TSTP Solution File: HWC003-1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : HWC003-1 : TPTP v8.2.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Mon May 20 21:34:58 EDT 2024
% Result : Unsatisfiable 14.90s 4.18s
% Output : Refutation 14.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 51
% Syntax : Number of formulae : 76 ( 39 unt; 27 typ; 0 def)
% Number of atoms : 65 ( 32 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 720 ( 18 ~; 16 |; 0 &; 686 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 17 con; 0-10 aty)
% Number of variables : 172 ( 0 ^ 172 !; 0 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
thf(output_type,type,
output: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(n0_type,type,
n0: $i ).
thf(n1_type,type,
n1: $i ).
thf(list_reversion_type,type,
list_reversion: $i > $i > $i ).
thf(make_reverse_list_type,type,
make_reverse_list: $i > $i ).
thf(end_type,type,
end: $i ).
thf(not_reversion_type,type,
not_reversion: $i ).
thf(possible_reversion_type,type,
possible_reversion: $i > $i > $i > $i ).
thf(list_type,type,
list: $i > $i > $i ).
thf(inverter_table_type,type,
inverter_table: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(r00m_type,type,
r00m: $i ).
thf(r01m_type,type,
r01m: $i ).
thf(r10m_type,type,
r10m: $i ).
thf(r11m_type,type,
r11m: $i ).
thf(r0m0_type,type,
r0m0: $i ).
thf(r0m1_type,type,
r0m1: $i ).
thf(r1m0_type,type,
r1m0: $i ).
thf(r1m1_type,type,
r1m1: $i ).
thf(rm00_type,type,
rm00: $i ).
thf(rm01_type,type,
rm01: $i ).
thf(rm10_type,type,
rm10: $i ).
thf(rm11_type,type,
rm11: $i ).
thf(add_inverter_type,type,
add_inverter: $i > $i > $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(test_type,type,
test: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(18,axiom,
! [A: $i] :
( ( possible_reversion @ A @ n1 @ n0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',possible_reversion1) ).
thf(56,plain,
! [A: $i] :
( ( possible_reversion @ A @ n1 @ n0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
( ( not @ n0 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition1) ).
thf(52,plain,
( ( not @ n0 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i] :
( ( or @ A @ n0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition1) ).
thf(46,plain,
! [A: $i] :
( ( or @ A @ n0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( output @ A @ B @ C @ D @ E @ F @ G @ H @ I )
| ( test @ ( not @ A ) @ ( not @ B ) @ ( not @ C ) @ ( not @ D ) @ ( not @ E ) @ ( not @ F ) @ ( not @ G ) @ ( not @ H ) @ ( add_inverter @ I @ ( inverter_table @ ( not @ A ) @ ( not @ B ) @ ( not @ C ) @ ( not @ D ) @ ( not @ E ) @ ( not @ F ) @ ( not @ G ) @ ( not @ H ) ) ) @ ( make_reverse_list @ ( list @ ( inverter_table @ ( not @ A ) @ ( not @ B ) @ ( not @ C ) @ ( not @ D ) @ ( not @ E ) @ ( not @ F ) @ ( not @ G ) @ ( not @ H ) ) @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverter_test) ).
thf(60,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( output @ A @ B @ C @ D @ E @ F @ G @ H @ I )
| ( test @ ( not @ A ) @ ( not @ B ) @ ( not @ C ) @ ( not @ D ) @ ( not @ E ) @ ( not @ F ) @ ( not @ G ) @ ( not @ H ) @ ( add_inverter @ I @ ( inverter_table @ ( not @ A ) @ ( not @ B ) @ ( not @ C ) @ ( not @ D ) @ ( not @ E ) @ ( not @ F ) @ ( not @ G ) @ ( not @ H ) ) ) @ ( make_reverse_list @ ( list @ ( inverter_table @ ( not @ A ) @ ( not @ B ) @ ( not @ C ) @ ( not @ D ) @ ( not @ E ) @ ( not @ F ) @ ( not @ G ) @ ( not @ H ) ) @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( output @ A @ B @ C @ D @ E @ F @ G @ H @ I )
| ~ ( output @ J @ K @ L @ M @ N @ O @ P @ Q @ I )
| ( output @ ( or @ A @ J ) @ ( or @ B @ K ) @ ( or @ C @ L ) @ ( or @ D @ M ) @ ( or @ E @ N ) @ ( or @ F @ O ) @ ( or @ G @ P ) @ ( or @ H @ Q ) @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_output_definition) ).
