%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO038-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 : Thu Sep 24 08:39:19 AM UTC 2026
% Result : Unsatisfiable 249.46s 249.88s
% Output : Proof 249.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 33 ( 25 unt; 0 nHn; 30 RR)
% Number of literals : 50 ( 22 equ; 19 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 18 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_equidistance,axiom,
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('GEO002-0.ax',identity_for_equidistance) ).
cnf(segment_construction1,axiom,
between(X,Y,extension(X,Y,W,V)),
file('GEO002-0.ax',segment_construction1) ).
cnf(d1,axiom,
equidistant(U,V,U,V),
file('theBenchmark.p',d1) ).
cnf(y_is_extension,hypothesis,
y = extension(u,v,w,x),
file('theBenchmark.p',y_is_extension) ).
cnf(prove_corollary,negated_conjecture,
~ between(u,v,y),
file('theBenchmark.p',prove_corollary) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_10,axiom,
( between(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ between(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ between(u,v,y),
inference(start,[status(thm),parent(0:0)],[prove_corollary]) ).
cnf(t2,plain,
( extension(u,v,w,x) != y
| ~ between(u,v,extension(u,v,w,x))
| v != v
| u != u
| between(u,v,y) ),
inference(extension,[status(thm),parent(t1:1)],[equality_10]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ equidistant(u,u,u,u)
| u = u ),
inference(extension,[status(thm),parent(t2:2)],[identity_for_equidistance]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
equidistant(u,u,u,u),
inference(extension,[status(thm),parent(t4:2)],[d1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ equidistant(v,v,v,v)
| v = v ),
inference(extension,[status(thm),parent(t2:3)],[identity_for_equidistance]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
equidistant(v,v,v,v),
inference(extension,[status(thm),parent(t8:2)],[d1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( extension(u,v,w,x) != extension(u,v,w,x)
| ~ between(u,v,extension(u,v,w,x))
| v != v
| u != u
| between(u,v,extension(u,v,w,x)) ),
inference(extension,[status(thm),parent(t2:4)],[equality_10]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
u = u,
inference(extension,[status(thm),parent(t12:2)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
v = v,
inference(extension,[status(thm),parent(t12:3)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
between(u,v,extension(u,v,w,x)),
inference(extension,[status(thm),parent(t12:4)],[segment_construction1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:4]) ).
cnf(t20,plain,
extension(u,v,w,x) = extension(u,v,w,x),
inference(extension,[status(thm),parent(t12:5)],[equality_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t12:5]) ).
cnf(t22,plain,
( y != extension(u,v,w,x)
| extension(u,v,w,x) = y ),
inference(extension,[status(thm),parent(t2:5)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:5]) ).
cnf(t24,plain,
y = extension(u,v,w,x),
inference(extension,[status(thm),parent(t22:2)],[y_is_extension]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO038-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.01 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 19 07:14:53 UTC 2026
% 0.02/0.30 % CPUTime :
% 249.46/249.88 % SZS status Unsatisfiable for theBenchmark
% 249.46/249.88 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------