%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO147+1 : TPTP v9.3.1. Released v2.4.0.
% 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 : n019.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 08:39:36 AM UTC 2026
% Result : Theorem 30.37s 30.60s
% Output : Proof 30.37s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(part_of_defn,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ),
file('GEO004+0.ax',part_of_defn) ).
fof(sum_defn,axiom,
! [C,C1,C2] :
( C = sum(C1,C2)
<=> ! [Q] :
( incident_c(Q,C)
<=> ( incident_c(Q,C2)
| incident_c(Q,C1) ) ) ),
file('GEO004+0.ax',sum_defn) ).
fof(end_point_defn,axiom,
! [P,C] :
( end_point(P,C)
<=> ( ! [C1,C2] :
( ( incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
=> ( part_of(C2,C1)
| part_of(C1,C2) ) )
& incident_c(P,C) ) ),
file('GEO004+0.ax',end_point_defn) ).
fof(inner_point_defn,axiom,
! [P,C] :
( inner_point(P,C)
<=> ( ~ end_point(P,C)
& incident_c(P,C) ) ),
file('GEO004+0.ax',inner_point_defn) ).
fof(meet_defn,axiom,
! [P,C,C1] :
( meet(P,C,C1)
<=> ( ! [Q] :
( ( incident_c(Q,C1)
& incident_c(Q,C) )
=> ( end_point(Q,C1)
& end_point(Q,C) ) )
& incident_c(P,C1)
& incident_c(P,C) ) ),
file('GEO004+0.ax',meet_defn) ).
fof(closed_defn,axiom,
! [C] :
( closed(C)
<=> ~ ? [P] : end_point(P,C) ),
file('GEO004+0.ax',closed_defn) ).
fof(open_defn,axiom,
! [C] :
( open(C)
<=> ? [P] : end_point(P,C) ),
file('GEO004+0.ax',open_defn) ).
fof(c1,axiom,
! [C,C1] :
( ( C1 != C
& part_of(C1,C) )
=> open(C1) ),
file('GEO004+0.ax',c1) ).
fof(c2,axiom,
! [C,C1,C2,C3] :
( ( ? [P] :
( end_point(P,C3)
& end_point(P,C2)
& end_point(P,C1) )
& part_of(C3,C)
& part_of(C2,C)
& part_of(C1,C) )
=> ( part_of(C3,C1)
| part_of(C1,C3)
| part_of(C2,C1)
| part_of(C1,C2)
| part_of(C3,C2)
| part_of(C2,C3) ) ),
file('GEO004+0.ax',c2) ).
fof(c3,axiom,
! [C] :
? [P] : inner_point(P,C),
file('GEO004+0.ax',c3) ).
fof(c4,axiom,
! [C,P] :
( inner_point(P,C)
=> ? [C1,C2] :
( C = sum(C1,C2)
& meet(P,C1,C2) ) ),
file('GEO004+0.ax',c4) ).
fof(c5,axiom,
! [C,P,Q,R] :
( ( end_point(R,C)
& end_point(Q,C)
& end_point(P,C) )
=> ( Q = R
| P = R
| P = Q ) ),
file('GEO004+0.ax',c5) ).
fof(c6,axiom,
! [C,P] :
( end_point(P,C)
=> ? [Q] :
( P != Q
& end_point(Q,C) ) ),
file('GEO004+0.ax',c6) ).
fof(c7,axiom,
! [C,C1,C2,P] :
( ( C = sum(C1,C2)
& meet(P,C1,C2)
& closed(C) )
=> ! [Q] :
( end_point(Q,C1)
=> meet(Q,C1,C2) ) ),
file('GEO004+0.ax',c7) ).
fof(c8,axiom,
! [C1,C2] :
( ? [P] : meet(P,C1,C2)
=> ? [C] : C = sum(C1,C2) ),
file('GEO004+0.ax',c8) ).
fof(c9,axiom,
! [C,C1] :
( ! [P] :
( incident_c(P,C)
<=> incident_c(P,C1) )
=> C = C1 ),
file('GEO004+0.ax',c9) ).
fof(between_c_defn,axiom,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
<=> ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R ) ),
file('GEO004+1.ax',between_c_defn) ).
fof(between_o_defn,axiom,
! [O,P,Q,R] :
( between_o(O,P,Q,R)
<=> ( ( ordered_by(O,Q,P)
& ordered_by(O,R,Q) )
| ( ordered_by(O,Q,R)
& ordered_by(O,P,Q) ) ) ),
file('GEO004+2.ax',between_o_defn) ).
fof(start_point_defn,axiom,
! [P,O] :
( start_point(P,O)
<=> ( ! [Q] :
( ( incident_o(Q,O)
& P != Q )
=> ordered_by(O,P,Q) )
& incident_o(P,O) ) ),
file('GEO004+2.ax',start_point_defn) ).
fof(finish_point_defn,axiom,
! [P,O] :
( finish_point(P,O)
<=> ( ! [Q] :
( ( incident_o(Q,O)
& P != Q )
=> ordered_by(O,Q,P) )
& incident_o(P,O) ) ),
file('GEO004+2.ax',finish_point_defn) ).
fof(o1,axiom,
! [O,P,Q] :
( ordered_by(O,P,Q)
=> ( incident_o(Q,O)
& incident_o(P,O) ) ),
file('GEO004+2.ax',o1) ).
fof(o2,axiom,
! [O] :
? [C] :
( ! [P] :
( incident_o(P,O)
<=> incident_c(P,C) )
& open(C) ),
file('GEO004+2.ax',o2) ).
fof(o3,axiom,
! [P,Q,R,O] :
( between_o(O,P,Q,R)
<=> ? [C] :
( between_c(C,P,Q,R)
& ! [P] :
( incident_o(P,O)
<=> incident_c(P,C) ) ) ),
file('GEO004+2.ax',o3) ).
fof(o4,axiom,
! [O] :
? [P] : start_point(P,O),
file('GEO004+2.ax',o4) ).
fof(o5,axiom,
! [P,Q,C] :
( ( incident_c(Q,C)
& incident_c(P,C)
& P != Q
& open(C) )
=> ? [O] :
( ordered_by(O,P,Q)
& ! [R] :
( incident_o(R,O)
<=> incident_c(R,C) ) ) ),
file('GEO004+2.ax',o5) ).
fof(o6,axiom,
! [O1,O2] :
( ! [P,Q] :
( ordered_by(O1,P,Q)
<=> ordered_by(O2,P,Q) )
=> O1 = O2 ),
file('GEO004+2.ax',o6) ).
fof(underlying_curve_defn,axiom,
! [C,O] :
( C = underlying_curve(O)
<=> ! [P] :
( incident_o(P,O)
<=> incident_c(P,C) ) ),
file('GEO004+2.ax',underlying_curve_defn) ).
fof(connect_defn,axiom,
! [X,Y,P] :
( connect(X,Y,P)
<=> once(at_the_same_time(at(X,P),at(Y,P))) ),
file('GEO004+3.ax',connect_defn) ).
fof(symmetry_of_at_the_same_time,axiom,
! [A,B] :
( once(at_the_same_time(A,B))
<=> once(at_the_same_time(B,A)) ),
file('GEO004+3.ax',symmetry_of_at_the_same_time) ).
fof(assciativity_of_at_the_same_time,axiom,
! [A,B,C] :
( once(at_the_same_time(at_the_same_time(A,B),C))
<=> once(at_the_same_time(A,at_the_same_time(B,C))) ),
file('GEO004+3.ax',assciativity_of_at_the_same_time) ).
