TSTP Solution File: GEO111+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO111+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : Fri May 19 11:09:23 EDT 2023
% Result : Theorem 4.08s 1.98s
% Output : Refutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 27
% Syntax : Number of formulae : 47 ( 3 unt; 9 typ; 0 def)
% Number of atoms : 211 ( 33 equ; 0 cnn)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 582 ( 24 ~; 22 |; 89 &; 385 @)
% ( 10 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 1 con; 0-4 aty)
% Number of variables : 136 ( 0 ^; 113 !; 23 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(between_c_type,type,
between_c: $i > $i > $i > $i > $o ).
thf(incident_c_type,type,
incident_c: $i > $i > $o ).
thf(meet_type,type,
meet: $i > $i > $i > $o ).
thf(sum_type,type,
sum: $i > $i > $i ).
thf(closed_type,type,
closed: $i > $o ).
thf(end_point_type,type,
end_point: $i > $i > $o ).
thf(part_of_type,type,
part_of: $i > $i > $o ).
thf(inner_point_type,type,
inner_point: $i > $i > $o ).
thf(open_type,type,
open: $i > $o ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( part_of @ B @ A )
<=> ! [C: $i] :
( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn) ).
thf(142,plain,
! [A: $i,B: $i] :
( ( ( part_of @ B @ A )
=> ! [C: $i] :
( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) ) )
& ( ! [C: $i] :
( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) )
=> ( part_of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( meet @ C @ A @ B )
=> ? [C: $i] :
( C
= ( sum @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c8) ).
thf(24,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( meet @ C @ A @ B )
=> ? [C: $i] :
( C
= ( sum @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( part_of @ B @ A )
& ( B != A ) )
=> ( open @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( ( part_of @ B @ A )
& ( B != A ) )
=> ( open @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( end_point @ A @ B )
<=> ( ( incident_c @ A @ B )
& ! [C: $i,D: $i] :
( ( ( part_of @ C @ B )
& ( part_of @ D @ B )
& ( incident_c @ A @ C )
& ( incident_c @ A @ D ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( ( end_point @ A @ B )
=> ( ( incident_c @ A @ B )
& ! [C: $i,D: $i] :
( ( ( part_of @ C @ B )
& ( part_of @ D @ B )
& ( incident_c @ A @ C )
& ( incident_c @ A @ D ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C ) ) ) ) )
& ( ( ( incident_c @ A @ B )
& ! [C: $i,D: $i] :
( ( ( part_of @ C @ B )
& ( part_of @ D @ B )
& ( incident_c @ A @ C )
& ( incident_c @ A @ D ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C ) ) ) )
=> ( end_point @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i] :
( ( open @ A )
<=> ? [B: $i] : ( end_point @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',open_defn) ).
thf(38,plain,
! [A: $i] :
( ( ( open @ A )
=> ? [B: $i] : ( end_point @ B @ A ) )
& ( ? [B: $i] : ( end_point @ B @ A )
=> ( open @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( A
= ( sum @ B @ C ) )
<=> ! [D: $i] :
( ( incident_c @ D @ A )
<=> ( ( incident_c @ D @ B )
| ( incident_c @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn) ).
thf(92,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( sum @ B @ C ) )
=> ! [D: $i] :
( ( ( incident_c @ D @ A )
=> ( ( incident_c @ D @ B )
| ( incident_c @ D @ C ) ) )
& ( ( ( incident_c @ D @ B )
| ( incident_c @ D @ C ) )
=> ( incident_c @ D @ A ) ) ) )
& ( ! [D: $i] :
( ( ( incident_c @ D @ A )
=> ( ( incident_c @ D @ B )
| ( incident_c @ D @ C ) ) )
& ( ( ( incident_c @ D @ B )
| ( incident_c @ D @ C ) )
=> ( incident_c @ D @ A ) ) )
=> ( A
= ( sum @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( inner_point @ A @ B )
<=> ( ( incident_c @ A @ B )
& ~ ( end_point @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( ( inner_point @ A @ B )
=> ( ( incident_c @ A @ B )
& ~ ( end_point @ A @ B ) ) )
& ( ( ( incident_c @ A @ B )
& ~ ( end_point @ A @ B ) )
=> ( inner_point @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( between_c @ A @ B @ C @ D )
<=> ( ( B != D )
& ? [E: $i] :
( ( part_of @ E @ A )
& ( end_point @ B @ E )
& ( end_point @ D @ E )
& ( inner_point @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_c_defn) ).
thf(130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( between_c @ A @ B @ C @ D )
=> ( ( B != D )
& ? [E: $i] :
( ( part_of @ E @ A )
& ( end_point @ B @ E )
& ( end_point @ D @ E )
& ( inner_point @ C @ E ) ) ) )
& ( ( ( B != D )
& ? [E: $i] :
( ( part_of @ E @ A )
& ( end_point @ B @ E )
& ( end_point @ D @ E )
& ( inner_point @ C @ E ) ) )
=> ( between_c @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: $i] :
? [B: $i] : ( inner_point @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3) ).
thf(50,plain,
! [A: $i] :
? [B: $i] : ( inner_point @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( end_point @ B @ A )
& ( end_point @ C @ A )
& ( end_point @ D @ A ) )
=> ( ( B = C )
| ( B = D )
| ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c5) ).
