TSTP Solution File: RNG008-3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG008-3 : TPTP v8.1.2. Released v1.0.0.
% 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 11:49:01 EDT 2023
% Result : Unsatisfiable 2.84s 1.62s
% Output : Refutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 46 ( 39 unt; 7 typ; 0 def)
% Number of atoms : 39 ( 38 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 166 ( 2 ~; 0 |; 0 &; 164 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $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(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_multiplication) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [A: $i] :
( ( add @ A @ ( additive_inverse @ A ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(41,plain,
! [A: $i] :
( ( add @ A @ ( additive_inverse @ A ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i] :
( ( multiply @ additive_identity @ A )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id2) ).
thf(45,plain,
! [A: $i] :
( ( multiply @ additive_identity @ A )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( add @ ( add @ A @ B ) @ C )
= ( add @ A @ ( add @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_addition) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( add @ ( add @ A @ B ) @ C )
= ( add @ A @ ( add @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ ( additive_inverse @ B ) )
= ( additive_inverse @ ( multiply @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_inverse1) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( additive_inverse @ B ) )
= ( additive_inverse @ ( multiply @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i] :
( ( add @ additive_identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(39,plain,
! [A: $i] :
( ( add @ additive_identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i] :
( ( additive_inverse @ ( additive_inverse @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(35,plain,
! [A: $i] :
( ( additive_inverse @ ( additive_inverse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(31,plain,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ C )
= ( add @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
thf(43,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)],[12]) ).
thf(18,axiom,
! [A: $i] :
( ( multiply @ A @ additive_identity )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id1) ).
thf(55,plain,
! [A: $i] :
( ( multiply @ A @ additive_identity )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( additive_inverse @ A ) @ B )
= ( additive_inverse @ ( multiply @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_inverse2) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( multiply @ ( additive_inverse @ A ) @ B )
= ( additive_inverse @ ( multiply @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [A: $i] :
( ( multiply @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolean_ring) ).
thf(47,plain,
! [A: $i] :
( ( multiply @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i] :
( ( add @ ( additive_inverse @ A ) @ A )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_inverse) ).
thf(37,plain,
! [A: $i] :
( ( add @ ( additive_inverse @ A ) @ A )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutative_addition) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( multiply @ a @ b )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
thf(20,plain,
( ( multiply @ a @ b )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ C ) )
= ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
thf(57,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)],[19]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( additive_inverse @ ( add @ A @ B ) )
= ( add @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute_additive_inverse) ).
thf(29,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)],[5]) ).
thf(2,negated_conjecture,
( ( multiply @ b @ a )
!= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
thf(21,plain,
( ( multiply @ b @ a )
!= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
( ( additive_inverse @ additive_identity )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_identity) ).
thf(33,plain,
( ( additive_inverse @ additive_identity )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(62,plain,
$false,
inference(e,[status(thm)],[53,41,45,27,49,39,35,31,43,55,51,47,37,25,20,57,29,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG008-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n028.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu May 18 20:41:49 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.10/0.98 % [INFO] Parsing done (134ms).
% 1.10/0.99 % [INFO] Running in sequential loop mode.
% 1.69/1.19 % [INFO] eprover registered as external prover.
% 1.69/1.19 % [INFO] cvc4 registered as external prover.
% 1.69/1.20 % [INFO] Scanning for conjecture ...
% 1.85/1.24 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 1.85/1.28 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 1.85/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.85/1.30 % [INFO] Type checking passed.
% 1.85/1.30 % [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 ...
% 2.59/1.62 % External prover 'e' found a proof!
% 2.59/1.62 % [INFO] Killing All external provers ...
% 2.84/1.62 % Time passed: 1120ms (effective reasoning time: 625ms)
% 2.84/1.62 % 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)>
% 2.84/1.62 % Axioms used in derivation (17): additive_inverse_additive_inverse, left_identity, multiply_additive_id1, boolean_ring, multiply_additive_inverse2, right_identity, additive_inverse_identity, distribute1, commutative_addition, distribute2, associative_addition, right_inverse, associative_multiplication, multiply_additive_id2, left_additive_inverse, distribute_additive_inverse, multiply_additive_inverse1
% 2.84/1.62 % No. of inferences in proof: 39
% 2.84/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1120 ms resp. 625 ms w/o parsing
% 2.84/1.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.84/1.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------