fof(idempotence_of_at_the_same_time,axiom,
! [A] :
( once(A)
=> once(at_the_same_time(A,A)) ),
file('GEO004+3.ax',idempotence_of_at_the_same_time) ).
fof(conjunction_at_the_same_time,axiom,
! [A,B] :
( once(at_the_same_time(A,B))
=> ( once(B)
& once(A) ) ),
file('GEO004+3.ax',conjunction_at_the_same_time) ).
fof(at_on_trajectory,axiom,
! [X,P] :
( once(at(X,P))
<=> incident_o(P,trajectory_of(X)) ),
file('GEO004+3.ax',at_on_trajectory) ).
fof(trajectories_are_oriented_curves,axiom,
! [X] :
? [O] : trajectory_of(X) = O,
file('GEO004+3.ax',trajectories_are_oriented_curves) ).
fof(homogeneous_behaviour,axiom,
! [P1,P2,Q1,Q2,X,Y] :
( ( once(at_the_same_time(at(X,Q1),at(Y,Q2)))
& once(at_the_same_time(at(X,P1),at(Y,P2))) )
=> ~ ( ordered_by(trajectory_of(Y),Q2,P2)
& ordered_by(trajectory_of(X),P1,Q1) ) ),
file('GEO004+3.ax',homogeneous_behaviour) ).
fof(localization,axiom,
! [A] :
( once(A)
=> ! [X] :
? [P] : once(at_the_same_time(A,at(X,P))) ),
file('GEO004+3.ax',localization) ).
fof(t13,conjecture,
! [P,X,Y] :
( connect(X,Y,P)
=> ( incident_o(P,trajectory_of(Y))
& incident_o(P,trajectory_of(X)) ) ),
file('theBenchmark.p',t13) ).
fof(f_1_1,plain,
! [C,C1] :
( ( part_of(C1,C)
| ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) )
& ( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(fof_nnf,[status(thm)],[part_of_defn]) ).
fof(f_1_2,plain,
! [U_3,U_2] :
( ( part_of(U_2,U_3)
| ? [U_1] :
( ~ incident_c(U_1,U_3)
& incident_c(U_1,U_2) ) )
& ( ! [U_0] :
( incident_c(U_0,U_3)
| ~ incident_c(U_0,U_2) )
| ~ part_of(U_2,U_3) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_7,U_5] :
( part_of(U_5,U_7)
| ? [U_1] :
( ~ incident_c(U_1,U_7)
& incident_c(U_1,U_5) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( incident_c(U_0,U_6)
| ~ incident_c(U_0,U_4) )
| ~ part_of(U_4,U_6) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_7,U_5] :
( part_of(U_5,U_7)
| ( ~ incident_c(sK1(U_7,U_5),U_7)
& incident_c(sK1(U_7,U_5),U_5) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( incident_c(U_0,U_6)
| ~ incident_c(U_0,U_4) )
| ~ part_of(U_4,U_6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1(U_7,U_5))],[f_1_3]) ).
fof(f_1_5,plain,
( ! [U_7,U_5] :
( ~ incident_c(sK1(U_7,U_5),U_7)
| ~ sP0(U_7,U_5) )
& ! [U_7,U_5] :
( incident_c(sK1(U_7,U_5),U_5)
| ~ sP0(U_7,U_5) )
& ! [U_7,U_5] :
( part_of(U_5,U_7)
| sP0(U_7,U_5) )
& ! [U_6,U_4,U_0] :
( incident_c(U_0,U_6)
| ~ incident_c(U_0,U_4)
| ~ part_of(U_4,U_6) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_1_4]) ).
cnf(f_1_6,plain,
( incident_c(U_0,U_6)
| ~ incident_c(U_0,U_4)
| ~ part_of(U_4,U_6) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_7,plain,
( part_of(U_5,U_7)
| sP0(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_8,plain,
( incident_c(sK1(U_7,U_5),U_5)
| ~ sP0(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_9,plain,
( ~ incident_c(sK1(U_7,U_5),U_7)
| ~ sP0(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_5]) ).
fof(f_2_1,plain,
! [C,C1,C2] :
( ( C = sum(C1,C2)
| ? [Q] :
( ( ~ incident_c(Q,C)
& ( incident_c(Q,C2)
| incident_c(Q,C1) ) )
| ( ~ incident_c(Q,C2)
& ~ incident_c(Q,C1)
& incident_c(Q,C) ) ) )
& ( ! [Q] :
( ( incident_c(Q,C)
| ( ~ incident_c(Q,C2)
& ~ incident_c(Q,C1) ) )
& ( incident_c(Q,C2)
| incident_c(Q,C1)
| ~ incident_c(Q,C) ) )
| C != sum(C1,C2) ) ),
inference(fof_nnf,[status(thm)],[sum_defn]) ).
fof(f_2_2,plain,
! [U_12,U_11,U_10] :
( ( U_12 = sum(U_11,U_10)
| ? [U_9] :
( ( ~ incident_c(U_9,U_12)
& ( incident_c(U_9,U_10)
| incident_c(U_9,U_11) ) )
| ( ~ incident_c(U_9,U_10)
& ~ incident_c(U_9,U_11)
& incident_c(U_9,U_12) ) ) )
& ( ! [U_8] :
( ( incident_c(U_8,U_12)
| ( ~ incident_c(U_8,U_10)
& ~ incident_c(U_8,U_11) ) )
& ( incident_c(U_8,U_10)
| incident_c(U_8,U_11)
| ~ incident_c(U_8,U_12) ) )
| U_12 != sum(U_11,U_10) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_22,U_20,U_18] :
( U_22 = sum(U_20,U_18)
| ? [U_16] :
( ~ incident_c(U_16,U_22)
& ( incident_c(U_16,U_18)
| incident_c(U_16,U_20) ) )
| ? [U_15] :
( ~ incident_c(U_15,U_18)
& ~ incident_c(U_15,U_20)
& incident_c(U_15,U_22) ) )
& ! [U_21,U_19,U_17] :
( ( ! [U_14] :
( incident_c(U_14,U_21)
| ( ~ incident_c(U_14,U_17)
& ~ incident_c(U_14,U_19) ) )
& ! [U_13] :
( incident_c(U_13,U_17)
| incident_c(U_13,U_19)
| ~ incident_c(U_13,U_21) ) )
| U_21 != sum(U_19,U_17) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_22,U_20,U_18] :
( U_22 = sum(U_20,U_18)
| ? [U_16] :
( ~ incident_c(U_16,U_22)
& ( incident_c(U_16,U_18)
| incident_c(U_16,U_20) ) )
| ( ~ incident_c(sK2(U_22,U_20,U_18),U_18)
& ~ incident_c(sK2(U_22,U_20,U_18),U_20)
& incident_c(sK2(U_22,U_20,U_18),U_22) ) )
& ! [U_21,U_19,U_17] :
( ( ! [U_14] :
( incident_c(U_14,U_21)
| ( ~ incident_c(U_14,U_17)
& ~ incident_c(U_14,U_19) ) )
& ! [U_13] :
( incident_c(U_13,U_17)
| incident_c(U_13,U_19)
| ~ incident_c(U_13,U_21) ) )
| U_21 != sum(U_19,U_17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_22,U_20,U_18))],[f_2_3]) ).
