%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 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 : n006.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 08:39:11 AM UTC 2026
% Result : Unsatisfiable 258.65s 258.99s
% Output : Proof 258.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 153 ( 108 unt; 0 nHn; 118 RR)
% Number of literals : 232 ( 0 equ; 81 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 170 ( 37 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_for_betweeness,axiom,
( between(X,Y,Z)
| ~ between(Y,Z,V)
| ~ between(X,Y,V) ),
file('theBenchmark.p',transitivity_for_betweeness) ).
cnf(identity_for_equidistance,axiom,
( equalish(X,Y)
| ~ equidistant(X,Y,Z,Z) ),
file('theBenchmark.p',identity_for_equidistance) ).
cnf(outer_pasch1,axiom,
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('theBenchmark.p',outer_pasch1) ).
cnf(outer_pasch2,axiom,
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('theBenchmark.p',outer_pasch2) ).
cnf(segment_construction1,axiom,
between(X,Y,extension(X,Y,W,V)),
file('theBenchmark.p',segment_construction1) ).
cnf(segment_construction2,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('theBenchmark.p',segment_construction2) ).
cnf(between_substitution3,axiom,
( between(W,Z,Y)
| ~ between(W,Z,X)
| ~ equalish(X,Y) ),
file('theBenchmark.p',between_substitution3) ).
cnf(prove_a_between_a_and_b,negated_conjecture,
~ between(a,a,b),
file('theBenchmark.p',prove_a_between_a_and_b) ).
cnf(t1,plain,
~ between(a,a,b),
inference(start,[status(thm),parent(0:0)],[prove_a_between_a_and_b]) ).
cnf(t2,plain,
( ~ between(a,a,outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a))
| ~ between(a,b,outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a))
| between(a,a,b) ),
inference(extension,[status(thm),parent(t1:1)],[transitivity_for_betweeness]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ between(a,b,b)
| ~ between(b,outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b)
| between(a,b,outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a)) ),
inference(extension,[status(thm),parent(t2:2)],[transitivity_for_betweeness]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ between(b,outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),extension(U_4006,b,U_4008,U_4008))
| ~ between(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,extension(U_4006,b,U_4008,U_4008))
| between(b,outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b) ),
inference(extension,[status(thm),parent(t4:2)],[transitivity_for_betweeness]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ between(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,b)
| ~ equalish(b,extension(U_4006,b,U_4008,U_4008))
| between(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,extension(U_4006,b,U_4008,U_4008)) ),
inference(extension,[status(thm),parent(t6:2)],[between_substitution3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ equidistant(b,extension(U_4006,b,U_4008,U_4008),U_4008,U_4008)
| equalish(b,extension(U_4006,b,U_4008,U_4008)) ),
inference(extension,[status(thm),parent(t8:2)],[identity_for_equidistance]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
equidistant(b,extension(U_4006,b,U_4008,U_4008),U_4008,U_4008),
inference(extension,[status(thm),parent(t10:2)],[segment_construction2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ between(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,extension(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,U_4039,U_4039))
| ~ between(b,b,extension(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,U_4039,U_4039))
| between(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,b) ),
inference(extension,[status(thm),parent(t8:3)],[transitivity_for_betweeness]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:3]) ).
cnf(t16,plain,
( ~ between(b,b,b)
| ~ equalish(b,extension(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,U_4039,U_4039))
| between(b,b,extension(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,U_4039,U_4039)) ),
inference(extension,[status(thm),parent(t14:2)],[between_substitution3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ equidistant(b,extension(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,U_4039,U_4039),U_4039,U_4039)
| equalish(b,extension(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,U_4039,U_4039)) ),
inference(extension,[status(thm),parent(t16:2)],[identity_for_equidistance]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
equidistant(b,extension(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,U_4039,U_4039),U_4039,U_4039),
inference(extension,[status(thm),parent(t18:2)],[segment_construction2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ between(b,b,extension(b,b,U_4034,U_4035))
| ~ between(b,b,extension(b,b,U_4034,U_4035))
| between(b,b,b) ),
inference(extension,[status(thm),parent(t16:3)],[transitivity_for_betweeness]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:3]) ).
cnf(t24,plain,
between(b,b,extension(b,b,U_4034,U_4035)),
inference(extension,[status(thm),parent(t22:2)],[segment_construction1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
between(b,b,extension(b,b,U_4034,U_4035)),
inference(extension,[status(thm),parent(t22:3)],[segment_construction1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
between(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,extension(outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),b,U_4039,U_4039)),
inference(extension,[status(thm),parent(t14:3)],[segment_construction1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t14:3]) ).