thf(43,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( end_point @ B @ A )
& ( end_point @ C @ A )
& ( end_point @ D @ A ) )
=> ( ( B = C )
| ( B = D )
| ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( closed @ A )
& ( meet @ D @ B @ C )
& ( A
= ( sum @ B @ C ) ) )
=> ! [E: $i] :
( ( end_point @ E @ B )
=> ( meet @ E @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c7) ).
thf(55,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( closed @ A )
& ( meet @ D @ B @ C )
& ( A
= ( sum @ B @ C ) ) )
=> ! [E: $i] :
( ( end_point @ E @ B )
=> ( meet @ E @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( incident_c @ C @ A )
<=> ( incident_c @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9) ).
thf(82,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( incident_c @ C @ A )
=> ( incident_c @ C @ B ) )
& ( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( between_c @ A @ B @ C @ D )
=> ( ( incident_c @ B @ A )
& ( incident_c @ C @ A )
& ( incident_c @ D @ A )
& ( B != C )
& ( C != D )
& ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_3_8_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( between_c @ A @ B @ C @ D )
=> ( ( incident_c @ B @ A )
& ( incident_c @ C @ A )
& ( incident_c @ D @ A )
& ( B != C )
& ( C != D )
& ( B != D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( between_c @ A @ B @ C @ D )
=> ( ( incident_c @ B @ A )
& ( incident_c @ C @ A )
& ( incident_c @ D @ A )
& ( B != C )
& ( C != D )
& ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( end_point @ B @ A )
=> ? [C: $i] :
( ( end_point @ C @ A )
& ( B != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( end_point @ B @ A )
=> ? [C: $i] :
( ( end_point @ C @ A )
& ( B != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( part_of @ B @ A )
& ( part_of @ C @ A )
& ( part_of @ D @ A )
& ? [E: $i] :
( ( end_point @ E @ B )
& ( end_point @ E @ C )
& ( end_point @ E @ D ) ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C )
| ( part_of @ B @ C )
| ( part_of @ C @ B )
| ( part_of @ B @ D )
| ( part_of @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2) ).
thf(32,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( part_of @ B @ A )
& ( part_of @ C @ A )
& ( part_of @ D @ A )
& ? [E: $i] :
( ( end_point @ E @ B )
& ( end_point @ E @ C )
& ( end_point @ E @ D ) ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C )
| ( part_of @ B @ C )
| ( part_of @ C @ B )
| ( part_of @ B @ D )
| ( part_of @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( inner_point @ B @ A )
=> ? [C: $i,D: $i] :
( ( meet @ B @ C @ D )
& ( A
= ( sum @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( inner_point @ B @ A )
=> ? [C: $i,D: $i] :
( ( meet @ B @ C @ D )
& ( A
= ( sum @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( meet @ A @ B @ C )
<=> ( ( incident_c @ A @ B )
& ( incident_c @ A @ C )
& ! [D: $i] :
( ( ( incident_c @ D @ B )
& ( incident_c @ D @ C ) )
=> ( ( end_point @ D @ B )
& ( end_point @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn) ).
thf(118,plain,
! [A: $i,B: $i,C: $i] :
( ( ( meet @ A @ B @ C )
=> ( ( incident_c @ A @ B )
& ( incident_c @ A @ C )
& ! [D: $i] :
( ( ( incident_c @ D @ B )
& ( incident_c @ D @ C ) )
=> ( ( end_point @ D @ B )
& ( end_point @ D @ C ) ) ) ) )
& ( ( ( incident_c @ A @ B )
& ( incident_c @ A @ C )
& ! [D: $i] :
( ( ( incident_c @ D @ B )
& ( incident_c @ D @ C ) )
=> ( ( end_point @ D @ B )
& ( end_point @ D @ C ) ) ) )
=> ( meet @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i] :
( ( closed @ A )
<=> ~ ? [B: $i] : ( end_point @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closed_defn) ).
thf(27,plain,
! [A: $i] :
( ( ( closed @ A )
=> ~ ? [B: $i] : ( end_point @ B @ A ) )
& ( ~ ? [B: $i] : ( end_point @ B @ A )
=> ( closed @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(152,plain,
$false,
inference(e,[status(thm)],[142,24,52,60,38,92,76,130,50,43,55,82,20,46,32,34,118,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO111+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.15 % 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 : Fri May 19 04:46:59 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.89/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.99 % [INFO] Parsing done (134ms).
% 1.18/1.00 % [INFO] Running in sequential loop mode.
% 1.82/1.19 % [INFO] eprover registered as external prover.
% 1.82/1.20 % [INFO] cvc4 registered as external prover.
% 1.82/1.20 % [INFO] Scanning for conjecture ...
% 1.95/1.26 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 1.95/1.30 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.19/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 2.19/1.34 % [INFO] Type checking passed.
% 2.19/1.35 % [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 ...
% 4.08/1.98 % External prover 'e' found a proof!
% 4.08/1.98 % [INFO] Killing All external provers ...
% 4.08/1.98 % Time passed: 1455ms (effective reasoning time: 981ms)
% 4.08/1.98 % 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)>
% 4.08/1.98 % Axioms used in derivation (17): end_point_defn, c8, meet_defn, part_of_defn, c9, sum_defn, closed_defn, inner_point_defn, c3, c4, c5, c2, c1, c6, open_defn, c7, between_c_defn
% 4.08/1.98 % No. of inferences in proof: 38
% 4.08/1.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1455 ms resp. 981 ms w/o parsing
% 4.42/2.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.42/2.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------