TSTP Solution File: HWV003-2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : HWV003-2 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 11:17:03 EDT 2023
% Result : Unsatisfiable 23.22s 4.67s
% Output : Refutation 23.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 56
% Syntax : Number of formulae : 93 ( 71 unt; 20 typ; 0 def)
% Number of atoms : 75 ( 74 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 310 ( 4 ~; 2 |; 0 &; 304 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 17 con; 0-2 aty)
% Number of variables : 80 ( 0 ^; 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(xor_type,type,
xor: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(cin_type,type,
cin: $i ).
thf(sum_def_type,type,
sum_def: $i ).
thf(or_type,type,
or: $i > $i > $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(carry_def_type,type,
carry_def: $i ).
thf(t1_type,type,
t1: $i ).
thf(t2_type,type,
t2: $i ).
thf(t3_type,type,
t3: $i ).
thf(t4_type,type,
t4: $i ).
thf(t5_type,type,
t5: $i ).
thf(t6_type,type,
t6: $i ).
thf(t7_type,type,
t7: $i ).
thf(sum_type,type,
sum: $i ).
thf(carry_type,type,
carry: $i ).
thf(ll0_type,type,
ll0: $i ).
thf(ll1_type,type,
ll1: $i ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( and @ A @ ( or @ B @ C ) )
= ( or @ ( and @ A @ B ) @ ( and @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_distributive) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( and @ A @ ( or @ B @ C ) )
= ( or @ ( and @ A @ B ) @ ( and @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( xor @ A @ B )
= ( xor @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutative) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( xor @ A @ B )
= ( xor @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( or @ A @ ( and @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_absorption) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( and @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
( ( not @ ll1 )
= ll0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ll1_inverse) ).
thf(92,plain,
( ( not @ ll1 )
= ll0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(30,axiom,
! [A: $i] :
( ( not @ ( not @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_involution) ).
thf(96,plain,
! [A: $i] :
( ( not @ ( not @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,negated_conjecture,
( ( not @ ( and @ t5 @ cin ) )
= t7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7) ).
thf(41,plain,
( ( not @ ( and @ t5 @ cin ) )
= t7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,negated_conjecture,
( ( not @ ( and @ t4 @ cin ) )
= t5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5) ).
thf(44,plain,
( ( not @ ( and @ t4 @ cin ) )
= t5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,axiom,
! [A: $i] :
( ( and @ A @ ll1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_identity) ).
thf(86,plain,
! [A: $i] :
( ( and @ A @ ll1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(22,axiom,
! [A: $i] :
( ( or @ A @ ll0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_identity) ).
thf(80,plain,
! [A: $i] :
( ( or @ A @ ll0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,negated_conjecture,
( ( not @ ( and @ a @ t1 ) )
= t2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(48,plain,
( ( not @ ( and @ a @ t1 ) )
= t2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(34,axiom,
! [A: $i] :
( ( and @ A @ ( not @ A ) )
= ll0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_complement) ).
thf(104,plain,
! [A: $i] :
( ( and @ A @ ( not @ A ) )
= ll0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(6,negated_conjecture,
( ( not @ ( and @ t2 @ t3 ) )
= t4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4) ).
thf(40,plain,
( ( not @ ( and @ t2 @ t3 ) )
= t4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,axiom,
! [A: $i] :
( ( or @ A @ ( not @ A ) )
= ll1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_complement) ).
thf(82,plain,
! [A: $i] :
( ( or @ A @ ( not @ A ) )
= ll1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( or @ ( or @ A @ B ) @ C )
= ( or @ A @ ( or @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_associative) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( or @ A @ B ) @ C )
= ( or @ A @ ( or @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(2,negated_conjecture,
( ( or @ ( and @ cin @ ( or @ a @ b ) ) @ ( and @ ( not @ cin ) @ ( and @ a @ b ) ) )
= carry_def ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',carry_def) ).
thf(42,plain,
( ( or @ ( and @ cin @ ( or @ a @ b ) ) @ ( and @ ( not @ cin ) @ ( and @ a @ b ) ) )
= carry_def ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,negated_conjecture,
( ( not @ ( and @ b @ t1 ) )
= t3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(37,plain,
( ( not @ ( and @ b @ t1 ) )
= t3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,negated_conjecture,
( ( not @ ( and @ t1 @ t5 ) )
= carry ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',carry) ).
