TSTP Solution File: RNG001-5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG001-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 11:48:58 EDT 2023
% Result : Unsatisfiable 32.10s 7.93s
% Output : Refutation 32.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 38
% Syntax : Number of formulae : 69 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 163 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 684 ( 104 ~; 102 |; 0 &; 478 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 218 ( 0 ^; 218 !; 0 ?; 218 :)
% 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(equalish_type,type,
equalish: $i > $i > $o ).
thf(sum_type,type,
sum: $i > $i > $i > $o ).
thf(add_type,type,
add: $i > $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(additive_inverse_type,type,
additive_inverse: $i > $i ).
thf(21,axiom,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(69,plain,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i] : ( equalish @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(52,plain,
! [A: $i] : ( equalish @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,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(65,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)],[19]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( sum @ A @ C @ D )
| ( sum @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution1) ).
thf(53,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( sum @ A @ C @ D )
| ( sum @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution1) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
! [A: $i] : ( sum @ A @ ( additive_inverse @ A ) @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(73,plain,
! [A: $i] : ( sum @ A @ ( additive_inverse @ A ) @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
thf(45,plain,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,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(59,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)],[16]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_substitution) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(83,plain,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( sum @ C @ D @ A )
| ( sum @ C @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution3) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( sum @ C @ D @ A )
| ( sum @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( sum @ C @ A @ D )
| ( sum @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution2) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( sum @ C @ A @ D )
| ( sum @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ A @ D )
| ( product @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
thf(78,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ A @ D )
| ( product @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ A @ C @ D )
| ( product @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ A @ C @ D )
| ( product @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(25,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(74,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)],[25]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ D @ A )
| ( product @ C @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
thf(70,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ D @ A )
| ( product @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,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(81,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)],[29]) ).
thf(26,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(76,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)],[26]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( add @ A @ C ) @ ( add @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_substitution1) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( add @ A @ C ) @ ( add @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(80,plain,
! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ B @ D )
| ( equalish @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ B @ D )
| ( equalish @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,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(48,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)],[10]) ).
thf(18,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(63,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)],[18]) ).
thf(11,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(50,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)],[11]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,negated_conjecture,
~ ( product @ a @ additive_identity @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiplicative_identity_axiom) ).
thf(31,plain,
~ ( product @ a @ additive_identity @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,axiom,
! [A: $i] : ( sum @ A @ additive_identity @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
thf(72,plain,
! [A: $i] : ( sum @ A @ additive_identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,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(43,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5171,plain,
$false,
inference(cvc4,[status(thm)],[69,37,52,65,53,41,73,45,59,55,83,46,57,78,61,74,70,33,81,76,39,80,35,48,63,50,67,31,72,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG001-5 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n001.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 20:57:21 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.93/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (130ms).
% 1.21/0.97 % [INFO] Running in sequential loop mode.
% 1.71/1.17 % [INFO] eprover registered as external prover.
% 1.71/1.17 % [INFO] cvc4 registered as external prover.
% 1.71/1.18 % [INFO] Scanning for conjecture ...
% 1.71/1.23 % [INFO] Found a conjecture and 29 axioms. Running axiom selection ...
% 2.00/1.26 % [INFO] Axiom selection finished. Selected 29 axioms (removed 0 axioms).
% 2.00/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 2.00/1.30 % [INFO] Type checking passed.
% 2.00/1.30 % [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 ...
% 32.10/7.92 % External prover 'cvc4' found a proof!
% 32.10/7.92 % [INFO] Killing All external provers ...
% 32.10/7.93 % Time passed: 7414ms (effective reasoning time: 6952ms)
% 32.10/7.93 % 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)>
% 32.10/7.93 % Axioms used in derivation (29): product_substitution2, addition_is_well_defined, sum_substitution2, commutativity_of_addition, associativity_of_multiplication2, reflexivity, product_substitution1, distributivity1, add_substitution1, closure_of_multiplication, associativity_of_addition2, distributivity4, closure_of_addition, distributivity3, multiply_substitution1, product_substitution3, additive_identity2, distributivity2, associativity_of_addition1, additive_inverse_substitution, additive_identity1, left_inverse, multiplication_is_well_defined, right_inverse, sum_substitution3, transitivity, associativity_of_multiplication1, symmetry, sum_substitution1
% 32.10/7.93 % No. of inferences in proof: 61
% 32.10/7.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7414 ms resp. 6952 ms w/o parsing
% 32.10/7.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.10/7.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------