%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:11:58 AM UTC 2026
% Result : Unsatisfiable 5.35s 3.16s
% Output : Refutation 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 7 unt; 0 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 : 0 ( 0 >; 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_decl,type,
between: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(equidistant_decl,type,
equidistant: $i > $i > $i > $i > $o ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(outer_pasch_decl,type,
outer_pasch: $i > $i > $i > $i > $i > $i ).
thf(extension_decl,type,
extension: $i > $i > $i > $i > $i ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
thf(20,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ between ) ) )
| ~ ( A @ ( D @ ( C @ between ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_substitution3) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ between ) ) )
| ~ ( A @ ( D @ ( C @ between ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
~ ( b @ ( a @ ( a @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
thf(9,plain,
~ ( b @ ( a @ ( a @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ( A @ ( B @ outer_pasch ) ) ) ) @ ( B @ ( E @ between ) ) )
| ~ ( E @ ( C @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_pasch2) ).
thf(17,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ( A @ ( B @ outer_pasch ) ) ) ) @ ( B @ ( E @ between ) ) )
| ~ ( E @ ( C @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
thf(11,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( A @ ( B @ outer_pasch ) ) ) ) @ ( A @ between ) ) )
| ~ ( E @ ( C @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_pasch1) ).
thf(15,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( A @ ( B @ outer_pasch ) ) ) ) @ ( A @ between ) ) )
| ~ ( E @ ( C @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,plain,
$false,
inference(e,[status(thm)],[20,21,9,13,17,11,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n014.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 12:29:02 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.26/1.24 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.63/1.45 % [INFO] Parsing done (205ms).
% 1.63/1.47 % [INFO] Running in sequential loop mode.
% 2.64/2.08 % [INFO] eprover registered as external prover.
% 2.64/2.09 % [INFO] Scanning for conjecture ...
% 2.95/2.21 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.95/2.24 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.95/2.26 % [INFO] Problem is propositional (TPTP CNF).
% 2.95/2.26 % [INFO] Type checking passed.
% 2.95/2.27 % [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 ...
% 5.35/3.16 % External prover 'e' found a proof!
% 5.35/3.16 % [INFO] Killing All external provers ...
% 5.35/3.16 % Time passed: 2519ms (effective reasoning time: 1682ms)
% 5.35/3.16 % Axioms used in derivation (7): between_substitution3, outer_pasch1, outer_pasch2, segment_construction2, segment_construction1, identity_for_equidistance, transitivity_for_betweeness
% 5.35/3.16 % No. of inferences in proof: 17
% 5.35/3.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2519 ms resp. 1682 ms w/o parsing
% 5.42/3.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.42/3.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------