cnf(t30,plain,
( ~ between(extension(U_4006,b,U_4008,U_4008),a,a)
| ~ between(b,a,a)
| between(b,outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a),extension(U_4006,b,U_4008,U_4008)) ),
inference(extension,[status(thm),parent(t6:3)],[outer_pasch1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t6:3]) ).
cnf(t32,plain,
( ~ between(b,a,extension(b,a,U_4075,U_4075))
| ~ between(a,a,extension(b,a,U_4075,U_4075))
| between(b,a,a) ),
inference(extension,[status(thm),parent(t30:2)],[transitivity_for_betweeness]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( ~ between(a,a,a)
| ~ equalish(a,extension(b,a,U_4075,U_4075))
| between(a,a,extension(b,a,U_4075,U_4075)) ),
inference(extension,[status(thm),parent(t32:2)],[between_substitution3]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( ~ equidistant(a,extension(b,a,U_4075,U_4075),U_4075,U_4075)
| equalish(a,extension(b,a,U_4075,U_4075)) ),
inference(extension,[status(thm),parent(t34:2)],[identity_for_equidistance]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
equidistant(a,extension(b,a,U_4075,U_4075),U_4075,U_4075),
inference(extension,[status(thm),parent(t36:2)],[segment_construction2]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( ~ between(a,a,extension(a,a,U_4070,U_4071))
| ~ between(a,a,extension(a,a,U_4070,U_4071))
| between(a,a,a) ),
inference(extension,[status(thm),parent(t34:3)],[transitivity_for_betweeness]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t34:3]) ).
cnf(t42,plain,
between(a,a,extension(a,a,U_4070,U_4071)),
inference(extension,[status(thm),parent(t40:2)],[segment_construction1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
between(a,a,extension(a,a,U_4070,U_4071)),
inference(extension,[status(thm),parent(t40:3)],[segment_construction1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
between(b,a,extension(b,a,U_4075,U_4075)),
inference(extension,[status(thm),parent(t32:3)],[segment_construction1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t32:3]) ).
cnf(t48,plain,
( ~ between(extension(U_4006,b,U_4008,U_4008),a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4106,U_4106))
| ~ between(a,a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4106,U_4106))
| between(extension(U_4006,b,U_4008,U_4008),a,a) ),
inference(extension,[status(thm),parent(t30:3)],[transitivity_for_betweeness]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t30:3]) ).
cnf(t50,plain,
( ~ between(a,a,a)
| ~ equalish(a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4106,U_4106))
| between(a,a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4106,U_4106)) ),
inference(extension,[status(thm),parent(t48:2)],[between_substitution3]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
( ~ equidistant(a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4106,U_4106),U_4106,U_4106)
| equalish(a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4106,U_4106)) ),
inference(extension,[status(thm),parent(t50:2)],[identity_for_equidistance]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
equidistant(a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4106,U_4106),U_4106,U_4106),
inference(extension,[status(thm),parent(t52:2)],[segment_construction2]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
( ~ between(a,a,extension(a,a,U_4101,U_4102))
| ~ between(a,a,extension(a,a,U_4101,U_4102))
| between(a,a,a) ),
inference(extension,[status(thm),parent(t50:3)],[transitivity_for_betweeness]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t50:3]) ).
cnf(t58,plain,
between(a,a,extension(a,a,U_4101,U_4102)),
inference(extension,[status(thm),parent(t56:2)],[segment_construction1]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
between(a,a,extension(a,a,U_4101,U_4102)),
inference(extension,[status(thm),parent(t56:3)],[segment_construction1]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t56:3]) ).
cnf(t62,plain,
between(extension(U_4006,b,U_4008,U_4008),a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4106,U_4106)),
inference(extension,[status(thm),parent(t48:3)],[segment_construction1]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t48:3]) ).
cnf(t64,plain,
( ~ between(a,b,extension(a,b,U_4156,U_4156))
| ~ between(b,b,extension(a,b,U_4156,U_4156))
| between(a,b,b) ),
inference(extension,[status(thm),parent(t4:3)],[transitivity_for_betweeness]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t4:3]) ).
