%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO210+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n015.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 07:12:48 AM UTC 2026
% Result : Theorem 6.46s 3.78s
% Output : Refutation 6.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 21
% Syntax : Number of formulae : 44 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 120 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 369 ( 25 ~; 32 |; 13 &; 268 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 109 ( 0 ^; 109 !; 0 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
thf(apart_point_and_line_decl,type,
apart_point_and_line: $i > $i > $o ).
thf(unorthogonal_lines_decl,type,
unorthogonal_lines: $i > $i > $o ).
thf(distinct_lines_decl,type,
distinct_lines: $i > $i > $o ).
thf(orthogonal_through_point_decl,type,
orthogonal_through_point: $i > $i > $i ).
thf(convergent_lines_decl,type,
convergent_lines: $i > $i > $o ).
thf(parallel_through_point_decl,type,
parallel_through_point: $i > $i > $i ).
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
thf(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cup1) ).
thf(88,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(6,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
thf(37,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
thf(85,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
thf(59,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
=> ( ( B @ ( C @ distinct_points ) )
& ( A @ ( C @ distinct_points ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
thf(54,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
=> ( ( B @ ( C @ distinct_points ) )
& ( A @ ( C @ distinct_points ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
thf(48,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ distinct_lines ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).
thf(43,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ distinct_lines ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,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',apart5) ).
thf(82,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)],[19]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( C @ ( A @ apart_point_and_line ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
thf(51,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( C @ ( A @ apart_point_and_line ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
thf(79,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( ( B @ ( C @ apart_point_and_line ) )
| ( A @ ( C @ apart_point_and_line ) ) )
=> ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con2) ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( ( B @ ( C @ apart_point_and_line ) )
| ( A @ ( C @ apart_point_and_line ) ) )
=> ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( B @ ( A @ distinct_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( B @ ( A @ distinct_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
thf(28,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oac1) ).
thf(70,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart6) ).
thf(34,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ouo1) ).
thf(45,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( B @ ( C @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).
thf(67,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( B @ ( C @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,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',apart4) ).
thf(31,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)],[4]) ).
thf(7,axiom,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(40,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ unorthogonal_lines ) )
& ~ ( B @ ( A @ apart_point_and_line ) ) )
=> ~ ( A @ ( C @ orthogonal_through_point ) @ ( B @ distinct_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ unorthogonal_lines ) )
& ~ ( B @ ( A @ apart_point_and_line ) ) )
=> ~ ( A @ ( C @ orthogonal_through_point ) @ ( B @ distinct_lines ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ unorthogonal_lines ) )
& ~ ( B @ ( A @ apart_point_and_line ) ) )
=> ~ ( A @ ( C @ orthogonal_through_point ) @ ( B @ distinct_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(92,plain,
$false,
inference(e,[status(thm)],[88,37,85,77,59,54,48,43,82,51,79,62,90,28,70,34,45,67,31,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO210+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.24/0.48 % Computer : n015.cluster.edu
% 0.24/0.48 % Model : x86_64 x86_64
% 0.24/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.48 % Memory : 8046.5625MB
% 0.24/0.48 % OS : Linux 6.8.0-71-generic
% 0.24/0.48 % CPULimit : 300
% 0.24/0.48 % WCLimit : 300
% 0.24/0.48 % DateTime : Fri Sep 25 13:09:27 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 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
% 1.41/1.37 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.88/1.68 % [INFO] Parsing done (298ms).
% 2.27/1.70 % [INFO] Running in sequential loop mode.
% 3.16/2.30 % [INFO] eprover registered as external prover.
% 3.16/2.31 % [INFO] Scanning for conjecture ...
% 3.35/2.45 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 3.51/2.56 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 3.74/2.63 % [INFO] Problem is first-order (TPTP FOF).
% 3.74/2.64 % [INFO] Type checking passed.
% 3.74/2.65 % [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 ...
% 6.46/3.77 % External prover 'e' found a proof!
% 6.46/3.77 % [INFO] Killing All external provers ...
% 6.46/3.77 % Time passed: 3080ms (effective reasoning time: 2063ms)
% 6.46/3.77 % 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)>
% 6.46/3.78 % Axioms used in derivation (20): con2, ouo1, apart4, ceq2, oac1, apart5, apart1, occu1, con1, apart2, cp2, apart3, ooc1, ceq3, cup1, apart6, ooc2, cp1, ceq1, cu1
% 6.46/3.78 % No. of inferences in proof: 44
% 6.46/3.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3080 ms resp. 2063 ms w/o parsing
% 6.84/3.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.84/3.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------