TSTP Solution File: RNG023-7 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG023-7 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 11:49:05 EDT 2023
% Result : Unsatisfiable 2.87s 1.59s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 31
% Syntax : Number of formulae : 55 ( 47 unt; 8 typ; 0 def)
% Number of atoms : 47 ( 46 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 318 ( 2 ~; 0 |; 0 &; 316 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 90 ( 0 ^; 90 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(associator_type,type,
associator: $i > $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(y_type,type,
y: $i ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(additive_inverse_type,type,
additive_inverse: $i > $i ).
thf(commutator_type,type,
commutator: $i > $i > $i ).
thf(23,axiom,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_identity) ).
thf(69,plain,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [A: $i] :
( ( add @ additive_identity @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).
thf(61,plain,
! [A: $i] :
( ( add @ additive_identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( add @ A @ ( additive_inverse @ B ) ) @ C )
= ( add @ ( multiply @ A @ C ) @ ( additive_inverse @ ( multiply @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_of_difference2) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( add @ A @ ( additive_inverse @ B ) ) @ C )
= ( add @ ( multiply @ A @ C ) @ ( additive_inverse @ ( multiply @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [A: $i] :
( ( multiply @ A @ additive_identity )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_zero) ).
thf(65,plain,
! [A: $i] :
( ( multiply @ A @ additive_identity )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ B )
= ( multiply @ A @ ( multiply @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_alternative) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ B )
= ( multiply @ A @ ( multiply @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) )
= ( multiply @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_of_inverses) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( multiply @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) )
= ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i] :
( ( additive_inverse @ ( additive_inverse @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(49,plain,
! [A: $i] :
( ( additive_inverse @ ( additive_inverse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ ( additive_inverse @ C ) )
= ( add @ ( additive_inverse @ ( multiply @ A @ C ) ) @ ( additive_inverse @ ( multiply @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_of_difference4) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ ( additive_inverse @ C ) )
= ( add @ ( additive_inverse @ ( multiply @ A @ C ) ) @ ( additive_inverse @ ( multiply @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ C )
= ( add @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ C )
= ( add @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [A: $i] :
( ( multiply @ additive_identity @ A )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_multiplicative_zero) ).
thf(63,plain,
! [A: $i] :
( ( multiply @ additive_identity @ A )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( additive_inverse @ A ) @ ( add @ B @ C ) )
= ( add @ ( additive_inverse @ ( multiply @ A @ B ) ) @ ( additive_inverse @ ( multiply @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_of_difference3) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( additive_inverse @ A ) @ ( add @ B @ C ) )
= ( add @ ( additive_inverse @ ( multiply @ A @ B ) ) @ ( additive_inverse @ ( multiply @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( add @ A @ ( add @ B @ C ) )
= ( add @ ( add @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( add @ A @ ( add @ B @ C ) )
= ( add @ ( add @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ ( additive_inverse @ B ) )
= ( additive_inverse @ ( multiply @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product2) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( additive_inverse @ B ) )
= ( additive_inverse @ ( multiply @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ A ) @ B )
= ( multiply @ A @ ( multiply @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_alternative) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ A ) @ B )
= ( multiply @ A @ ( multiply @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
( ( associator @ x @ x @ y )
!= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_alternative) ).
thf(24,plain,
( ( associator @ x @ x @ y )
!= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ ( additive_inverse @ C ) ) )
= ( add @ ( multiply @ A @ B ) @ ( additive_inverse @ ( multiply @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_of_difference1) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ ( additive_inverse @ C ) ) )
= ( add @ ( multiply @ A @ B ) @ ( additive_inverse @ ( multiply @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( associator @ A @ B @ C )
= ( add @ ( multiply @ ( multiply @ A @ B ) @ C ) @ ( additive_inverse @ ( multiply @ A @ ( multiply @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( associator @ A @ B @ C )
= ( add @ ( multiply @ ( multiply @ A @ B ) @ C ) @ ( additive_inverse @ ( multiply @ A @ ( multiply @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( additive_inverse @ A ) @ B )
= ( additive_inverse @ ( multiply @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product1) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( multiply @ ( additive_inverse @ A ) @ B )
= ( additive_inverse @ ( multiply @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [A: $i] :
( ( add @ A @ ( additive_inverse @ A ) )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).
thf(59,plain,
! [A: $i] :
( ( add @ A @ ( additive_inverse @ A ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ C ) )
= ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ C ) )
= ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [A: $i] :
( ( add @ ( additive_inverse @ A ) @ A )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_inverse) ).
thf(67,plain,
! [A: $i] :
( ( add @ ( additive_inverse @ A ) @ A )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( commutator @ A @ B )
= ( add @ ( multiply @ B @ A ) @ ( additive_inverse @ ( multiply @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( commutator @ A @ B )
= ( add @ ( multiply @ B @ A ) @ ( additive_inverse @ ( multiply @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(71,plain,
$false,
inference(e,[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
% 0.00/0.10 % Problem : RNG023-7 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : run_Leo-III %s %d
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu May 18 20:31:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.89/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.93 % [INFO] Parsing done (114ms).
% 1.31/0.94 % [INFO] Running in sequential loop mode.
% 1.59/1.13 % [INFO] eprover registered as external prover.
% 1.59/1.13 % [INFO] cvc4 registered as external prover.
% 1.59/1.13 % [INFO] Scanning for conjecture ...
% 1.85/1.18 % [INFO] Found a conjecture and 22 axioms. Running axiom selection ...
% 1.90/1.22 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.04/1.24 % [INFO] Problem is propositional (TPTP CNF).
% 2.04/1.25 % [INFO] Type checking passed.
% 2.04/1.25 % [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 ...
% 2.87/1.59 % External prover 'e' found a proof!
% 2.87/1.59 % [INFO] Killing All external provers ...
% 2.87/1.59 % Time passed: 1094ms (effective reasoning time: 648ms)
% 2.87/1.59 % 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)>
% 2.87/1.59 % Axioms used in derivation (22): distributivity_of_difference2, distributivity_of_difference3, product_of_inverses, left_multiplicative_zero, right_multiplicative_zero, inverse_product2, left_additive_identity, right_alternative, inverse_product1, commutativity_for_addition, additive_inverse_additive_inverse, associativity_for_addition, associator, left_alternative, distribute2, distributivity_of_difference4, right_additive_inverse, left_additive_inverse, distributivity_of_difference1, right_additive_identity, distribute1, commutator
% 2.87/1.59 % No. of inferences in proof: 47
% 2.87/1.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1094 ms resp. 648 ms w/o parsing
% 3.39/1.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.39/1.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------