%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO238+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 : n007.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 07:12:57 AM UTC 2026
% Result : Theorem 5.60s 3.49s
% Output : Refutation 5.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 13
% Syntax : Number of formulae : 28 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 94 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 304 ( 17 ~; 28 |; 16 &; 221 @)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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; 0-3 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(divides_points_decl,type,
divides_points: $i > $i > $i > $o ).
thf(distinct_lines_decl,type,
distinct_lines: $i > $i > $o ).
thf(reverse_line_decl,type,
reverse_line: $i > $i ).
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(apart_point_and_line_decl,type,
apart_point_and_line: $i > $i > $o ).
thf(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
thf(left_apart_point_decl,type,
left_apart_point: $i > $i > $o ).
thf(right_apart_point_decl,type,
right_apart_point: $i > $i > $o ).
thf(7,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_basics) ).
thf(33,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( ( B @ reverse_line @ ( A @ left_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_basics) ).
thf(41,plain,
! [A: $i,B: $i] :
~ ( ( B @ reverse_line @ ( A @ left_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ distinct_lines ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( D @ reverse_line @ ( B @ left_apart_point ) )
| ( D @ reverse_line @ ( A @ left_apart_point ) )
| ( C @ reverse_line @ ( B @ left_apart_point ) )
| ( C @ reverse_line @ ( A @ left_apart_point ) )
| ( D @ ( B @ left_apart_point ) )
| ( D @ ( A @ left_apart_point ) )
| ( C @ ( B @ left_apart_point ) )
| ( C @ ( A @ left_apart_point ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_uniq_cons) ).
thf(39,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ distinct_lines ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( D @ reverse_line @ ( B @ left_apart_point ) )
| ( D @ reverse_line @ ( A @ left_apart_point ) )
| ( C @ reverse_line @ ( B @ left_apart_point ) )
| ( C @ reverse_line @ ( A @ left_apart_point ) )
| ( D @ ( B @ left_apart_point ) )
| ( D @ ( A @ left_apart_point ) )
| ( C @ ( B @ left_apart_point ) )
| ( C @ ( A @ left_apart_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ divides_points ) ) )
<=> ( ( ( C @ ( B @ left_apart_point ) )
& ( C @ ( A @ right_apart_point ) ) )
| ( ( C @ ( B @ right_apart_point ) )
& ( C @ ( A @ left_apart_point ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8_defns) ).
thf(63,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C @ ( B @ left_apart_point ) )
& ( C @ ( A @ right_apart_point ) ) )
| ( ( C @ ( B @ right_apart_point ) )
& ( C @ ( A @ left_apart_point ) ) ) )
=> ( B @ ( A @ ( C @ divides_points ) ) ) )
& ( ( B @ ( A @ ( C @ divides_points ) ) )
=> ( ( ( C @ ( B @ left_apart_point ) )
& ( C @ ( A @ right_apart_point ) ) )
| ( ( C @ ( B @ right_apart_point ) )
& ( C @ ( A @ left_apart_point ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,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(36,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)],[8]) ).
thf(3,axiom,
! [A: $i] :
~ ( A @ reverse_line @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_cons_objs) ).
thf(20,plain,
! [A: $i] :
~ ( A @ reverse_line @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ right_apart_point ) )
<=> ( B @ reverse_line @ ( A @ left_apart_point ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_defns) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( B @ reverse_line @ ( A @ left_apart_point ) )
=> ( B @ ( A @ right_apart_point ) ) )
& ( ( B @ ( A @ right_apart_point ) )
=> ( B @ reverse_line @ ( A @ left_apart_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,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(29,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)],[6]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4_basics) ).
thf(26,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ left_apart_point ) )
=> ( ( C @ ( B @ left_apart_point ) )
| ( B @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_subs) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ left_apart_point ) )
=> ( ( C @ ( B @ left_apart_point ) )
| ( B @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_basics) ).
thf(23,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ apart_point_and_line ) )
<=> ( ( B @ ( A @ right_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_defns) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ right_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) )
=> ( B @ ( A @ apart_point_and_line ) ) )
& ( ( B @ ( A @ apart_point_and_line ) )
=> ( ( B @ ( A @ right_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( D @ divides_points ) ) )
& ( B @ ( A @ ( D @ divides_points ) ) ) )
=> ~ ( C @ ( B @ ( D @ divides_points ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( D @ divides_points ) ) )
& ( B @ ( A @ ( D @ divides_points ) ) ) )
=> ~ ( C @ ( B @ ( D @ divides_points ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( D @ divides_points ) ) )
& ( B @ ( A @ ( D @ divides_points ) ) ) )
=> ~ ( C @ ( B @ ( D @ divides_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(74,plain,
$false,
inference(e,[status(thm)],[33,41,39,63,36,20,57,29,26,55,23,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO238+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.23/0.48 % Computer : n007.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Fri Sep 25 13:07:23 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 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
% 1.44/1.31 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.06/1.60 % [INFO] Parsing done (290ms).
% 2.06/1.62 % [INFO] Running in sequential loop mode.
% 3.03/2.21 % [INFO] eprover registered as external prover.
% 3.03/2.22 % [INFO] Scanning for conjecture ...
% 3.21/2.35 % [INFO] Found a conjecture (or negated_conjecture) and 36 axioms. Running axiom selection ...
% 3.38/2.44 % [INFO] Axiom selection finished. Selected 12 axioms (removed 24 axioms).
% 3.38/2.49 % [INFO] Problem is first-order (TPTP FOF).
% 3.38/2.50 % [INFO] Type checking passed.
% 3.60/2.51 % [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 ...
% 5.60/3.49 % External prover 'e' found a proof!
% 5.60/3.49 % [INFO] Killing All external provers ...
% 5.60/3.49 % Time passed: 2795ms (effective reasoning time: 1860ms)
% 5.60/3.49 % 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)>
% 5.60/3.49 % Axioms used in derivation (12): ax3_basics, ax1_subs, ax8_cons_objs, ax2_basics, ax10_basics, a8_defns, a2_defns, ax4_basics, a6_defns, ax1_basics, ax1_uniq_cons, ax5_cons_objs
% 5.60/3.49 % No. of inferences in proof: 28
% 5.60/3.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2795 ms resp. 1860 ms w/o parsing
% 5.95/3.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.95/3.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------