thf(46,plain,
( ( not @ ( and @ t1 @ t5 ) )
= carry ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( xor @ A @ ( xor @ B @ C ) )
= ( xor @ ( xor @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_associative) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( xor @ A @ ( xor @ B @ C ) )
= ( xor @ ( xor @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( and @ ( and @ A @ B ) @ C )
= ( and @ A @ ( and @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_associative) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( and @ ( and @ A @ B ) @ C )
= ( and @ A @ ( and @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( or @ ( and @ ( not @ A ) @ B ) @ ( and @ A @ ( not @ B ) ) )
= ( xor @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_definition) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( or @ ( and @ ( not @ A ) @ B ) @ ( and @ A @ ( not @ B ) ) )
= ( xor @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,negated_conjecture,
( ( not @ ( and @ t6 @ t7 ) )
= sum ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
thf(38,plain,
( ( not @ ( and @ t6 @ t7 ) )
= sum ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( not @ ( or @ A @ B ) )
= ( and @ ( not @ A ) @ ( not @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_demorgan) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( not @ ( or @ A @ B ) )
= ( and @ ( not @ A ) @ ( not @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,negated_conjecture,
( ( not @ ( and @ a @ b ) )
= t1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(45,plain,
( ( not @ ( and @ a @ b ) )
= t1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( and @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutative) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( and @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
! [A: $i] :
( ( and @ A @ ll0 )
= ll0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_boundedness) ).
thf(76,plain,
! [A: $i] :
( ( and @ A @ ll0 )
= ll0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,negated_conjecture,
( ( xor @ ( xor @ a @ b ) @ cin )
= sum_def ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_def) ).
thf(39,plain,
( ( xor @ ( xor @ a @ b ) @ cin )
= sum_def ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( or @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutative) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( or @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(15,axiom,
! [A: $i] :
( ( and @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_idempotent) ).
thf(66,plain,
! [A: $i] :
( ( and @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( and @ A @ ( or @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_absorption) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( and @ A @ ( or @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( not @ ( and @ A @ B ) )
= ( or @ ( not @ A ) @ ( not @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_demorgan) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( not @ ( and @ A @ B ) )
= ( or @ ( not @ A ) @ ( not @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,negated_conjecture,
( ( sum != sum_def )
| ( carry != carry_def ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_circuit) ).
thf(43,plain,
( ( sum != sum_def )
| ( carry != carry_def ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,negated_conjecture,
( ( not @ ( and @ t4 @ t5 ) )
= t6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
thf(47,plain,
( ( not @ ( and @ t4 @ t5 ) )
= t6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( and @ B @ C ) )
= ( and @ ( or @ A @ B ) @ ( or @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_distributive) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( and @ B @ C ) )
= ( and @ ( or @ A @ B ) @ ( or @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i] :
( ( or @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_idempotent) ).
thf(62,plain,
! [A: $i] :
( ( or @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
( ( not @ ll0 )
= ll1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ll0_inverse) ).
thf(90,plain,
( ( not @ ll0 )
= ll1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(32,axiom,
! [A: $i] :
( ( or @ A @ ll1 )
= ll1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_boundedness) ).
thf(100,plain,
! [A: $i] :
( ( or @ A @ ll1 )
= ll1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(7414,plain,
$false,
inference(e,[status(thm)],[88,74,102,92,96,41,44,86,80,48,104,40,82,94,42,37,46,78,106,84,38,70,45,64,76,39,98,66,108,72,43,47,68,62,90,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.17 % Problem : HWV003-2 : TPTP v8.1.2. Released v2.7.0.
% 0.14/0.20 % Command : run_Leo-III %s %d
% 0.17/0.42 % Computer : n019.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8042.1875MB
% 0.17/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri May 19 03:42:58 EDT 2023
% 0.17/0.42 % CPUTime :
% 1.03/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.07 % [INFO] Parsing done (132ms).
% 1.27/1.07 % [INFO] Running in sequential loop mode.
% 1.73/1.28 % [INFO] eprover registered as external prover.
% 1.73/1.28 % [INFO] cvc4 registered as external prover.
% 1.73/1.28 % [INFO] Scanning for conjecture ...
% 1.89/1.35 % [INFO] Found a conjecture and 24 axioms. Running axiom selection ...
% 2.01/1.40 % [INFO] Axiom selection finished. Selected 24 axioms (removed 0 axioms).
% 2.01/1.42 % [INFO] Problem is propositional (TPTP CNF).
% 2.01/1.42 % [INFO] Type checking passed.
% 2.01/1.43 % [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 ...
% 23.22/4.67 % External prover 'e' found a proof!
% 23.22/4.67 % [INFO] Killing All external provers ...
% 23.22/4.67 % Time passed: 4080ms (effective reasoning time: 3591ms)
% 23.22/4.67 % 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)>
% 23.22/4.67 % Axioms used in derivation (24): or_idempotent, or_identity, or_associative, and_complement, and_absorption, xor_associative, and_commutative, ll1_inverse, and_identity, and_boundedness, or_complement, and_distributive, or_commutative, or_demorgan, and_idempotent, and_associative, and_demorgan, or_absorption, or_boundedness, xor_definition, xor_commutative, not_involution, or_distributive, ll0_inverse
% 23.22/4.67 % No. of inferences in proof: 73
% 23.22/4.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4080 ms resp. 3591 ms w/o parsing
% 23.22/4.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.22/4.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------