fof(f_2_5,plain,
( ! [U_22,U_20,U_18] :
( U_22 = sum(U_20,U_18)
| ( ~ incident_c(sK3(U_22,U_20,U_18),U_22)
& ( incident_c(sK3(U_22,U_20,U_18),U_18)
| incident_c(sK3(U_22,U_20,U_18),U_20) ) )
| ( ~ incident_c(sK2(U_22,U_20,U_18),U_18)
& ~ incident_c(sK2(U_22,U_20,U_18),U_20)
& incident_c(sK2(U_22,U_20,U_18),U_22) ) )
& ! [U_21,U_19,U_17] :
( ( ! [U_14] :
( incident_c(U_14,U_21)
| ( ~ incident_c(U_14,U_17)
& ~ incident_c(U_14,U_19) ) )
& ! [U_13] :
( incident_c(U_13,U_17)
| incident_c(U_13,U_19)
| ~ incident_c(U_13,U_21) ) )
| U_21 != sum(U_19,U_17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_16,sK3(U_22,U_20,U_18))],[f_2_4]) ).
fof(f_2_6,plain,
( ! [U_18,U_20,U_22] :
( ~ incident_c(sK3(U_22,U_20,U_18),U_22)
| ~ sP4(U_18,U_20,U_22) )
& ! [U_18,U_20,U_22] :
( incident_c(sK3(U_22,U_20,U_18),U_18)
| incident_c(sK3(U_22,U_20,U_18),U_20)
| ~ sP4(U_18,U_20,U_22) )
& ! [U_18,U_20,U_22] :
( ~ incident_c(sK2(U_22,U_20,U_18),U_18)
| ~ sP3(U_18,U_20,U_22) )
& ! [U_18,U_20,U_22] :
( ~ incident_c(sK2(U_22,U_20,U_18),U_20)
| ~ sP3(U_18,U_20,U_22) )
& ! [U_18,U_20,U_22] :
( incident_c(sK2(U_22,U_20,U_18),U_22)
| ~ sP3(U_18,U_20,U_22) )
& ! [U_17,U_14,U_19] :
( ~ incident_c(U_14,U_17)
| ~ sP1(U_17,U_14,U_19) )
& ! [U_17,U_14,U_19] :
( ~ incident_c(U_14,U_19)
| ~ sP1(U_17,U_14,U_19) )
& ! [U_17,U_13,U_21,U_14,U_19] :
( incident_c(U_14,U_21)
| sP1(U_17,U_14,U_19)
| ~ sP2(U_17,U_13,U_21,U_14,U_19) )
& ! [U_17,U_13,U_21,U_14,U_19] :
( incident_c(U_13,U_17)
| incident_c(U_13,U_19)
| ~ incident_c(U_13,U_21)
| ~ sP2(U_17,U_13,U_21,U_14,U_19) )
& ! [U_18,U_20,U_22] :
( U_22 = sum(U_20,U_18)
| sP4(U_18,U_20,U_22)
| sP3(U_18,U_20,U_22) )
& ! [U_17,U_13,U_21,U_14,U_19] :
( sP2(U_17,U_13,U_21,U_14,U_19)
| U_21 != sum(U_19,U_17) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2,sP3,sP4])],[f_2_5]) ).
cnf(f_2_7,plain,
( sP2(U_17,U_13,U_21,U_14,U_19)
| U_21 != sum(U_19,U_17) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_8,plain,
( U_22 = sum(U_20,U_18)
| sP4(U_18,U_20,U_22)
| sP3(U_18,U_20,U_22) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_9,plain,
( incident_c(U_13,U_17)
| incident_c(U_13,U_19)
| ~ incident_c(U_13,U_21)
| ~ sP2(U_17,U_13,U_21,U_14,U_19) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_10,plain,
( incident_c(U_14,U_21)
| sP1(U_17,U_14,U_19)
| ~ sP2(U_17,U_13,U_21,U_14,U_19) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_11,plain,
( ~ incident_c(U_14,U_19)
| ~ sP1(U_17,U_14,U_19) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_12,plain,
( ~ incident_c(U_14,U_17)
| ~ sP1(U_17,U_14,U_19) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_13,plain,
( incident_c(sK2(U_22,U_20,U_18),U_22)
| ~ sP3(U_18,U_20,U_22) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_14,plain,
( ~ incident_c(sK2(U_22,U_20,U_18),U_20)
| ~ sP3(U_18,U_20,U_22) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_15,plain,
( ~ incident_c(sK2(U_22,U_20,U_18),U_18)
| ~ sP3(U_18,U_20,U_22) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_16,plain,
( incident_c(sK3(U_22,U_20,U_18),U_18)
| incident_c(sK3(U_22,U_20,U_18),U_20)
| ~ sP4(U_18,U_20,U_22) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_17,plain,
( ~ incident_c(sK3(U_22,U_20,U_18),U_22)
| ~ sP4(U_18,U_20,U_22) ),
inference(clausify,[status(thm)],[f_2_6]) ).
fof(f_3_1,plain,
! [P,C] :
( ( end_point(P,C)
| ? [C1,C2] :
( ~ part_of(C2,C1)
& ~ part_of(C1,C2)
& incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
| ~ incident_c(P,C) )
& ( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(fof_nnf,[status(thm)],[end_point_defn]) ).
fof(f_3_2,plain,
! [U_28,U_27] :
( ( end_point(U_28,U_27)
| ? [U_26,U_25] :
( ~ part_of(U_25,U_26)
& ~ part_of(U_26,U_25)
& incident_c(U_28,U_25)
& incident_c(U_28,U_26)
& part_of(U_25,U_27)
& part_of(U_26,U_27) )
| ~ incident_c(U_28,U_27) )
& ( ( ! [U_24,U_23] :
( part_of(U_23,U_24)
| part_of(U_24,U_23)
| ~ incident_c(U_28,U_23)
| ~ incident_c(U_28,U_24)
| ~ part_of(U_23,U_27)
| ~ part_of(U_24,U_27) )
& incident_c(U_28,U_27) )
| ~ end_point(U_28,U_27) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_32,U_30] :
( end_point(U_32,U_30)
| ? [U_26,U_25] :
( ~ part_of(U_25,U_26)
& ~ part_of(U_26,U_25)
& incident_c(U_32,U_25)
& incident_c(U_32,U_26)
& part_of(U_25,U_30)
& part_of(U_26,U_30) )
| ~ incident_c(U_32,U_30) )
& ! [U_31,U_29] :
( ( ! [U_24,U_23] :
( part_of(U_23,U_24)
| part_of(U_24,U_23)
| ~ incident_c(U_31,U_23)
| ~ incident_c(U_31,U_24)
| ~ part_of(U_23,U_29)
| ~ part_of(U_24,U_29) )
& incident_c(U_31,U_29) )
| ~ end_point(U_31,U_29) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_32,U_30] :
( end_point(U_32,U_30)
| ? [U_25] :
( ~ part_of(U_25,sK4(U_32,U_30))
& ~ part_of(sK4(U_32,U_30),U_25)
& incident_c(U_32,U_25)
& incident_c(U_32,sK4(U_32,U_30))
& part_of(U_25,U_30)
& part_of(sK4(U_32,U_30),U_30) )
| ~ incident_c(U_32,U_30) )
& ! [U_31,U_29] :
( ( ! [U_24,U_23] :
( part_of(U_23,U_24)
| part_of(U_24,U_23)
| ~ incident_c(U_31,U_23)
| ~ incident_c(U_31,U_24)
| ~ part_of(U_23,U_29)
| ~ part_of(U_24,U_29) )
& incident_c(U_31,U_29) )
| ~ end_point(U_31,U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4(U_32,U_30))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_32,U_30] :
( end_point(U_32,U_30)
| ( ~ part_of(sK5(U_32,U_30),sK4(U_32,U_30))
& ~ part_of(sK4(U_32,U_30),sK5(U_32,U_30))
& incident_c(U_32,sK5(U_32,U_30))
& incident_c(U_32,sK4(U_32,U_30))
& part_of(sK5(U_32,U_30),U_30)
& part_of(sK4(U_32,U_30),U_30) )
| ~ incident_c(U_32,U_30) )
& ! [U_31,U_29] :
( ( ! [U_24,U_23] :
( part_of(U_23,U_24)
| part_of(U_24,U_23)
| ~ incident_c(U_31,U_23)
| ~ incident_c(U_31,U_24)
| ~ part_of(U_23,U_29)
| ~ part_of(U_24,U_29) )
& incident_c(U_31,U_29) )
| ~ end_point(U_31,U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_25,sK5(U_32,U_30))],[f_3_4]) ).
