%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO003-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 08:39:12 AM UTC 2026
% Result : Unsatisfiable 61.26s 61.50s
% Output : Proof 61.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 34 ( 23 unt; 0 nHn; 26 RR)
% Number of literals : 54 ( 14 equ; 22 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 : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 42 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_equidistance,axiom,
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('GEO001-0.ax',identity_for_equidistance) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
file('GEO001-0.ax',transitivity_for_equidistance) ).
cnf(segment_construction1,axiom,
between(X,Y,extension(X,Y,W,V)),
file('GEO001-0.ax',segment_construction1) ).
cnf(segment_construction2,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('GEO001-0.ax',segment_construction2) ).
cnf(prove_b_between_a_and_b,negated_conjecture,
~ between(a,b,b),
file('theBenchmark.p',prove_b_between_a_and_b) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_9,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(a,b,b),
inference(start,[status(thm),parent(0:0)],[prove_b_between_a_and_b]) ).
cnf(t2,plain,
( b != b
| extension(a,b,U_788,U_788) != b
| ~ between(a,b,extension(a,b,U_788,U_788))
| a != a
| between(a,b,b) ),
inference(extension,[status(thm),parent(t1:1)],[equality_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ equidistant(a,a,a,a)
| a = a ),
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_772,extension(U_773,U_772,a,a),a,a)
| ~ equidistant(U_772,extension(U_773,U_772,a,a),a,a)
| equidistant(a,a,a,a) ),
inference(extension,[status(thm),parent(t4:2)],[transitivity_for_equidistance]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
equidistant(U_772,extension(U_773,U_772,a,a),a,a),
inference(extension,[status(thm),parent(t6:2)],[segment_construction2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
equidistant(U_772,extension(U_773,U_772,a,a),a,a),
inference(extension,[status(thm),parent(t6:3)],[segment_construction2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
between(a,b,extension(a,b,U_788,U_788)),
inference(extension,[status(thm),parent(t2:3)],[segment_construction1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
( b != extension(a,b,U_788,U_788)
| extension(a,b,U_788,U_788) = b ),
inference(extension,[status(thm),parent(t2:4)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:4]) ).
cnf(t16,plain,
( ~ equidistant(b,extension(a,b,U_788,U_788),U_788,U_788)
| b = extension(a,b,U_788,U_788) ),
inference(extension,[status(thm),parent(t14:2)],[identity_for_equidistance]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
equidistant(b,extension(a,b,U_788,U_788),U_788,U_788),
inference(extension,[status(thm),parent(t16:2)],[segment_construction2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ equidistant(b,b,b,b)
| b = b ),
inference(extension,[status(thm),parent(t2:5)],[identity_for_equidistance]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:5]) ).
cnf(t22,plain,
( ~ equidistant(U_802,extension(U_803,U_802,b,b),b,b)
| ~ equidistant(U_802,extension(U_803,U_802,b,b),b,b)
| equidistant(b,b,b,b) ),
inference(extension,[status(thm),parent(t20:2)],[transitivity_for_equidistance]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
equidistant(U_802,extension(U_803,U_802,b,b),b,b),
inference(extension,[status(thm),parent(t22:2)],[segment_construction2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
equidistant(U_802,extension(U_803,U_802,b,b),b,b),
inference(extension,[status(thm),parent(t22:3)],[segment_construction2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO003-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n008.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 19 07:18:53 UTC 2026
% 0.07/0.34 % CPUTime :
% 61.26/61.50 % SZS status Unsatisfiable for theBenchmark
% 61.26/61.50 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------