| ( sum @ F @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,axiom,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
thf(73,plain,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(23,axiom,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
thf(66,plain,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ E )
| ~ ( sum @ A @ D @ F )
| ~ ( product @ F @ B @ G )
| ( sum @ C @ E @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
thf(58,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ E )
| ~ ( sum @ A @ D @ F )
| ~ ( product @ F @ B @ G )
| ( sum @ C @ E @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ D @ B @ E )
| ~ ( product @ A @ D @ F )
| ~ ( sum @ F @ B @ G )
| ( product @ C @ E @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity7) ).
thf(62,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ D @ B @ E )
| ~ ( product @ A @ D @ F )
| ~ ( sum @ F @ B @ G )
| ( product @ C @ E @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,negated_conjecture,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
thf(29,plain,
y != z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ E )
| ~ ( sum @ A @ D @ F )
| ~ ( sum @ C @ E @ G )
| ( product @ F @ B @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
thf(70,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ E )
| ~ ( sum @ A @ D @ F )
| ~ ( sum @ C @ E @ G )
| ( product @ F @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(4,negated_conjecture,
product @ x @ z @ additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity2) ).
thf(33,plain,
product @ x @ z @ additive_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,negated_conjecture,
product @ x @ y @ additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity1) ).
thf(32,plain,
product @ x @ y @ additive_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i] : ( sum @ A @ additive_identity @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
thf(45,plain,
! [A: $i] : ( sum @ A @ additive_identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ E )
| ~ ( sum @ B @ D @ F )
| ~ ( product @ A @ F @ G )
| ( sum @ C @ E @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(64,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ E )
| ~ ( sum @ B @ D @ F )
| ~ ( product @ A @ F @ G )
| ( sum @ C @ E @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ E )
| ~ ( sum @ B @ D @ F )
| ~ ( sum @ C @ E @ G )
| ( product @ A @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(54,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ E )
| ~ ( sum @ B @ D @ F )
| ~ ( sum @ C @ E @ G )
| ( product @ A @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(49,plain,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [A: $i] : ( product @ A @ multiplicative_identity @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
thf(50,plain,
! [A: $i] : ( product @ A @ multiplicative_identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ D @ E )
| ~ ( product @ B @ D @ F )
| ~ ( product @ C @ E @ G )
| ( sum @ A @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity6) ).
thf(67,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ D @ E )
| ~ ( product @ B @ D @ F )
| ~ ( product @ C @ E @ G )
| ( sum @ A @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(2,negated_conjecture,
sum @ x @ z @ multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
thf(31,plain,
sum @ x @ z @ multiplicative_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,axiom,
! [A: $i] : ( sum @ ( inverse @ A ) @ A @ multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
thf(72,plain,
! [A: $i] : ( sum @ ( inverse @ A ) @ A @ multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(9,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ D @ E )
| ~ ( product @ B @ D @ F )
| ~ ( sum @ A @ F @ G )
| ( product @ C @ E @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity5) ).
thf(43,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ D @ E )
| ~ ( product @ B @ D @ F )
| ~ ( sum @ A @ F @ G )
| ( product @ C @ E @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_is_an_involution) ).
thf(36,plain,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
sum @ x @ y @ multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
thf(30,plain,
sum @ x @ y @ multiplicative_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(104,plain,
$false,
inference(e,[status(thm)],[69,56,61,60,53,41,73,66,58,62,46,29,38,70,33,32,45,64,54,49,50,67,31,72,43,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO013-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n004.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 21:01:10 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.94/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.02 % [INFO] Parsing done (130ms).
% 1.25/1.03 % [INFO] Running in sequential loop mode.
% 1.82/1.24 % [INFO] eprover registered as external prover.
% 1.82/1.25 % [INFO] cvc4 registered as external prover.
% 1.82/1.25 % [INFO] Scanning for conjecture ...
% 1.91/1.32 % [INFO] Found a conjecture and 23 axioms. Running axiom selection ...
% 2.09/1.36 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 2.20/1.39 % [INFO] Problem is propositional (TPTP CNF).
% 2.20/1.40 % [INFO] Type checking passed.
% 2.20/1.40 % [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 ...
% 3.88/2.00 % External prover 'e' found a proof!
% 3.88/2.00 % [INFO] Killing All external provers ...
% 3.88/2.00 % Time passed: 1461ms (effective reasoning time: 970ms)
% 3.88/2.00 % 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)>
% 3.88/2.00 % Axioms used in derivation (23): distributivity8, distributivity6, addition_is_well_defined, commutativity_of_multiplication, additive_inverse2, commutativity_of_addition, additive_identity2, distributivity2, multiplication_is_well_defined, multiplicative_identity1, multiplicative_identity2, multiplicative_inverse1, inverse_is_an_involution, distributivity7, distributivity4, closure_of_addition, distributivity3, multiplicative_inverse2, additive_identity1, additive_inverse1, distributivity1, closure_of_multiplication, distributivity5
% 3.88/2.00 % No. of inferences in proof: 57
% 3.88/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1461 ms resp. 970 ms w/o parsing
% 3.88/2.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.88/2.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------