%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO027-3 : 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 : n009.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 08:39:17 AM UTC 2026
% Result : Unsatisfiable 3.45s 3.73s
% Output : Proof 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 17 unt; 2 nHn; 21 RR)
% Number of literals : 35 ( 12 equ; 14 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 : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 18 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(segment_construction2,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('GEO002-0.ax',segment_construction2) ).
cnf(d2,axiom,
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
file('theBenchmark.p',d2) ).
cnf(b0,axiom,
( between(U,V,Y)
| Y != extension(U,V,W,X) ),
file('theBenchmark.p',b0) ).
cnf(d9,axiom,
( W = X
| U = V
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
file('theBenchmark.p',d9) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(u_not_v,hypothesis,
u != v,
file('theBenchmark.p',u_not_v) ).
cnf(prove_w_is_an_extension,negated_conjecture,
w != extension(u,v,v,w),
file('theBenchmark.p',prove_w_is_an_extension) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
u != v,
inference(start,[status(thm),parent(0:0)],[u_not_v]) ).
cnf(t2,plain,
( ~ between(u,v,extension(u,v,v,w))
| ~ equidistant(v,w,v,extension(u,v,v,w))
| w = extension(u,v,v,w)
| ~ between(u,v,w)
| u = v ),
inference(extension,[status(thm),parent(t1:1)],[d9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
between(u,v,w),
inference(extension,[status(thm),parent(t2:2)],[v_between_u_and_w]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
w != extension(u,v,v,w),
inference(extension,[status(thm),parent(t2:3)],[prove_w_is_an_extension]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ equidistant(v,extension(u,v,v,w),v,w)
| equidistant(v,w,v,extension(u,v,v,w)) ),
inference(extension,[status(thm),parent(t2:4)],[d2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
equidistant(v,extension(u,v,v,w),v,w),
inference(extension,[status(thm),parent(t8:2)],[segment_construction2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( extension(u,v,v,w) != extension(u,v,v,w)
| between(u,v,extension(u,v,v,w)) ),
inference(extension,[status(thm),parent(t2:5)],[b0]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:5]) ).
cnf(t14,plain,
extension(u,v,v,w) = extension(u,v,v,w),
inference(extension,[status(thm),parent(t12:2)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO027-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 07:08:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 3.45/3.73 % SZS status Unsatisfiable for theBenchmark
% 3.45/3.73 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------