thf(54,plain,
! [Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( output @ A @ B @ C @ D @ E @ F @ G @ H @ I )
| ~ ( output @ J @ K @ L @ M @ N @ O @ P @ Q @ I )
| ( output @ ( or @ A @ J ) @ ( or @ B @ K ) @ ( or @ C @ L ) @ ( or @ D @ M ) @ ( or @ E @ N ) @ ( or @ F @ O ) @ ( or @ G @ P ) @ ( or @ H @ Q ) @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,axiom,
( ( not @ n1 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition2) ).
thf(66,plain,
( ( not @ n1 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
! [A: $i] :
( ( possible_reversion @ A @ n0 @ n1 )
= not_reversion ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',possible_reversion2) ).
thf(48,plain,
! [A: $i] :
( ( possible_reversion @ A @ n0 @ n1 )
= not_reversion ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
! [Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( output @ A @ B @ C @ D @ E @ F @ G @ H @ I )
| ~ ( output @ J @ K @ L @ M @ N @ O @ P @ Q @ I )
| ( output @ ( and @ A @ J ) @ ( and @ B @ K ) @ ( and @ C @ L ) @ ( and @ D @ M ) @ ( and @ E @ N ) @ ( and @ F @ O ) @ ( and @ G @ P ) @ ( and @ H @ Q ) @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_output_definition) ).
thf(50,plain,
! [Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( output @ A @ B @ C @ D @ E @ F @ G @ H @ I )
| ~ ( output @ J @ K @ L @ M @ N @ O @ P @ Q @ I )
| ( output @ ( and @ A @ J ) @ ( and @ B @ K ) @ ( and @ C @ L ) @ ( and @ D @ M ) @ ( and @ E @ N ) @ ( and @ F @ O ) @ ( and @ G @ P ) @ ( and @ H @ Q ) @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [A: $i] :
( ( and @ A @ n1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition2) ).
thf(58,plain,
! [A: $i] :
( ( and @ A @ n1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( add_inverter @ ( list @ A @ B ) @ C )
= ( list @ A @ ( add_inverter @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_inverter_definition1) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( add_inverter @ ( list @ A @ B ) @ C )
= ( list @ A @ ( add_inverter @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,negated_conjecture,
! [A: $i] : ( output @ n0 @ n0 @ n0 @ n0 @ n1 @ n1 @ n1 @ n1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',input1) ).
thf(25,plain,
! [A: $i] : ( output @ n0 @ n0 @ n0 @ n0 @ n1 @ n1 @ n1 @ n1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ~ ( output @ n1 @ n1 @ n1 @ n1 @ n0 @ n0 @ n0 @ n0 @ A )
| ~ ( output @ n1 @ n1 @ n0 @ n0 @ n1 @ n1 @ n0 @ n0 @ A )
| ~ ( output @ n1 @ n0 @ n1 @ n0 @ n1 @ n0 @ n1 @ n0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cannot_construct_this) ).
thf(28,plain,
! [A: $i] :
( ~ ( output @ n1 @ n1 @ n1 @ n1 @ n0 @ n0 @ n0 @ n0 @ A )
| ~ ( output @ n1 @ n1 @ n0 @ n0 @ n1 @ n1 @ n0 @ n0 @ A )
| ~ ( output @ n1 @ n0 @ n1 @ n0 @ n1 @ n0 @ n1 @ n0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( possible_reversion @ A @ B @ B )
= not_reversion ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',possible_reversion3) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( possible_reversion @ A @ B @ B )
= not_reversion ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,axiom,
! [A: $i] :
( ( or @ A @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition2) ).
thf(64,plain,
! [A: $i] :
( ( or @ A @ n1 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( list_reversion @ A @ ( list_reversion @ B @ C ) )
= ( list_reversion @ B @ ( list_reversion @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',list_reversion_definition2) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( list_reversion @ A @ ( list_reversion @ B @ C ) )
= ( list_reversion @ B @ ( list_reversion @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i] :
( ( make_reverse_list @ A )
= end ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',make_reverse_list_definition2) ).
thf(34,plain,
! [A: $i] :
( ( make_reverse_list @ A )
= end ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( add_inverter @ A @ B )
= ( list @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_inverter_definition2) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( add_inverter @ A @ B )
= ( list @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,negated_conjecture,
! [A: $i] : ( output @ n0 @ n1 @ n0 @ n1 @ n0 @ n1 @ n0 @ n1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',input3) ).