cnf(t66,plain,
( ~ between(b,b,b)
| ~ equalish(b,extension(a,b,U_4156,U_4156))
| between(b,b,extension(a,b,U_4156,U_4156)) ),
inference(extension,[status(thm),parent(t64:2)],[between_substitution3]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
( ~ equidistant(b,extension(a,b,U_4156,U_4156),U_4156,U_4156)
| equalish(b,extension(a,b,U_4156,U_4156)) ),
inference(extension,[status(thm),parent(t66:2)],[identity_for_equidistance]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
equidistant(b,extension(a,b,U_4156,U_4156),U_4156,U_4156),
inference(extension,[status(thm),parent(t68:2)],[segment_construction2]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t68:2]) ).
cnf(t72,plain,
( ~ between(b,b,extension(b,b,U_4152,U_4152))
| ~ between(b,b,extension(b,b,U_4152,U_4152))
| between(b,b,b) ),
inference(extension,[status(thm),parent(t66:3)],[transitivity_for_betweeness]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t66:3]) ).
cnf(t74,plain,
( ~ between(b,b,b)
| ~ equalish(b,extension(b,b,U_4152,U_4152))
| between(b,b,extension(b,b,U_4152,U_4152)) ),
inference(extension,[status(thm),parent(t72:2)],[between_substitution3]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(t76,plain,
( ~ equidistant(b,extension(b,b,U_4152,U_4152),U_4152,U_4152)
| equalish(b,extension(b,b,U_4152,U_4152)) ),
inference(extension,[status(thm),parent(t74:2)],[identity_for_equidistance]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t74:2]) ).
cnf(t78,plain,
equidistant(b,extension(b,b,U_4152,U_4152),U_4152,U_4152),
inference(extension,[status(thm),parent(t76:2)],[segment_construction2]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t76:2]) ).
cnf(t80,plain,
( ~ between(b,b,extension(b,b,U_4147,U_4148))
| ~ between(b,b,extension(b,b,U_4147,U_4148))
| between(b,b,b) ),
inference(extension,[status(thm),parent(t74:3)],[transitivity_for_betweeness]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t74:3]) ).
cnf(t82,plain,
between(b,b,extension(b,b,U_4147,U_4148)),
inference(extension,[status(thm),parent(t80:2)],[segment_construction1]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t80:2]) ).
cnf(t84,plain,
between(b,b,extension(b,b,U_4147,U_4148)),
inference(extension,[status(thm),parent(t80:3)],[segment_construction1]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t80:3]) ).
cnf(t86,plain,
between(b,b,extension(b,b,U_4152,U_4152)),
inference(extension,[status(thm),parent(t72:3)],[segment_construction1]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t72:3]) ).
cnf(t88,plain,
between(a,b,extension(a,b,U_4156,U_4156)),
inference(extension,[status(thm),parent(t64:3)],[segment_construction1]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t64:3]) ).
cnf(t90,plain,
( ~ between(b,a,a)
| ~ between(extension(U_4006,b,U_4008,U_4008),a,a)
| between(a,a,outer_pasch(a,b,extension(U_4006,b,U_4008,U_4008),a,a)) ),
inference(extension,[status(thm),parent(t2:3)],[outer_pasch2]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t2:3]) ).
cnf(t92,plain,
( ~ between(extension(U_4006,b,U_4008,U_4008),a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4207,U_4207))
| ~ between(a,a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4207,U_4207))
| between(extension(U_4006,b,U_4008,U_4008),a,a) ),
inference(extension,[status(thm),parent(t90:2)],[transitivity_for_betweeness]) ).
cnf(t93,plain,
$false,
inference(connection,[status(thm),parent(t92:1)],[t92:1,t90:2]) ).
cnf(t94,plain,
( ~ between(a,a,a)
| ~ equalish(a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4207,U_4207))
| between(a,a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4207,U_4207)) ),
inference(extension,[status(thm),parent(t92:2)],[between_substitution3]) ).
cnf(t95,plain,
$false,
inference(connection,[status(thm),parent(t94:1)],[t94:1,t92:2]) ).
cnf(t96,plain,
( ~ equidistant(a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4207,U_4207),U_4207,U_4207)
| equalish(a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4207,U_4207)) ),
inference(extension,[status(thm),parent(t94:2)],[identity_for_equidistance]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t94:2]) ).
cnf(t98,plain,
equidistant(a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4207,U_4207),U_4207,U_4207),
inference(extension,[status(thm),parent(t96:2)],[segment_construction2]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t96:2]) ).