fof(f_3_6,plain,
( ! [U_30,U_32] :
( ~ part_of(sK5(U_32,U_30),sK4(U_32,U_30))
| ~ sP6(U_30,U_32) )
& ! [U_30,U_32] :
( ~ part_of(sK4(U_32,U_30),sK5(U_32,U_30))
| ~ sP6(U_30,U_32) )
& ! [U_30,U_32] :
( incident_c(U_32,sK5(U_32,U_30))
| ~ sP6(U_30,U_32) )
& ! [U_30,U_32] :
( incident_c(U_32,sK4(U_32,U_30))
| ~ sP6(U_30,U_32) )
& ! [U_30,U_32] :
( part_of(sK5(U_32,U_30),U_30)
| ~ sP6(U_30,U_32) )
& ! [U_30,U_32] :
( part_of(sK4(U_32,U_30),U_30)
| ~ sP6(U_30,U_32) )
& ! [U_31,U_24,U_23,U_29] :
( part_of(U_23,U_24)
| part_of(U_24,U_23)
| ~ incident_c(U_31,U_23)
| ~ incident_c(U_31,U_24)
| ~ part_of(U_23,U_29)
| ~ part_of(U_24,U_29)
| ~ sP5(U_31,U_24,U_23,U_29) )
& ! [U_31,U_24,U_23,U_29] :
( incident_c(U_31,U_29)
| ~ sP5(U_31,U_24,U_23,U_29) )
& ! [U_30,U_32] :
( end_point(U_32,U_30)
| sP6(U_30,U_32)
| ~ incident_c(U_32,U_30) )
& ! [U_31,U_24,U_23,U_29] :
( sP5(U_31,U_24,U_23,U_29)
| ~ end_point(U_31,U_29) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5,sP6])],[f_3_5]) ).
cnf(f_3_7,plain,
( sP5(U_31,U_24,U_23,U_29)
| ~ end_point(U_31,U_29) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_8,plain,
( end_point(U_32,U_30)
| sP6(U_30,U_32)
| ~ incident_c(U_32,U_30) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_9,plain,
( incident_c(U_31,U_29)
| ~ sP5(U_31,U_24,U_23,U_29) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_10,plain,
( part_of(U_23,U_24)
| part_of(U_24,U_23)
| ~ incident_c(U_31,U_23)
| ~ incident_c(U_31,U_24)
| ~ part_of(U_23,U_29)
| ~ part_of(U_24,U_29)
| ~ sP5(U_31,U_24,U_23,U_29) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_11,plain,
( part_of(sK4(U_32,U_30),U_30)
| ~ sP6(U_30,U_32) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_12,plain,
( part_of(sK5(U_32,U_30),U_30)
| ~ sP6(U_30,U_32) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_13,plain,
( incident_c(U_32,sK4(U_32,U_30))
| ~ sP6(U_30,U_32) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_14,plain,
( incident_c(U_32,sK5(U_32,U_30))
| ~ sP6(U_30,U_32) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_15,plain,
( ~ part_of(sK4(U_32,U_30),sK5(U_32,U_30))
| ~ sP6(U_30,U_32) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_16,plain,
( ~ part_of(sK5(U_32,U_30),sK4(U_32,U_30))
| ~ sP6(U_30,U_32) ),
inference(clausify,[status(thm)],[f_3_6]) ).
fof(f_4_1,plain,
! [P,C] :
( ( inner_point(P,C)
| end_point(P,C)
| ~ incident_c(P,C) )
& ( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(fof_nnf,[status(thm)],[inner_point_defn]) ).
fof(f_4_2,plain,
! [U_34,U_33] :
( ( inner_point(U_34,U_33)
| end_point(U_34,U_33)
| ~ incident_c(U_34,U_33) )
& ( ( ~ end_point(U_34,U_33)
& incident_c(U_34,U_33) )
| ~ inner_point(U_34,U_33) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_38,U_36] :
( inner_point(U_38,U_36)
| end_point(U_38,U_36)
| ~ incident_c(U_38,U_36) )
& ! [U_37,U_35] :
( ( ~ end_point(U_37,U_35)
& incident_c(U_37,U_35) )
| ~ inner_point(U_37,U_35) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_35,U_37] :
( ~ end_point(U_37,U_35)
| ~ sP7(U_35,U_37) )
& ! [U_35,U_37] :
( incident_c(U_37,U_35)
| ~ sP7(U_35,U_37) )
& ! [U_36,U_38] :
( inner_point(U_38,U_36)
| end_point(U_38,U_36)
| ~ incident_c(U_38,U_36) )
& ! [U_35,U_37] :
( sP7(U_35,U_37)
| ~ inner_point(U_37,U_35) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_4_3]) ).
cnf(f_4_5,plain,
( sP7(U_35,U_37)
| ~ inner_point(U_37,U_35) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( inner_point(U_38,U_36)
| end_point(U_38,U_36)
| ~ incident_c(U_38,U_36) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( incident_c(U_37,U_35)
| ~ sP7(U_35,U_37) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_8,plain,
( ~ end_point(U_37,U_35)
| ~ sP7(U_35,U_37) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
! [P,C,C1] :
( ( meet(P,C,C1)
| ? [Q] :
( ( ~ end_point(Q,C1)
| ~ end_point(Q,C) )
& incident_c(Q,C1)
& incident_c(Q,C) )
| ~ incident_c(P,C1)
| ~ incident_c(P,C) )
& ( ( ! [Q] :
( ( end_point(Q,C1)
& end_point(Q,C) )
| ~ incident_c(Q,C1)
| ~ incident_c(Q,C) )
& incident_c(P,C1)
& incident_c(P,C) )
| ~ meet(P,C,C1) ) ),
inference(fof_nnf,[status(thm)],[meet_defn]) ).
