TSTP Solution File: RNG008-5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG008-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 3.82s 1.83s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 35
% Syntax : Number of formulae : 62 ( 31 unt; 9 typ; 0 def)
% Number of atoms : 119 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 512 ( 68 ~; 66 |; 0 &; 378 @)
% ( 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 : 11 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 158 ( 0 ^; 158 !; 0 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(b_type,type,
b: $i ).
thf(a_type,type,
a: $i ).
thf(c_type,type,
c: $i ).
thf(sum_type,type,
sum: $i > $i > $i > $o ).
thf(additive_inverse_type,type,
additive_inverse: $i > $i ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(20,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(56,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)],[20]) ).
thf(8,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(37,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)],[8]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(52,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)],[18]) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
thf(61,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)],[23]) ).
thf(22,axiom,
! [A: $i] : ( product @ additive_identity @ A @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id2) ).
thf(60,plain,
! [A: $i] : ( product @ additive_identity @ A @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(9,axiom,
! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(39,plain,
! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
! [A: $i] : ( product @ A @ additive_identity @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id1) ).
thf(66,plain,
! [A: $i] : ( product @ A @ additive_identity @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
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/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
thf(35,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(11,axiom,
! [B: $i,A: $i] : ( sum @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) @ ( additive_inverse @ ( add @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute_additive_inverse) ).
thf(43,plain,
! [B: $i,A: $i] : ( sum @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) @ ( additive_inverse @ ( add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
thf(58,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)],[21]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
thf(46,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)],[14]) ).
thf(2,axiom,
! [A: $i] : ( sum @ ( additive_inverse @ ( additive_inverse @ A ) ) @ additive_identity @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(29,plain,
! [A: $i] : ( sum @ ( additive_inverse @ ( additive_inverse @ A ) ) @ additive_identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(45,plain,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
thf(64,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)],[25]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
thf(34,plain,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
sum @ ( additive_inverse @ additive_identity ) @ additive_identity @ additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_identity) ).
thf(44,plain,
sum @ ( additive_inverse @ additive_identity ) @ additive_identity @ additive_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
~ ( product @ b @ a @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
thf(27,plain,
~ ( product @ b @ a @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(15,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(48,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)],[15]) ).
thf(24,axiom,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(63,plain,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(16,axiom,
product @ a @ b @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
thf(50,plain,
product @ a @ b @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [A: $i] : ( sum @ A @ ( additive_inverse @ A ) @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(31,plain,
! [A: $i] : ( sum @ A @ ( additive_inverse @ A ) @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(40,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)],[10]) ).
thf(19,axiom,
! [B: $i,A: $i] : ( product @ A @ ( additive_inverse @ B ) @ ( additive_inverse @ ( multiply @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_inverse) ).
thf(55,plain,
! [B: $i,A: $i] : ( product @ A @ ( additive_inverse @ B ) @ ( additive_inverse @ ( multiply @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i] : ( sum @ A @ additive_identity @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
thf(30,plain,
! [A: $i] : ( sum @ A @ additive_identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: $i] : ( product @ A @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_squared_is_x) ).
thf(51,plain,
! [A: $i] : ( product @ A @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(94,plain,
$false,
inference(e,[status(thm)],[56,37,52,61,60,39,66,35,43,58,46,29,45,64,32,34,44,27,48,63,50,31,40,55,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG008-5 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n024.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 : Thu May 18 20:28:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.97 % [INFO] Parsing done (126ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.54/1.17 % [INFO] eprover registered as external prover.
% 1.54/1.17 % [INFO] cvc4 registered as external prover.
% 1.54/1.17 % [INFO] Scanning for conjecture ...
% 1.83/1.22 % [INFO] Found a conjecture and 25 axioms. Running axiom selection ...
% 1.89/1.26 % [INFO] Axiom selection finished. Selected 25 axioms (removed 0 axioms).
% 1.89/1.29 % [INFO] Problem is propositional (TPTP CNF).
% 1.89/1.29 % [INFO] Type checking passed.
% 1.89/1.29 % [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 ...
% 3.82/1.82 % External prover 'e' found a proof!
% 3.82/1.82 % [INFO] Killing All external provers ...
% 3.82/1.82 % Time passed: 1305ms (effective reasoning time: 846ms)
% 3.82/1.82 % 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)>
% 3.82/1.83 % Axioms used in derivation (25): multiply_additive_inverse, addition_is_well_defined, additive_inverse_additive_inverse, x_squared_is_x, multiply_additive_id1, commutativity_of_addition, additive_identity2, additive_identity1, associativity_of_multiplication2, distributivity1, additive_inverse_identity, closure_of_multiplication, distribute_additive_inverse, associativity_of_addition2, associativity_of_multiplication1, distributivity4, a_times_b_is_c, closure_of_addition, distributivity3, distributivity2, associativity_of_addition1, left_inverse, multiplication_is_well_defined, right_inverse, multiply_additive_id2
% 3.82/1.83 % No. of inferences in proof: 53
% 3.82/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1305 ms resp. 846 ms w/o parsing
% 3.82/1.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.82/1.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------