cnf(t100,plain,
( ~ between(a,a,extension(U_4189,a,U_4191,U_4191))
| ~ between(a,a,extension(U_4189,a,U_4191,U_4191))
| between(a,a,a) ),
inference(extension,[status(thm),parent(t94:3)],[transitivity_for_betweeness]) ).
cnf(t101,plain,
$false,
inference(connection,[status(thm),parent(t100:1)],[t100:1,t94:3]) ).
cnf(t102,plain,
( ~ between(a,a,a)
| ~ equalish(a,extension(U_4189,a,U_4191,U_4191))
| between(a,a,extension(U_4189,a,U_4191,U_4191)) ),
inference(extension,[status(thm),parent(t100:2)],[between_substitution3]) ).
cnf(t103,plain,
$false,
inference(connection,[status(thm),parent(t102:1)],[t102:1,t100:2]) ).
cnf(t104,plain,
( ~ equidistant(a,extension(U_4189,a,U_4191,U_4191),U_4191,U_4191)
| equalish(a,extension(U_4189,a,U_4191,U_4191)) ),
inference(extension,[status(thm),parent(t102:2)],[identity_for_equidistance]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t102:2]) ).
cnf(t106,plain,
equidistant(a,extension(U_4189,a,U_4191,U_4191),U_4191,U_4191),
inference(extension,[status(thm),parent(t104:2)],[segment_construction2]) ).
cnf(t107,plain,
$false,
inference(connection,[status(thm),parent(t106:1)],[t106:1,t104:2]) ).
cnf(t108,plain,
( ~ between(a,a,extension(a,a,U_4202,U_4203))
| ~ between(a,a,extension(a,a,U_4202,U_4203))
| between(a,a,a) ),
inference(extension,[status(thm),parent(t102:3)],[transitivity_for_betweeness]) ).
cnf(t109,plain,
$false,
inference(connection,[status(thm),parent(t108:1)],[t108:1,t102:3]) ).
cnf(t110,plain,
between(a,a,extension(a,a,U_4202,U_4203)),
inference(extension,[status(thm),parent(t108:2)],[segment_construction1]) ).
cnf(t111,plain,
$false,
inference(connection,[status(thm),parent(t110:1)],[t110:1,t108:2]) ).
cnf(t112,plain,
between(a,a,extension(a,a,U_4202,U_4203)),
inference(extension,[status(thm),parent(t108:3)],[segment_construction1]) ).
cnf(t113,plain,
$false,
inference(connection,[status(thm),parent(t112:1)],[t112:1,t108:3]) ).
cnf(l51,lemma,
between(a,a,extension(U_4189,a,U_4191,U_4191)),
inference(lemma,[status(cth),parent(t100:2),below(t94:3)],[t100:2]) ).
cnf(t114,plain,
between(a,a,extension(U_4189,a,U_4191,U_4191)),
inference(lemma_extension,[status(thm),parent(t100:3)],[l51:1]) ).
cnf(t115,plain,
$false,
inference(connection,[status(thm),parent(t114:1)],[t114:1,t100:3]) ).
cnf(t116,plain,
between(extension(U_4006,b,U_4008,U_4008),a,extension(extension(U_4006,b,U_4008,U_4008),a,U_4207,U_4207)),
inference(extension,[status(thm),parent(t92:3)],[segment_construction1]) ).
cnf(t117,plain,
$false,
inference(connection,[status(thm),parent(t116:1)],[t116:1,t92:3]) ).
cnf(t118,plain,
( ~ between(b,a,extension(b,a,U_4253,U_4253))
| ~ between(a,a,extension(b,a,U_4253,U_4253))
| between(b,a,a) ),
inference(extension,[status(thm),parent(t90:3)],[transitivity_for_betweeness]) ).
cnf(t119,plain,
$false,
inference(connection,[status(thm),parent(t118:1)],[t118:1,t90:3]) ).
cnf(t120,plain,
( ~ between(a,a,a)
| ~ equalish(a,extension(b,a,U_4253,U_4253))
| between(a,a,extension(b,a,U_4253,U_4253)) ),
inference(extension,[status(thm),parent(t118:2)],[between_substitution3]) ).
cnf(t121,plain,
$false,
inference(connection,[status(thm),parent(t120:1)],[t120:1,t118:2]) ).
