%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO055-2 : 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 : 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 : Thu Sep 24 08:39:22 AM UTC 2026
% Result : Unsatisfiable 1.14s 1.49s
% Output : Proof 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 28 ( 20 unt; 0 nHn; 25 RR)
% Number of literals : 44 ( 18 equ; 18 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 21 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(reflexivity_for_equidistance,axiom,
equidistant(X,Y,Y,X),
file('GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(identity_for_equidistance,axiom,
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('GEO002-0.ax',identity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('GEO002-0.ax',segment_construction2) ).
cnf(reflection,axiom,
reflection(U,V) = extension(U,V,U,V),
file('GEO002-2.ax',reflection) ).
cnf(prove_equidistance,negated_conjecture,
~ equidistant(v,reflection(u,v),u,v),
file('theBenchmark.p',prove_equidistance) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_10,axiom,
( equidistant(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ equidistant(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| 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,
~ equidistant(v,reflection(u,v),u,v),
inference(start,[status(thm),parent(0:0)],[prove_equidistance]) ).
cnf(t2,plain,
( extension(u,v,u,v) != reflection(u,v)
| u != u
| v != v
| ~ equidistant(v,extension(u,v,u,v),u,v)
| v != v
| equidistant(v,reflection(u,v),u,v) ),
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(v,v,v,v)
| v = v ),
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(v,v,v,v),
inference(extension,[status(thm),parent(t4:2)],[reflexivity_for_equidistance]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
equidistant(v,extension(u,v,u,v),u,v),
inference(extension,[status(thm),parent(t2:3)],[segment_construction2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( ~ equidistant(v,v,v,v)
| v = v ),
inference(extension,[status(thm),parent(t2:4)],[identity_for_equidistance]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:4]) ).
cnf(t12,plain,
equidistant(v,v,v,v),
inference(extension,[status(thm),parent(t10:2)],[reflexivity_for_equidistance]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ equidistant(u,u,u,u)
| u = u ),
inference(extension,[status(thm),parent(t2:5)],[identity_for_equidistance]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:5]) ).
cnf(t16,plain,
equidistant(u,u,u,u),
inference(extension,[status(thm),parent(t14:2)],[reflexivity_for_equidistance]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( reflection(u,v) != extension(u,v,u,v)
| extension(u,v,u,v) = reflection(u,v) ),
inference(extension,[status(thm),parent(t2:6)],[equality_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:6]) ).
cnf(t20,plain,
reflection(u,v) = extension(u,v,u,v),
inference(extension,[status(thm),parent(t18:2)],[reflection]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO055-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 07:11:50 UTC 2026
% 0.10/0.38 % CPUTime :
% 1.14/1.49 % SZS status Unsatisfiable for theBenchmark
% 1.14/1.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------