fof(f_5_2,plain,
! [U_43,U_42,U_41] :
( ( meet(U_43,U_42,U_41)
| ? [U_40] :
( ( ~ end_point(U_40,U_41)
| ~ end_point(U_40,U_42) )
& incident_c(U_40,U_41)
& incident_c(U_40,U_42) )
| ~ incident_c(U_43,U_41)
| ~ incident_c(U_43,U_42) )
& ( ( ! [U_39] :
( ( end_point(U_39,U_41)
& end_point(U_39,U_42) )
| ~ incident_c(U_39,U_41)
| ~ incident_c(U_39,U_42) )
& incident_c(U_43,U_41)
& incident_c(U_43,U_42) )
| ~ meet(U_43,U_42,U_41) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_49,U_47,U_45] :
( meet(U_49,U_47,U_45)
| ? [U_40] :
( ( ~ end_point(U_40,U_45)
| ~ end_point(U_40,U_47) )
& incident_c(U_40,U_45)
& incident_c(U_40,U_47) )
| ~ incident_c(U_49,U_45)
| ~ incident_c(U_49,U_47) )
& ! [U_48,U_46,U_44] :
( ( ! [U_39] :
( ( end_point(U_39,U_44)
& end_point(U_39,U_46) )
| ~ incident_c(U_39,U_44)
| ~ incident_c(U_39,U_46) )
& incident_c(U_48,U_44)
& incident_c(U_48,U_46) )
| ~ meet(U_48,U_46,U_44) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_49,U_47,U_45] :
( meet(U_49,U_47,U_45)
| ( ( ~ end_point(sK6(U_49,U_47,U_45),U_45)
| ~ end_point(sK6(U_49,U_47,U_45),U_47) )
& incident_c(sK6(U_49,U_47,U_45),U_45)
& incident_c(sK6(U_49,U_47,U_45),U_47) )
| ~ incident_c(U_49,U_45)
| ~ incident_c(U_49,U_47) )
& ! [U_48,U_46,U_44] :
( ( ! [U_39] :
( ( end_point(U_39,U_44)
& end_point(U_39,U_46) )
| ~ incident_c(U_39,U_44)
| ~ incident_c(U_39,U_46) )
& incident_c(U_48,U_44)
& incident_c(U_48,U_46) )
| ~ meet(U_48,U_46,U_44) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_40,sK6(U_49,U_47,U_45))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_47,U_49,U_45] :
( ~ end_point(sK6(U_49,U_47,U_45),U_45)
| ~ end_point(sK6(U_49,U_47,U_45),U_47)
| ~ sP10(U_47,U_49,U_45) )
& ! [U_47,U_49,U_45] :
( incident_c(sK6(U_49,U_47,U_45),U_45)
| ~ sP10(U_47,U_49,U_45) )
& ! [U_47,U_49,U_45] :
( incident_c(sK6(U_49,U_47,U_45),U_47)
| ~ sP10(U_47,U_49,U_45) )
& ! [U_46,U_44,U_39] :
( end_point(U_39,U_44)
| ~ sP8(U_46,U_44,U_39) )
& ! [U_46,U_44,U_39] :
( end_point(U_39,U_46)
| ~ sP8(U_46,U_44,U_39) )
& ! [U_48,U_46,U_44,U_39] :
( sP8(U_46,U_44,U_39)
| ~ incident_c(U_39,U_44)
| ~ incident_c(U_39,U_46)
| ~ sP9(U_48,U_46,U_44,U_39) )
& ! [U_48,U_46,U_44,U_39] :
( incident_c(U_48,U_44)
| ~ sP9(U_48,U_46,U_44,U_39) )
& ! [U_48,U_46,U_44,U_39] :
( incident_c(U_48,U_46)
| ~ sP9(U_48,U_46,U_44,U_39) )
& ! [U_47,U_49,U_45] :
( meet(U_49,U_47,U_45)
| sP10(U_47,U_49,U_45)
| ~ incident_c(U_49,U_45)
| ~ incident_c(U_49,U_47) )
& ! [U_48,U_46,U_44,U_39] :
( sP9(U_48,U_46,U_44,U_39)
| ~ meet(U_48,U_46,U_44) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8,sP9,sP10])],[f_5_4]) ).
cnf(f_5_6,plain,
( sP9(U_48,U_46,U_44,U_39)
| ~ meet(U_48,U_46,U_44) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( meet(U_49,U_47,U_45)
| sP10(U_47,U_49,U_45)
| ~ incident_c(U_49,U_45)
| ~ incident_c(U_49,U_47) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( incident_c(U_48,U_46)
| ~ sP9(U_48,U_46,U_44,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( incident_c(U_48,U_44)
| ~ sP9(U_48,U_46,U_44,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_10,plain,
( sP8(U_46,U_44,U_39)
| ~ incident_c(U_39,U_44)
| ~ incident_c(U_39,U_46)
| ~ sP9(U_48,U_46,U_44,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_11,plain,
( end_point(U_39,U_46)
| ~ sP8(U_46,U_44,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_12,plain,
( end_point(U_39,U_44)
| ~ sP8(U_46,U_44,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_13,plain,
( incident_c(sK6(U_49,U_47,U_45),U_47)
| ~ sP10(U_47,U_49,U_45) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_14,plain,
( incident_c(sK6(U_49,U_47,U_45),U_45)
| ~ sP10(U_47,U_49,U_45) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_15,plain,
( ~ end_point(sK6(U_49,U_47,U_45),U_45)
| ~ end_point(sK6(U_49,U_47,U_45),U_47)
| ~ sP10(U_47,U_49,U_45) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,plain,
! [C] :
( ( closed(C)
| ? [P] : end_point(P,C) )
& ( ! [P] : ~ end_point(P,C)
| ~ closed(C) ) ),
inference(fof_nnf,[status(thm)],[closed_defn]) ).
fof(f_6_2,plain,
! [U_52] :
( ( closed(U_52)
| ? [U_51] : end_point(U_51,U_52) )
& ( ! [U_50] : ~ end_point(U_50,U_52)
| ~ closed(U_52) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_54] :
( closed(U_54)
| ? [U_51] : end_point(U_51,U_54) )
& ! [U_53] :
( ! [U_50] : ~ end_point(U_50,U_53)
| ~ closed(U_53) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_54] :
( closed(U_54)
| end_point(sK7(U_54),U_54) )
& ! [U_53] :
( ! [U_50] : ~ end_point(U_50,U_53)
| ~ closed(U_53) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_51,sK7(U_54))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_54] :
( closed(U_54)
| end_point(sK7(U_54),U_54) )
& ! [U_50,U_53] :
( ~ end_point(U_50,U_53)
| ~ closed(U_53) ) ),
inference(definitional_conversion,[status(esa)],[f_6_4]) ).
cnf(f_6_6,plain,
( ~ end_point(U_50,U_53)
| ~ closed(U_53) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( closed(U_54)
| end_point(sK7(U_54),U_54) ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_7_1,plain,
! [C] :
( ( open(C)
| ! [P] : ~ end_point(P,C) )
& ( ? [P] : end_point(P,C)
| ~ open(C) ) ),
inference(fof_nnf,[status(thm)],[open_defn]) ).
fof(f_7_2,plain,
! [U_57] :
( ( open(U_57)
| ! [U_56] : ~ end_point(U_56,U_57) )
& ( ? [U_55] : end_point(U_55,U_57)
| ~ open(U_57) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_59] :
( open(U_59)
| ! [U_56] : ~ end_point(U_56,U_59) )
& ! [U_58] :
( ? [U_55] : end_point(U_55,U_58)
| ~ open(U_58) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_59] :
( open(U_59)
| ! [U_56] : ~ end_point(U_56,U_59) )
& ! [U_58] :
( end_point(sK8(U_58),U_58)
| ~ open(U_58) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_55,sK8(U_58))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_56,U_59] :
( open(U_59)
| ~ end_point(U_56,U_59) )
& ! [U_58] :
( end_point(sK8(U_58),U_58)
| ~ open(U_58) ) ),
inference(definitional_conversion,[status(esa)],[f_7_4]) ).
cnf(f_7_6,plain,
( end_point(sK8(U_58),U_58)
| ~ open(U_58) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,plain,
( open(U_59)
| ~ end_point(U_56,U_59) ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_8_1,plain,
! [C,C1] :
( open(C1)
| C1 = C
| ~ part_of(C1,C) ),
inference(fof_nnf,[status(thm)],[c1]) ).
fof(f_8_2,plain,
! [U_61,U_60] :
( open(U_60)
| U_60 = U_61
| ~ part_of(U_60,U_61) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_60,U_61] :
( open(U_60)
| U_60 = U_61
| ~ part_of(U_60,U_61) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( open(U_60)
| U_60 = U_61
| ~ part_of(U_60,U_61) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [C,C1,C2,C3] :
( part_of(C3,C1)
| part_of(C1,C3)
| part_of(C2,C1)
| part_of(C1,C2)
| part_of(C3,C2)
| part_of(C2,C3)
| ! [P] :
( ~ end_point(P,C3)
| ~ end_point(P,C2)
| ~ end_point(P,C1) )
| ~ part_of(C3,C)
| ~ part_of(C2,C)
| ~ part_of(C1,C) ),
inference(fof_nnf,[status(thm)],[c2]) ).
