TSTP Solution File: RNG002-1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : RNG002-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 : Tue May 21 02:37:18 EDT 2024
% Result : Unsatisfiable 3.14s 1.84s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 30
% Syntax : Number of formulae : 51 ( 19 unt; 10 typ; 0 def)
% Number of atoms : 107 ( 6 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 446 ( 68 ~; 66 |; 0 &; 312 @)
% ( 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 : 142 ( 0 ^ 142 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i > $i > $o ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(additive_inverse_type,type,
additive_inverse: $i > $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(d_type,type,
d: $i ).
thf(4,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
thf(29,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,axiom,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
thf(53,plain,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(19,axiom,
sum @ a @ c @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_plus_c_is_d) ).
thf(54,plain,
sum @ a @ c @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,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(48,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)],[16]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(31,plain,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(47,plain,
! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,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(42,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)],[12]) ).
thf(2,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(24,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)],[2]) ).
thf(9,axiom,
! [A: $i] : ( sum @ A @ ( additive_inverse @ A ) @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(37,plain,
! [A: $i] : ( sum @ A @ ( additive_inverse @ A ) @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,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(38,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)],[10]) ).
thf(1,negated_conjecture,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_equals_c) ).
thf(21,plain,
b != c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ B @ D @ E )
| ~ ( sum @ C @ D @ F )
| ( sum @ A @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
thf(45,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ B @ D @ E )
| ~ ( sum @ C @ D @ F )
| ( sum @ A @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,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(32,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)],[6]) ).
thf(7,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ B @ D @ E )
| ~ ( sum @ A @ E @ F )
| ( sum @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
thf(34,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ B @ D @ E )
| ~ ( sum @ A @ E @ F )
| ( sum @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
thf(44,plain,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ C @ D @ F )
| ( product @ A @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
thf(27,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ C @ D @ F )
| ( product @ A @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,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(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
sum @ a @ b @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_plus_b_is_d) ).
thf(55,plain,
sum @ a @ b @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [A: $i] : ( sum @ A @ additive_identity @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
thf(36,plain,
! [A: $i] : ( sum @ A @ additive_identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,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(51,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)],[17]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[29,53,54,48,31,47,42,24,37,38,21,45,32,34,44,27,40,55,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG002-1 : TPTP v8.2.0. Released v1.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 12:14:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.99 % [INFO] Parsing done (145ms).
% 1.17/1.01 % [INFO] Running in sequential loop mode.
% 1.70/1.27 % [INFO] eprover registered as external prover.
% 1.70/1.27 % [INFO] cvc4 registered as external prover.
% 1.70/1.27 % [INFO] Scanning for conjecture ...
% 1.97/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 1.97/1.37 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.16/1.40 % [INFO] Problem is propositional (TPTP CNF).
% 2.16/1.41 % [INFO] Type checking passed.
% 2.16/1.41 % [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 ...
% 3.14/1.84 % External prover 'e' found a proof!
% 3.14/1.84 % [INFO] Killing All external provers ...
% 3.14/1.84 % Time passed: 1334ms (effective reasoning time: 830ms)
% 3.14/1.84 % Axioms used in derivation (19): addition_is_well_defined, additive_identity2, additive_identity1, right_inverse, distributivity1, closure_of_multiplication, associativity_of_addition2, associativity_of_multiplication1, distributivity4, closure_of_addition, distributivity3, a_plus_b_is_d, commutativity_of_addition, distributivity2, associativity_of_addition1, left_inverse, multiplication_is_well_defined, associativity_of_multiplication2, a_plus_c_is_d
% 3.14/1.84 % No. of inferences in proof: 41
% 3.14/1.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1334 ms resp. 830 ms w/o parsing
% 3.14/1.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.14/1.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------