thf(27,plain,
! [A: $i] : ( output @ n0 @ n1 @ n0 @ n1 @ n0 @ n1 @ n0 @ n1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( make_reverse_list @ ( list @ ( inverter_table @ A @ B @ C @ D @ E @ F @ G @ H ) @ I ) )
= ( list_reversion @ ( possible_reversion @ r00m @ A @ B ) @ ( list_reversion @ ( possible_reversion @ r01m @ C @ D ) @ ( list_reversion @ ( possible_reversion @ r10m @ E @ F ) @ ( list_reversion @ ( possible_reversion @ r11m @ G @ H ) @ ( list_reversion @ ( possible_reversion @ r0m0 @ A @ C ) @ ( list_reversion @ ( possible_reversion @ r0m1 @ B @ D ) @ ( list_reversion @ ( possible_reversion @ r1m0 @ E @ G ) @ ( list_reversion @ ( possible_reversion @ r1m1 @ F @ H ) @ ( list_reversion @ ( possible_reversion @ rm00 @ A @ E ) @ ( list_reversion @ ( possible_reversion @ rm01 @ B @ F ) @ ( list_reversion @ ( possible_reversion @ rm10 @ C @ G ) @ ( list_reversion @ ( possible_reversion @ rm11 @ D @ H ) @ ( make_reverse_list @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',make_reverse_list_definition1) ).
thf(40,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( make_reverse_list @ ( list @ ( inverter_table @ A @ B @ C @ D @ E @ F @ G @ H ) @ I ) )
= ( list_reversion @ ( possible_reversion @ r00m @ A @ B ) @ ( list_reversion @ ( possible_reversion @ r01m @ C @ D ) @ ( list_reversion @ ( possible_reversion @ r10m @ E @ F ) @ ( list_reversion @ ( possible_reversion @ r11m @ G @ H ) @ ( list_reversion @ ( possible_reversion @ r0m0 @ A @ C ) @ ( list_reversion @ ( possible_reversion @ r0m1 @ B @ D ) @ ( list_reversion @ ( possible_reversion @ r1m0 @ E @ G ) @ ( list_reversion @ ( possible_reversion @ r1m1 @ F @ H ) @ ( list_reversion @ ( possible_reversion @ rm00 @ A @ E ) @ ( list_reversion @ ( possible_reversion @ rm01 @ B @ F ) @ ( list_reversion @ ( possible_reversion @ rm10 @ C @ G ) @ ( list_reversion @ ( possible_reversion @ rm11 @ D @ H ) @ ( make_reverse_list @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,negated_conjecture,
! [A: $i] : ( output @ n0 @ n0 @ n1 @ n1 @ n0 @ n0 @ n1 @ n1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',input2) ).
thf(26,plain,
! [A: $i] : ( output @ n0 @ n0 @ n1 @ n1 @ n0 @ n0 @ n1 @ n1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i] :
( ( list_reversion @ not_reversion @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',list_reversion_definition1) ).
thf(36,plain,
! [A: $i] :
( ( list_reversion @ not_reversion @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( list_reversion @ A @ ( list_reversion @ A @ B ) )
= ( list_reversion @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',list_reversion_definition3) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( list_reversion @ A @ ( list_reversion @ A @ B ) )
= ( list_reversion @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
! [A: $i] :
( ( and @ A @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition1) ).
thf(68,plain,
! [A: $i] :
( ( and @ A @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(21,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( test @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J )
| ( output @ A @ B @ C @ D @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',create_test) ).
thf(62,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( test @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J )
| ( output @ A @ B @ C @ D @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(525,plain,
$false,
inference(e,[status(thm)],[56,52,46,60,54,66,48,50,58,42,25,28,38,64,32,34,44,27,40,26,36,30,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWC003-1 : TPTP v8.2.0. Released v1.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n018.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 : Sun May 19 00:13:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.97 % [INFO] Parsing done (125ms).
% 1.22/0.98 % [INFO] Running in sequential loop mode.
% 1.77/1.20 % [INFO] eprover registered as external prover.
% 1.77/1.20 % [INFO] cvc4 registered as external prover.
% 1.77/1.21 % [INFO] Scanning for conjecture ...
% 1.90/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 2.11/1.32 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.11/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 2.11/1.36 % [INFO] Type checking passed.
% 2.11/1.36 % [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 ...
% 14.90/4.18 % External prover 'e' found a proof!
% 14.90/4.18 % [INFO] Killing All external provers ...
% 14.90/4.18 % Time passed: 3670ms (effective reasoning time: 3198ms)
% 14.90/4.18 % Axioms used in derivation (20): list_reversion_definition3, possible_reversion1, add_inverter_definition1, and_definition1, possible_reversion2, or_definition1, create_test, make_reverse_list_definition2, make_reverse_list_definition1, or_definition2, list_reversion_definition1, not_definition1, and_output_definition, or_output_definition, inverter_test, possible_reversion3, and_definition2, list_reversion_definition2, add_inverter_definition2, not_definition2
% 14.90/4.18 % No. of inferences in proof: 49
% 14.90/4.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3670 ms resp. 3198 ms w/o parsing
% 14.90/4.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.90/4.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------