fof(f_9_2,plain,
! [U_66,U_65,U_64,U_63] :
( part_of(U_63,U_65)
| part_of(U_65,U_63)
| part_of(U_64,U_65)
| part_of(U_65,U_64)
| part_of(U_63,U_64)
| part_of(U_64,U_63)
| ! [U_62] :
( ~ end_point(U_62,U_63)
| ~ end_point(U_62,U_64)
| ~ end_point(U_62,U_65) )
| ~ part_of(U_63,U_66)
| ~ part_of(U_64,U_66)
| ~ part_of(U_65,U_66) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_62,U_65,U_66,U_63,U_64] :
( part_of(U_63,U_65)
| part_of(U_65,U_63)
| part_of(U_64,U_65)
| part_of(U_65,U_64)
| part_of(U_63,U_64)
| part_of(U_64,U_63)
| ~ end_point(U_62,U_63)
| ~ end_point(U_62,U_64)
| ~ end_point(U_62,U_65)
| ~ part_of(U_63,U_66)
| ~ part_of(U_64,U_66)
| ~ part_of(U_65,U_66) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( part_of(U_63,U_65)
| part_of(U_65,U_63)
| part_of(U_64,U_65)
| part_of(U_65,U_64)
| part_of(U_63,U_64)
| part_of(U_64,U_63)
| ~ end_point(U_62,U_63)
| ~ end_point(U_62,U_64)
| ~ end_point(U_62,U_65)
| ~ part_of(U_63,U_66)
| ~ part_of(U_64,U_66)
| ~ part_of(U_65,U_66) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [C] :
? [P] : inner_point(P,C),
inference(fof_nnf,[status(thm)],[c3]) ).
fof(f_10_2,plain,
! [U_68] :
? [U_67] : inner_point(U_67,U_68),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_68] : inner_point(sK9(U_68),U_68),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_67,sK9(U_68))],[f_10_2]) ).
fof(f_10_4,plain,
! [U_68] : inner_point(sK9(U_68),U_68),
inference(definitional_conversion,[status(esa)],[f_10_3]) ).
cnf(f_10_5,plain,
inner_point(sK9(U_68),U_68),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
! [C,P] :
( ? [C1,C2] :
( C = sum(C1,C2)
& meet(P,C1,C2) )
| ~ inner_point(P,C) ),
inference(fof_nnf,[status(thm)],[c4]) ).
fof(f_11_2,plain,
! [U_72,U_71] :
( ? [U_70,U_69] :
( U_72 = sum(U_70,U_69)
& meet(U_71,U_70,U_69) )
| ~ inner_point(U_71,U_72) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_72,U_71] :
( ? [U_69] :
( U_72 = sum(sK10(U_72,U_71),U_69)
& meet(U_71,sK10(U_72,U_71),U_69) )
| ~ inner_point(U_71,U_72) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_70,sK10(U_72,U_71))],[f_11_2]) ).
fof(f_11_4,plain,
! [U_72,U_71] :
( ( U_72 = sum(sK10(U_72,U_71),sK11(U_72,U_71))
& meet(U_71,sK10(U_72,U_71),sK11(U_72,U_71)) )
| ~ inner_point(U_71,U_72) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_69,sK11(U_72,U_71))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_71,U_72] :
( U_72 = sum(sK10(U_72,U_71),sK11(U_72,U_71))
| ~ sP11(U_71,U_72) )
& ! [U_71,U_72] :
( meet(U_71,sK10(U_72,U_71),sK11(U_72,U_71))
| ~ sP11(U_71,U_72) )
& ! [U_71,U_72] :
( sP11(U_71,U_72)
| ~ inner_point(U_71,U_72) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_11_4]) ).
cnf(f_11_6,plain,
( sP11(U_71,U_72)
| ~ inner_point(U_71,U_72) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_7,plain,
( meet(U_71,sK10(U_72,U_71),sK11(U_72,U_71))
| ~ sP11(U_71,U_72) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_8,plain,
( U_72 = sum(sK10(U_72,U_71),sK11(U_72,U_71))
| ~ sP11(U_71,U_72) ),
inference(clausify,[status(thm)],[f_11_5]) ).
fof(f_12_1,plain,
! [C,P,Q,R] :
( Q = R
| P = R
| P = Q
| ~ end_point(R,C)
| ~ end_point(Q,C)
| ~ end_point(P,C) ),
inference(fof_nnf,[status(thm)],[c5]) ).
fof(f_12_2,plain,
! [U_76,U_75,U_74,U_73] :
( U_74 = U_73
| U_75 = U_73
| U_75 = U_74
| ~ end_point(U_73,U_76)
| ~ end_point(U_74,U_76)
| ~ end_point(U_75,U_76) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_74,U_75,U_73,U_76] :
( U_74 = U_73
| U_75 = U_73
| U_75 = U_74
| ~ end_point(U_73,U_76)
| ~ end_point(U_74,U_76)
| ~ end_point(U_75,U_76) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( U_74 = U_73
| U_75 = U_73
| U_75 = U_74
| ~ end_point(U_73,U_76)
| ~ end_point(U_74,U_76)
| ~ end_point(U_75,U_76) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [C,P] :
( ? [Q] :
( P != Q
& end_point(Q,C) )
| ~ end_point(P,C) ),
inference(fof_nnf,[status(thm)],[c6]) ).
fof(f_13_2,plain,
! [U_79,U_78] :
( ? [U_77] :
( U_78 != U_77
& end_point(U_77,U_79) )
| ~ end_point(U_78,U_79) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_79,U_78] :
( ( U_78 != sK12(U_79,U_78)
& end_point(sK12(U_79,U_78),U_79) )
| ~ end_point(U_78,U_79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_77,sK12(U_79,U_78))],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_78,U_79] :
( U_78 != sK12(U_79,U_78)
| ~ sP12(U_78,U_79) )
& ! [U_78,U_79] :
( end_point(sK12(U_79,U_78),U_79)
| ~ sP12(U_78,U_79) )
& ! [U_78,U_79] :
( sP12(U_78,U_79)
| ~ end_point(U_78,U_79) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_13_3]) ).
cnf(f_13_5,plain,
( sP12(U_78,U_79)
| ~ end_point(U_78,U_79) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_6,plain,
( end_point(sK12(U_79,U_78),U_79)
| ~ sP12(U_78,U_79) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_7,plain,
( U_78 != sK12(U_79,U_78)
| ~ sP12(U_78,U_79) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_1,plain,
! [C,C1,C2,P] :
( ! [Q] :
( meet(Q,C1,C2)
| ~ end_point(Q,C1) )
| C != sum(C1,C2)
| ~ meet(P,C1,C2)
| ~ closed(C) ),
inference(fof_nnf,[status(thm)],[c7]) ).
fof(f_14_2,plain,
! [U_84,U_83,U_82,U_81] :
( ! [U_80] :
( meet(U_80,U_83,U_82)
| ~ end_point(U_80,U_83) )
| U_84 != sum(U_83,U_82)
| ~ meet(U_81,U_83,U_82)
| ~ closed(U_84) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_84,U_83,U_82] :
( ! [U_81] : ~ meet(U_81,U_83,U_82)
| U_84 != sum(U_83,U_82)
| ~ closed(U_84)
| ! [U_80] :
( meet(U_80,U_83,U_82)
| ~ end_point(U_80,U_83) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
! [U_82,U_84,U_80,U_81,U_83] :
( ~ meet(U_81,U_83,U_82)
| U_84 != sum(U_83,U_82)
| ~ closed(U_84)
| meet(U_80,U_83,U_82)
| ~ end_point(U_80,U_83) ),
inference(definitional_conversion,[status(esa)],[f_14_3]) ).
