TSTP Solution File: RNG010-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG010-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 11:49:02 EDT 2023
% Result : Unsatisfiable 3.25s 1.70s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 57 ( 45 unt; 8 typ; 0 def)
% Number of atoms : 53 ( 52 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 344 ( 12 ~; 4 |; 0 &; 328 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 98 ( 0 ^; 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(associator_type,type,
associator: $i > $i > $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(cx_type,type,
cx: $i ).
thf(cy_type,type,
cy: $i ).
thf(cz_type,type,
cz: $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(additive_inverse_type,type,
additive_inverse: $i > $i ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(13,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',multiply_over_add2) ).
thf(56,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)],[13]) ).
thf(11,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',multiply_over_add1) ).
thf(52,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)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ B ) ) )
= ( multiply @ ( multiply @ ( multiply @ A @ B ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_moufang) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ B ) ) )
= ( multiply @ ( multiply @ ( multiply @ A @ B ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,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(74,plain,
! [B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ B )
= ( multiply @ A @ ( multiply @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,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(60,plain,
! [B: $i,A: $i] :
( ( multiply @ ( additive_inverse @ A ) @ B )
= ( additive_inverse @ ( multiply @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( additive_inverse @ ( add @ A @ B ) )
= ( add @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_of_inverses) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( additive_inverse @ ( add @ A @ B ) )
= ( add @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,axiom,
! [A: $i] :
( ( add @ additive_identity @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).
thf(35,plain,
! [A: $i] :
( ( add @ additive_identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( add @ A @ B )
!= ( add @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation_for_addition) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( ( add @ A @ B )
!= ( add @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [A: $i] :
( ( multiply @ additive_identity @ A )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_multiplicative_zero) ).
thf(58,plain,
! [A: $i] :
( ( multiply @ additive_identity @ A )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
( ( additive_inverse @ additive_identity )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_additive_identity) ).
thf(30,plain,
( ( additive_inverse @ additive_identity )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,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(79,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)],[24]) ).
thf(6,axiom,
! [A: $i] :
( ( add @ ( additive_inverse @ A ) @ A )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_inverse) ).
thf(37,plain,
! [A: $i] :
( ( add @ ( additive_inverse @ A ) @ A )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( associator @ ( multiply @ cx @ cx ) @ cy @ cz )
!= ( add @ ( multiply @ ( associator @ cx @ cy @ cz ) @ cx ) @ ( multiply @ cx @ ( associator @ cx @ cy @ cz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_skew_symmetry) ).
thf(25,plain,
( ( associator @ ( multiply @ cx @ cx ) @ cy @ cz )
!= ( add @ ( multiply @ ( associator @ cx @ cy @ cz ) @ cx ) @ ( multiply @ cx @ ( associator @ cx @ cy @ cz ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [A: $i] :
( ( additive_inverse @ ( additive_inverse @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(28,plain,
! [A: $i] :
( ( additive_inverse @ ( additive_inverse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,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(70,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( additive_inverse @ B ) )
= ( additive_inverse @ ( multiply @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( associator @ A @ B @ C )
!= ( additive_inverse @ ( associator @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator_skew_symmetry1) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( associator @ A @ B @ C )
!= ( additive_inverse @ ( associator @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,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(64,plain,
! [B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ A ) @ B )
= ( multiply @ A @ ( multiply @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( associator @ A @ B @ C )
!= ( additive_inverse @ ( associator @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator_skew_symmetry2) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( associator @ A @ B @ C )
!= ( additive_inverse @ ( associator @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( add @ A @ B )
!= ( add @ A @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation_for_addition) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ( add @ A @ B )
!= ( add @ A @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,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(72,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)],[21]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ A )
!= ( multiply @ A @ ( multiply @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',middle_law) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ A )
!= ( multiply @ A @ ( multiply @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ ( multiply @ B @ A ) ) @ C )
= ( multiply @ A @ ( multiply @ B @ ( multiply @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_moufang) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ ( multiply @ B @ A ) ) @ C )
= ( multiply @ A @ ( multiply @ B @ ( multiply @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [A: $i] :
( ( multiply @ A @ additive_identity )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_zero) ).
thf(62,plain,
! [A: $i] :
( ( multiply @ A @ additive_identity )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(81,plain,
$false,
inference(e,[status(thm)],[56,52,46,74,60,54,66,35,48,58,30,79,37,25,28,70,32,64,76,39,72,43,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG010-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n022.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Thu May 18 20:19:33 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (122ms).
% 1.18/0.98 % [INFO] Running in sequential loop mode.
% 1.56/1.18 % [INFO] eprover registered as external prover.
% 1.76/1.18 % [INFO] cvc4 registered as external prover.
% 1.76/1.19 % [INFO] Scanning for conjecture ...
% 1.90/1.24 % [INFO] Found a conjecture and 23 axioms. Running axiom selection ...
% 1.90/1.28 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 1.90/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.90/1.30 % [INFO] Type checking passed.
% 1.90/1.31 % [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 ...
% 3.25/1.70 % External prover 'e' found a proof!
% 3.25/1.70 % [INFO] Killing All external provers ...
% 3.25/1.70 % Time passed: 1169ms (effective reasoning time: 717ms)
% 3.25/1.70 % 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)>
% 3.25/1.70 % Axioms used in derivation (23): sum_of_inverses, associator_skew_symmetry1, middle_law, inverse_additive_identity, left_moufang, multiply_over_add2, right_multiplicative_zero, inverse_product2, right_alternative, commutativity_for_addition, additive_inverse_additive_inverse, associativity_for_addition, associator, left_alternative, right_moufang, left_cancellation_for_addition, associator_skew_symmetry2, right_cancellation_for_addition, left_multiplicative_zero, left_additive_identity, multiply_over_add1, add_inverse, inverse_product1
% 3.25/1.70 % No. of inferences in proof: 49
% 3.25/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1169 ms resp. 717 ms w/o parsing
% 3.53/1.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.53/1.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------