%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO111-1 : TPTP v9.3.1. Released v2.4.0.
% 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 : n014.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 08:39:31 AM UTC 2026
% Result : Unsatisfiable 47.26s 47.58s
% Output : Proof 47.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 15
% Syntax : Number of clauses : 98 ( 58 unt; 5 nHn; 97 RR)
% Number of literals : 164 ( 22 equ; 61 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 41 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(part_of_defn_1,axiom,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
file('GEO004-0.ax',part_of_defn_1) ).
cnf(end_point_defn_13,axiom,
( incident_c(A,B)
| ~ end_point(A,B) ),
file('GEO004-0.ax',end_point_defn_13) ).
cnf(inner_point_defn_21,axiom,
( incident_c(A,B)
| ~ inner_point(A,B) ),
file('GEO004-0.ax',inner_point_defn_21) ).
cnf(inner_point_defn_22,axiom,
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
file('GEO004-0.ax',inner_point_defn_22) ).
cnf(c9_45,axiom,
( B = A
| incident_c(ax0_sk13(A,B),A)
| incident_c(ax0_sk13(A,B),B) ),
file('GEO004-0.ax',c9_45) ).
cnf(c9_48,axiom,
( B = A
| ~ incident_c(ax0_sk13(A,B),B)
| ~ incident_c(ax0_sk13(A,B),A) ),
file('GEO004-0.ax',c9_48) ).
cnf(between_c_defn_1,axiom,
( B != D
| ~ between_c(A,B,C,D) ),
file('GEO004-1.ax',between_c_defn_1) ).
cnf(between_c_defn_2,axiom,
( part_of(ax1_sk1(D,C,B,A),A)
| ~ between_c(A,B,C,D) ),
file('GEO004-1.ax',between_c_defn_2) ).
cnf(between_c_defn_3,axiom,
( end_point(B,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
file('GEO004-1.ax',between_c_defn_3) ).
cnf(between_c_defn_4,axiom,
( end_point(D,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
file('GEO004-1.ax',between_c_defn_4) ).
cnf(between_c_defn_5,axiom,
( inner_point(C,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
file('GEO004-1.ax',between_c_defn_5) ).
cnf(theorem_3_8_1_77,negated_conjecture,
between_c(sk15,sk16,sk17,sk18),
file('theBenchmark.p',theorem_3_8_1_77) ).
cnf(theorem_3_8_1_78,negated_conjecture,
( sk16 = sk18
| sk17 = sk18
| sk16 = sk17
| ~ incident_c(sk18,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk16,sk15) ),
file('theBenchmark.p',theorem_3_8_1_78) ).
cnf(equality_21,axiom,
( end_point(Eq_y_0,Eq_y_1)
| ~ end_point(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( inner_point(Eq_y_0,Eq_y_1)
| ~ inner_point(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
( ~ incident_c(sk17,sk15)
| ~ incident_c(sk18,sk15)
| sk16 = sk17
| sk17 = sk18
| sk16 = sk18
| ~ incident_c(sk16,sk15) ),
inference(start,[status(thm),parent(0:0)],[theorem_3_8_1_78]) ).
cnf(t2,plain,
( ~ incident_c(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| incident_c(sk16,sk15) ),
inference(extension,[status(thm),parent(t1:1)],[part_of_defn_1]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15) ),
inference(extension,[status(thm),parent(t2:2)],[between_c_defn_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t4:2)],[theorem_3_8_1_77]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t2:3)],[end_point_defn_13]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t8:2)],[between_c_defn_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t10:2)],[theorem_3_8_1_77]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| sk16 != sk18 ),
inference(extension,[status(thm),parent(t1:2)],[between_c_defn_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t1:2]) ).
cnf(t16,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t14:2)],[theorem_3_8_1_77]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ax1_sk1(sk18,sk17,sk16,sk15) != ax1_sk1(sk18,sk17,sk16,sk15)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| inner_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| sk17 != sk18 ),
inference(extension,[status(thm),parent(t1:3)],[equality_22]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t1:3]) ).
cnf(t20,plain,
( ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ inner_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t18:2)],[inner_point_defn_22]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t20:2)],[between_c_defn_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t22:2)],[theorem_3_8_1_77]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t18:3)],[between_c_defn_5]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t18:3]) ).