cnf(f_14_5,plain,
( ~ meet(U_81,U_83,U_82)
| U_84 != sum(U_83,U_82)
| ~ closed(U_84)
| meet(U_80,U_83,U_82)
| ~ end_point(U_80,U_83) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
! [C1,C2] :
( ? [C] : C = sum(C1,C2)
| ! [P] : ~ meet(P,C1,C2) ),
inference(fof_nnf,[status(thm)],[c8]) ).
fof(f_15_2,plain,
! [U_88,U_87] :
( ? [U_86] : U_86 = sum(U_88,U_87)
| ! [U_85] : ~ meet(U_85,U_88,U_87) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_88,U_87] :
( sK13(U_88,U_87) = sum(U_88,U_87)
| ! [U_85] : ~ meet(U_85,U_88,U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_86,sK13(U_88,U_87))],[f_15_2]) ).
fof(f_15_4,plain,
! [U_85,U_88,U_87] :
( sK13(U_88,U_87) = sum(U_88,U_87)
| ~ meet(U_85,U_88,U_87) ),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
( sK13(U_88,U_87) = sum(U_88,U_87)
| ~ meet(U_85,U_88,U_87) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [C,C1] :
( C = C1
| ? [P] :
( ( ~ incident_c(P,C)
& incident_c(P,C1) )
| ( ~ incident_c(P,C1)
& incident_c(P,C) ) ) ),
inference(fof_nnf,[status(thm)],[c9]) ).
fof(f_16_2,plain,
! [U_91,U_90] :
( U_91 = U_90
| ? [U_89] :
( ( ~ incident_c(U_89,U_91)
& incident_c(U_89,U_90) )
| ( ~ incident_c(U_89,U_90)
& incident_c(U_89,U_91) ) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_91,U_90] :
( U_91 = U_90
| ? [U_93] :
( ~ incident_c(U_93,U_91)
& incident_c(U_93,U_90) )
| ? [U_92] :
( ~ incident_c(U_92,U_90)
& incident_c(U_92,U_91) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_91,U_90] :
( U_91 = U_90
| ? [U_93] :
( ~ incident_c(U_93,U_91)
& incident_c(U_93,U_90) )
| ( ~ incident_c(sK14(U_91,U_90),U_90)
& incident_c(sK14(U_91,U_90),U_91) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_92,sK14(U_91,U_90))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_91,U_90] :
( U_91 = U_90
| ( ~ incident_c(sK15(U_91,U_90),U_91)
& incident_c(sK15(U_91,U_90),U_90) )
| ( ~ incident_c(sK14(U_91,U_90),U_90)
& incident_c(sK14(U_91,U_90),U_91) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_93,sK15(U_91,U_90))],[f_16_4]) ).
fof(f_16_6,plain,
( ! [U_90,U_91] :
( ~ incident_c(sK15(U_91,U_90),U_91)
| ~ sP14(U_90,U_91) )
& ! [U_90,U_91] :
( incident_c(sK15(U_91,U_90),U_90)
| ~ sP14(U_90,U_91) )
& ! [U_90,U_91] :
( ~ incident_c(sK14(U_91,U_90),U_90)
| ~ sP13(U_90,U_91) )
& ! [U_90,U_91] :
( incident_c(sK14(U_91,U_90),U_91)
| ~ sP13(U_90,U_91) )
& ! [U_90,U_91] :
( U_91 = U_90
| sP14(U_90,U_91)
| sP13(U_90,U_91) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13,sP14])],[f_16_5]) ).
cnf(f_16_7,plain,
( U_91 = U_90
| sP14(U_90,U_91)
| sP13(U_90,U_91) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_8,plain,
( incident_c(sK14(U_91,U_90),U_91)
| ~ sP13(U_90,U_91) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_9,plain,
( ~ incident_c(sK14(U_91,U_90),U_90)
| ~ sP13(U_90,U_91) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_10,plain,
( incident_c(sK15(U_91,U_90),U_90)
| ~ sP14(U_90,U_91) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_11,plain,
( ~ incident_c(sK15(U_91,U_90),U_91)
| ~ sP14(U_90,U_91) ),
inference(clausify,[status(thm)],[f_16_6]) ).
fof(f_17_1,plain,
! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
| ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| P = R )
& ( ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(fof_nnf,[status(thm)],[between_c_defn]) ).
fof(f_17_2,plain,
! [U_99,U_98,U_97,U_96] :
( ( between_c(U_99,U_98,U_97,U_96)
| ! [U_95] :
( ~ inner_point(U_97,U_95)
| ~ end_point(U_96,U_95)
| ~ end_point(U_98,U_95)
| ~ part_of(U_95,U_99) )
| U_98 = U_96 )
& ( ( ? [U_94] :
( inner_point(U_97,U_94)
& end_point(U_96,U_94)
& end_point(U_98,U_94)
& part_of(U_94,U_99) )
& U_98 != U_96 )
| ~ between_c(U_99,U_98,U_97,U_96) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_107,U_105,U_103,U_101] :
( between_c(U_107,U_105,U_103,U_101)
| ! [U_95] :
( ~ inner_point(U_103,U_95)
| ~ end_point(U_101,U_95)
| ~ end_point(U_105,U_95)
| ~ part_of(U_95,U_107) )
| U_105 = U_101 )
& ! [U_106,U_104,U_102,U_100] :
( ( ? [U_94] :
( inner_point(U_102,U_94)
& end_point(U_100,U_94)
& end_point(U_104,U_94)
& part_of(U_94,U_106) )
& U_104 != U_100 )
| ~ between_c(U_106,U_104,U_102,U_100) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_107,U_105,U_103,U_101] :
( between_c(U_107,U_105,U_103,U_101)
| ! [U_95] :
( ~ inner_point(U_103,U_95)
| ~ end_point(U_101,U_95)
| ~ end_point(U_105,U_95)
| ~ part_of(U_95,U_107) )
| U_105 = U_101 )
& ! [U_106,U_104,U_102,U_100] :
( ( inner_point(U_102,sK16(U_106,U_104,U_102,U_100))
& end_point(U_100,sK16(U_106,U_104,U_102,U_100))
& end_point(U_104,sK16(U_106,U_104,U_102,U_100))
& part_of(sK16(U_106,U_104,U_102,U_100),U_106)
& U_104 != U_100 )
| ~ between_c(U_106,U_104,U_102,U_100) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_94,sK16(U_106,U_104,U_102,U_100))],[f_17_3]) ).
fof(f_17_5,plain,
( ! [U_104,U_106,U_102,U_100] :
( inner_point(U_102,sK16(U_106,U_104,U_102,U_100))
| ~ sP15(U_104,U_106,U_102,U_100) )
& ! [U_104,U_106,U_102,U_100] :
( end_point(U_100,sK16(U_106,U_104,U_102,U_100))
| ~ sP15(U_104,U_106,U_102,U_100) )
& ! [U_104,U_106,U_102,U_100] :
( end_point(U_104,sK16(U_106,U_104,U_102,U_100))
| ~ sP15(U_104,U_106,U_102,U_100) )
& ! [U_104,U_106,U_102,U_100] :
( part_of(sK16(U_106,U_104,U_102,U_100),U_106)
| ~ sP15(U_104,U_106,U_102,U_100) )
& ! [U_104,U_106,U_102,U_100] :
( U_104 != U_100
| ~ sP15(U_104,U_106,U_102,U_100) )
& ! [U_95,U_107,U_101,U_105,U_103] :
( between_c(U_107,U_105,U_103,U_101)
| ~ inner_point(U_103,U_95)
| ~ end_point(U_101,U_95)
| ~ end_point(U_105,U_95)
| ~ part_of(U_95,U_107)
| U_105 = U_101 )
& ! [U_104,U_106,U_102,U_100] :
( sP15(U_104,U_106,U_102,U_100)
| ~ between_c(U_106,U_104,U_102,U_100) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_17_4]) ).