cnf(t122,plain,
( ~ equidistant(a,extension(b,a,U_4253,U_4253),U_4253,U_4253)
| equalish(a,extension(b,a,U_4253,U_4253)) ),
inference(extension,[status(thm),parent(t120:2)],[identity_for_equidistance]) ).
cnf(t123,plain,
$false,
inference(connection,[status(thm),parent(t122:1)],[t122:1,t120:2]) ).
cnf(t124,plain,
equidistant(a,extension(b,a,U_4253,U_4253),U_4253,U_4253),
inference(extension,[status(thm),parent(t122:2)],[segment_construction2]) ).
cnf(t125,plain,
$false,
inference(connection,[status(thm),parent(t124:1)],[t124:1,t122:2]) ).
cnf(t126,plain,
( ~ between(a,a,extension(U_4235,a,U_4237,U_4237))
| ~ between(a,a,extension(U_4235,a,U_4237,U_4237))
| between(a,a,a) ),
inference(extension,[status(thm),parent(t120:3)],[transitivity_for_betweeness]) ).
cnf(t127,plain,
$false,
inference(connection,[status(thm),parent(t126:1)],[t126:1,t120:3]) ).
cnf(t128,plain,
( ~ between(a,a,a)
| ~ equalish(a,extension(U_4235,a,U_4237,U_4237))
| between(a,a,extension(U_4235,a,U_4237,U_4237)) ),
inference(extension,[status(thm),parent(t126:2)],[between_substitution3]) ).
cnf(t129,plain,
$false,
inference(connection,[status(thm),parent(t128:1)],[t128:1,t126:2]) ).
cnf(t130,plain,
( ~ equidistant(a,extension(U_4235,a,U_4237,U_4237),U_4237,U_4237)
| equalish(a,extension(U_4235,a,U_4237,U_4237)) ),
inference(extension,[status(thm),parent(t128:2)],[identity_for_equidistance]) ).
cnf(t131,plain,
$false,
inference(connection,[status(thm),parent(t130:1)],[t130:1,t128:2]) ).
cnf(t132,plain,
equidistant(a,extension(U_4235,a,U_4237,U_4237),U_4237,U_4237),
inference(extension,[status(thm),parent(t130:2)],[segment_construction2]) ).
cnf(t133,plain,
$false,
inference(connection,[status(thm),parent(t132:1)],[t132:1,t130:2]) ).
cnf(t134,plain,
( ~ between(a,a,extension(a,a,U_4248,U_4249))
| ~ between(a,a,extension(a,a,U_4248,U_4249))
| between(a,a,a) ),
inference(extension,[status(thm),parent(t128:3)],[transitivity_for_betweeness]) ).
cnf(t135,plain,
$false,
inference(connection,[status(thm),parent(t134:1)],[t134:1,t128:3]) ).
cnf(t136,plain,
between(a,a,extension(a,a,U_4248,U_4249)),
inference(extension,[status(thm),parent(t134:2)],[segment_construction1]) ).
cnf(t137,plain,
$false,
inference(connection,[status(thm),parent(t136:1)],[t136:1,t134:2]) ).
cnf(t138,plain,
between(a,a,extension(a,a,U_4248,U_4249)),
inference(extension,[status(thm),parent(t134:3)],[segment_construction1]) ).
cnf(t139,plain,
$false,
inference(connection,[status(thm),parent(t138:1)],[t138:1,t134:3]) ).
cnf(l63,lemma,
between(a,a,extension(U_4235,a,U_4237,U_4237)),
inference(lemma,[status(cth),parent(t126:2),below(t120:3)],[t126:2]) ).
cnf(t140,plain,
between(a,a,extension(U_4235,a,U_4237,U_4237)),
inference(lemma_extension,[status(thm),parent(t126:3)],[l63:1]) ).
cnf(t141,plain,
$false,
inference(connection,[status(thm),parent(t140:1)],[t140:1,t126:3]) ).
cnf(t142,plain,
between(b,a,extension(b,a,U_4253,U_4253)),
inference(extension,[status(thm),parent(t118:3)],[segment_construction1]) ).
cnf(t143,plain,
$false,
inference(connection,[status(thm),parent(t142:1)],[t142:1,t118:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_HRN 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
% 0.09/0.34 % Computer : n006.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 19 07:17:42 UTC 2026
% 0.09/0.34 % CPUTime :
% 258.65/258.99 % SZS status Unsatisfiable for theBenchmark
% 258.65/258.99 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------