TSTP Solution File: RNG001-3 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : RNG001-3 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 02:37:17 EDT 2024
% Result : Unsatisfiable 4.44s 2.86s
% Output : Refutation 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 23 ( 9 unt; 6 typ; 0 def)
% Number of atoms : 45 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 196 ( 30 ~; 28 |; 0 &; 138 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 60 ( 0 ^ 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(sum_type,type,
sum: $i > $i > $i > $o ).
thf(additive_inverse_type,type,
additive_inverse: $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
thf(20,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)],[8]) ).
thf(1,negated_conjecture,
~ ( product @ a @ additive_identity @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
thf(9,plain,
~ ( product @ a @ additive_identity @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).
thf(13,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)],[4]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(17,plain,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
thf(12,plain,
! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
thf(18,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)],[7]) ).
thf(2,axiom,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(11,plain,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
thf(15,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)],[5]) ).
thf(25,plain,
$false,
inference(cvc4,[status(thm)],[20,9,13,17,12,18,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG001-3 : TPTP v8.2.0. Released v1.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 12:10:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.27/1.20 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.63/1.41 % [INFO] Parsing done (204ms).
% 1.63/1.42 % [INFO] Running in sequential loop mode.
% 2.29/1.92 % [INFO] eprover registered as external prover.
% 2.29/1.92 % [INFO] cvc4 registered as external prover.
% 2.45/1.93 % [INFO] Scanning for conjecture ...
% 2.57/2.03 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.71/2.07 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.71/2.09 % [INFO] Problem is propositional (TPTP CNF).
% 2.71/2.10 % [INFO] Type checking passed.
% 2.71/2.10 % [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 ...
% 4.44/2.85 % External prover 'cvc4' found a proof!
% 4.44/2.86 % [INFO] Killing All external provers ...
% 4.44/2.86 % Time passed: 2316ms (effective reasoning time: 1425ms)
% 4.44/2.86 % Axioms used in derivation (7): additive_identity1, closure_of_multiplication, associativity_of_addition2, distributivity2, associativity_of_addition1, additive_inverse1, distributivity1
% 4.44/2.86 % No. of inferences in proof: 17
% 4.44/2.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2316 ms resp. 1425 ms w/o parsing
% 4.55/2.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.55/2.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------