cnf(t28,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t26:2)],[theorem_3_8_1_77]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( ~ incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15))
| ~ incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15))
| ax1_sk1(sk18,sk17,sk16,sk15) = ax1_sk1(sk18,sk17,sk16,sk15) ),
inference(extension,[status(thm),parent(t18:4)],[c9_48]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t18:4]) ).
cnf(t32,plain,
( ax1_sk1(sk18,sk17,sk16,sk15) = ax1_sk1(sk18,sk17,sk16,sk15)
| incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t30:2)],[c9_45]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
$false,
inference(reduction,[status(thm),parent(t32:2)],[t32:2,t30:2]) ).
cnf(t35,plain,
$false,
inference(reduction,[status(thm),parent(t32:3)],[t32:3,t18:4]) ).
cnf(l16,lemma,
incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15)),
inference(lemma,[status(cth),parent(t30:2),below(t18:4)],[t30:2]) ).
cnf(t36,plain,
incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15)),
inference(lemma_extension,[status(thm),parent(t30:3)],[l16:1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t30:3]) ).
cnf(t38,plain,
( ax1_sk1(sk18,sk17,sk16,sk15) != ax1_sk1(sk18,sk17,sk16,sk15)
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| sk16 != sk17 ),
inference(extension,[status(thm),parent(t1:4)],[equality_21]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t1:4]) ).
cnf(t40,plain,
( ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t38:2)],[inner_point_defn_22]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t40:2)],[between_c_defn_5]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t42:2)],[theorem_3_8_1_77]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t38:3)],[between_c_defn_3]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t38:3]) ).
cnf(t48,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t46:2)],[theorem_3_8_1_77]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
( ~ incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15))
| ~ incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15))
| ax1_sk1(sk18,sk17,sk16,sk15) = ax1_sk1(sk18,sk17,sk16,sk15) ),
inference(extension,[status(thm),parent(t38:4)],[c9_48]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t38:4]) ).
cnf(t52,plain,
( ax1_sk1(sk18,sk17,sk16,sk15) = ax1_sk1(sk18,sk17,sk16,sk15)
| incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t50:2)],[c9_45]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
$false,
inference(reduction,[status(thm),parent(t52:2)],[t52:2,t50:2]) ).
cnf(t55,plain,
$false,
inference(reduction,[status(thm),parent(t52:3)],[t52:3,t38:4]) ).
cnf(l26,lemma,
incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15)),
inference(lemma,[status(cth),parent(t50:2),below(t38:4)],[t50:2]) ).
cnf(t56,plain,
incident_c(ax0_sk13(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)),ax1_sk1(sk18,sk17,sk16,sk15)),
inference(lemma_extension,[status(thm),parent(t50:3)],[l26:1]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t50:3]) ).
cnf(t58,plain,
( ~ incident_c(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| incident_c(sk18,sk15) ),
inference(extension,[status(thm),parent(t1:5)],[part_of_defn_1]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t1:5]) ).
cnf(t60,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15) ),
inference(extension,[status(thm),parent(t58:2)],[between_c_defn_2]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t60:2)],[theorem_3_8_1_77]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
( ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t58:3)],[end_point_defn_13]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t58:3]) ).
cnf(t66,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t64:2)],[between_c_defn_4]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t66:2)],[theorem_3_8_1_77]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
( ~ incident_c(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| incident_c(sk17,sk15) ),
inference(extension,[status(thm),parent(t1:6)],[part_of_defn_1]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t1:6]) ).
cnf(t72,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15) ),
inference(extension,[status(thm),parent(t70:2)],[between_c_defn_2]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t70:2]) ).
cnf(t74,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t72:2)],[theorem_3_8_1_77]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(t76,plain,
( ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t70:3)],[inner_point_defn_21]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t70:3]) ).
cnf(t78,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(extension,[status(thm),parent(t76:2)],[between_c_defn_5]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t76:2]) ).
cnf(t80,plain,
between_c(sk15,sk16,sk17,sk18),
inference(extension,[status(thm),parent(t78:2)],[theorem_3_8_1_77]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t78:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO111-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n014.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 19 07:25:22 UTC 2026
% 0.07/0.36 % CPUTime :
% 47.26/47.58 % SZS status Unsatisfiable for theBenchmark
% 47.26/47.58 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------