TSTP Solution File: GEO002-4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO002-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:08:48 EDT 2023
% Result : Unsatisfiable 2.43s 1.62s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 24 ( 7 unt; 7 typ; 0 def)
% Number of atoms : 35 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 176 ( 20 ~; 18 |; 0 &; 138 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 3 con; 0-5 aty)
% Number of variables : 58 ( 0 ^; 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(between_type,type,
between: $i > $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(equidistant_type,type,
equidistant: $i > $i > $i > $i > $o ).
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(outer_pasch_type,type,
outer_pasch: $i > $i > $i > $i > $i > $i ).
thf(extension_type,type,
extension: $i > $i > $i > $i > $i ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
thf(20,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( between @ C @ D @ A )
| ( between @ C @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_substitution3) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( between @ C @ D @ A )
| ( between @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
~ ( between @ a @ a @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
thf(9,plain,
~ ( between @ a @ a @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( equalish @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( equalish @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ C @ E )
| ( between @ E @ B @ ( outer_pasch @ B @ A @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_pasch2) ).
thf(17,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ C @ E )
| ( between @ E @ B @ ( outer_pasch @ B @ A @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ D @ C )
| ( between @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
thf(11,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ D @ C )
| ( between @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ C @ E )
| ( between @ A @ ( outer_pasch @ B @ A @ D @ E @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_pasch1) ).
thf(15,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ C @ E )
| ( between @ A @ ( outer_pasch @ B @ A @ D @ E @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(26,plain,
$false,
inference(e,[status(thm)],[20,21,9,13,17,11,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO002-4 : TPTP v8.1.2. Released v1.1.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.15/0.38 % Computer : n013.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Fri May 19 04:20:36 EDT 2023
% 0.15/0.38 % CPUTime :
% 1.00/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.08/1.00 % [INFO] Parsing done (107ms).
% 1.08/1.00 % [INFO] Running in sequential loop mode.
% 1.67/1.21 % [INFO] eprover registered as external prover.
% 1.67/1.21 % [INFO] cvc4 registered as external prover.
% 1.67/1.21 % [INFO] Scanning for conjecture ...
% 1.72/1.26 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.72/1.27 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.72/1.29 % [INFO] Problem is propositional (TPTP CNF).
% 1.72/1.29 % [INFO] Type checking passed.
% 1.72/1.29 % [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 ...
% 2.43/1.61 % External prover 'e' found a proof!
% 2.43/1.62 % [INFO] Killing All external provers ...
% 2.43/1.62 % Time passed: 1076ms (effective reasoning time: 609ms)
% 2.43/1.62 % 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)>
% 2.43/1.62 % Axioms used in derivation (7): between_substitution3, outer_pasch1, outer_pasch2, segment_construction2, segment_construction1, identity_for_equidistance, transitivity_for_betweeness
% 2.43/1.62 % No. of inferences in proof: 17
% 2.43/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1076 ms resp. 609 ms w/o parsing
% 2.72/1.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.72/1.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------