%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO258+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 07:13:03 AM UTC 2026
% Result : Theorem 6.29s 3.71s
% Output : Refutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 216 ( 8 ~; 5 |; 19 &; 169 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 1 con; 0-4 aty)
% Number of variables : 44 ( 0 ^; 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(between_on_line_decl,type,
between_on_line: $i > $i > $i > $i > $o ).
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(equally_directed_lines_decl,type,
equally_directed_lines: $i > $i > $o ).
thf(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
thf(reverse_line_decl,type,
reverse_line: $i > $i ).
thf(apart_point_and_line_decl,type,
apart_point_and_line: $i > $i > $o ).
thf(before_on_line_decl,type,
before_on_line: $i > $i > $i > $o ).
thf(incident_point_and_line_decl,type,
incident_point_and_line: $i > $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_on_line ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ between_on_line ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_on_line ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ between_on_line ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_on_line ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ between_on_line ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( A @ ( B @ line_connecting ) @ reverse_line @ ( B @ ( A @ line_connecting ) @ equally_directed_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9_cons_objs) ).
thf(14,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( A @ ( B @ line_connecting ) @ reverse_line @ ( B @ ( A @ line_connecting ) @ equally_directed_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_basics) ).
thf(20,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ before_on_line ) ) )
<=> ( ( C @ ( B @ line_connecting ) @ ( A @ equally_directed_lines ) )
& ( A @ ( C @ incident_point_and_line ) )
& ( A @ ( B @ incident_point_and_line ) )
& ( C @ ( B @ distinct_points ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4_defns) ).
thf(28,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ line_connecting ) @ ( A @ equally_directed_lines ) )
& ( A @ ( C @ incident_point_and_line ) )
& ( A @ ( B @ incident_point_and_line ) )
& ( C @ ( B @ distinct_points ) ) )
=> ( C @ ( B @ ( A @ before_on_line ) ) ) )
& ( ( C @ ( B @ ( A @ before_on_line ) ) )
=> ( ( C @ ( B @ line_connecting ) @ ( A @ equally_directed_lines ) )
& ( A @ ( C @ incident_point_and_line ) )
& ( A @ ( B @ incident_point_and_line ) )
& ( C @ ( B @ distinct_points ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
& ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5_cons_objs) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
& ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( A @ equally_directed_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5_basics) ).
thf(23,plain,
! [A: $i] : ( A @ ( A @ equally_directed_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_on_line ) ) ) )
<=> ( ( ( B @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( D @ ( A @ before_on_line ) ) ) )
| ( ( D @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( B @ ( A @ before_on_line ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a9_defns) ).
thf(37,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( B @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( D @ ( A @ before_on_line ) ) ) )
| ( ( D @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( B @ ( A @ before_on_line ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ between_on_line ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ between_on_line ) ) ) )
=> ( ( ( B @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( D @ ( A @ before_on_line ) ) ) )
| ( ( D @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( B @ ( A @ before_on_line ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2_basics) ).
thf(25,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(52,plain,
$false,
inference(e,[status(thm)],[10,14,20,28,16,23,37,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO258+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.23/0.51 % Computer : n010.cluster.edu
% 0.23/0.51 % Model : x86_64 x86_64
% 0.23/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.51 % Memory : 8046.5625MB
% 0.23/0.51 % OS : Linux 6.8.0-71-generic
% 0.23/0.51 % CPULimit : 300
% 0.23/0.51 % WCLimit : 300
% 0.23/0.51 % DateTime : Fri Sep 25 13:11:29 UTC 2026
% 0.23/0.51 % CPUTime :
% 0.23/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.41/1.39 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.16/1.74 % [INFO] Parsing done (340ms).
% 2.16/1.76 % [INFO] Running in sequential loop mode.
% 3.15/2.37 % [INFO] eprover registered as external prover.
% 3.15/2.39 % [INFO] Scanning for conjecture ...
% 3.56/2.54 % [INFO] Found a conjecture (or negated_conjecture) and 36 axioms. Running axiom selection ...
% 3.72/2.63 % [INFO] Axiom selection finished. Selected 7 axioms (removed 29 axioms).
% 3.72/2.67 % [INFO] Problem is first-order (TPTP FOF).
% 3.72/2.68 % [INFO] Type checking passed.
% 3.72/2.69 % [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 ...
% 6.29/3.70 % External prover 'e' found a proof!
% 6.29/3.70 % [INFO] Killing All external provers ...
% 6.29/3.70 % Time passed: 2976ms (effective reasoning time: 1931ms)
% 6.29/3.70 % 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)>
% 6.29/3.71 % Axioms used in derivation (7): ax2_basics, a9_defns, ax4_defns, ax5_basics, ax9_cons_objs, ax1_basics, ax5_cons_objs
% 6.29/3.71 % No. of inferences in proof: 18
% 6.29/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2976 ms resp. 1931 ms w/o parsing
% 6.29/3.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.29/3.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------