cnf(f_17_6,plain,
( sP15(U_104,U_106,U_102,U_100)
| ~ between_c(U_106,U_104,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,plain,
( between_c(U_107,U_105,U_103,U_101)
| ~ inner_point(U_103,U_95)
| ~ end_point(U_101,U_95)
| ~ end_point(U_105,U_95)
| ~ part_of(U_95,U_107)
| U_105 = U_101 ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_8,plain,
( U_104 != U_100
| ~ sP15(U_104,U_106,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_9,plain,
( part_of(sK16(U_106,U_104,U_102,U_100),U_106)
| ~ sP15(U_104,U_106,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_10,plain,
( end_point(U_104,sK16(U_106,U_104,U_102,U_100))
| ~ sP15(U_104,U_106,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_11,plain,
( end_point(U_100,sK16(U_106,U_104,U_102,U_100))
| ~ sP15(U_104,U_106,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_12,plain,
( inner_point(U_102,sK16(U_106,U_104,U_102,U_100))
| ~ sP15(U_104,U_106,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_5]) ).
fof(f_18_1,plain,
! [O,P,Q,R] :
( ( between_o(O,P,Q,R)
| ( ( ~ ordered_by(O,Q,P)
| ~ ordered_by(O,R,Q) )
& ( ~ ordered_by(O,Q,R)
| ~ ordered_by(O,P,Q) ) ) )
& ( ( ordered_by(O,Q,P)
& ordered_by(O,R,Q) )
| ( ordered_by(O,Q,R)
& ordered_by(O,P,Q) )
| ~ between_o(O,P,Q,R) ) ),
inference(fof_nnf,[status(thm)],[between_o_defn]) ).
fof(f_18_2,plain,
! [U_111,U_110,U_109,U_108] :
( ( between_o(U_111,U_110,U_109,U_108)
| ( ( ~ ordered_by(U_111,U_109,U_110)
| ~ ordered_by(U_111,U_108,U_109) )
& ( ~ ordered_by(U_111,U_109,U_108)
| ~ ordered_by(U_111,U_110,U_109) ) ) )
& ( ( ordered_by(U_111,U_109,U_110)
& ordered_by(U_111,U_108,U_109) )
| ( ordered_by(U_111,U_109,U_108)
& ordered_by(U_111,U_110,U_109) )
| ~ between_o(U_111,U_110,U_109,U_108) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_119,U_117,U_115,U_113] :
( between_o(U_119,U_117,U_115,U_113)
| ( ( ~ ordered_by(U_119,U_115,U_117)
| ~ ordered_by(U_119,U_113,U_115) )
& ( ~ ordered_by(U_119,U_115,U_113)
| ~ ordered_by(U_119,U_117,U_115) ) ) )
& ! [U_118,U_116,U_114,U_112] :
( ( ordered_by(U_118,U_114,U_116)
& ordered_by(U_118,U_112,U_114) )
| ( ordered_by(U_118,U_114,U_112)
& ordered_by(U_118,U_116,U_114) )
| ~ between_o(U_118,U_116,U_114,U_112) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_113,U_115,U_119,U_117] :
( ~ ordered_by(U_119,U_115,U_117)
| ~ ordered_by(U_119,U_113,U_115)
| ~ sP18(U_113,U_115,U_119,U_117) )
& ! [U_113,U_115,U_119,U_117] :
( ~ ordered_by(U_119,U_115,U_113)
| ~ ordered_by(U_119,U_117,U_115)
| ~ sP18(U_113,U_115,U_119,U_117) )
& ! [U_112,U_114,U_118,U_116] :
( ordered_by(U_118,U_114,U_116)
| ~ sP17(U_112,U_114,U_118,U_116) )
& ! [U_112,U_114,U_118,U_116] :
( ordered_by(U_118,U_112,U_114)
| ~ sP17(U_112,U_114,U_118,U_116) )
& ! [U_112,U_114,U_118,U_116] :
( ordered_by(U_118,U_114,U_112)
| ~ sP16(U_112,U_114,U_118,U_116) )
& ! [U_112,U_114,U_118,U_116] :
( ordered_by(U_118,U_116,U_114)
| ~ sP16(U_112,U_114,U_118,U_116) )
& ! [U_113,U_115,U_119,U_117] :
( between_o(U_119,U_117,U_115,U_113)
| sP18(U_113,U_115,U_119,U_117) )
& ! [U_112,U_114,U_118,U_116] :
( sP17(U_112,U_114,U_118,U_116)
| sP16(U_112,U_114,U_118,U_116)
| ~ between_o(U_118,U_116,U_114,U_112) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16,sP17,sP18])],[f_18_3]) ).
cnf(f_18_5,plain,
( sP17(U_112,U_114,U_118,U_116)
| sP16(U_112,U_114,U_118,U_116)
| ~ between_o(U_118,U_116,U_114,U_112) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
( between_o(U_119,U_117,U_115,U_113)
| sP18(U_113,U_115,U_119,U_117) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_7,plain,
( ordered_by(U_118,U_116,U_114)
| ~ sP16(U_112,U_114,U_118,U_116) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_8,plain,
( ordered_by(U_118,U_114,U_112)
| ~ sP16(U_112,U_114,U_118,U_116) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_9,plain,
( ordered_by(U_118,U_112,U_114)
| ~ sP17(U_112,U_114,U_118,U_116) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_10,plain,
( ordered_by(U_118,U_114,U_116)
| ~ sP17(U_112,U_114,U_118,U_116) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_11,plain,
( ~ ordered_by(U_119,U_115,U_113)
| ~ ordered_by(U_119,U_117,U_115)
| ~ sP18(U_113,U_115,U_119,U_117) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_12,plain,
( ~ ordered_by(U_119,U_115,U_117)
| ~ ordered_by(U_119,U_113,U_115)
| ~ sP18(U_113,U_115,U_119,U_117) ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [P,O] :
( ( start_point(P,O)
| ? [Q] :
( ~ ordered_by(O,P,Q)
& incident_o(Q,O)
& P != Q )
| ~ incident_o(P,O) )
& ( ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(fof_nnf,[status(thm)],[start_point_defn]) ).
fof(f_19_2,plain,
! [U_123,U_122] :
( ( start_point(U_123,U_122)
| ? [U_121] :
( ~ ordered_by(U_122,U_123,U_121)
& incident_o(U_121,U_122)
& U_123 != U_121 )
| ~ incident_o(U_123,U_122) )
& ( ( ! [U_120] :
( ordered_by(U_122,U_123,U_120)
| ~ incident_o(U_120,U_122)
| U_123 = U_120 )
& incident_o(U_123,U_122) )
| ~ start_point(U_123,U_122) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_127,U_125] :
( start_point(U_127,U_125)
| ? [U_121] :
( ~ ordered_by(U_125,U_127,U_121)
& incident_o(U_121,U_125)
& U_127 != U_121 )
| ~ incident_o(U_127,U_125) )
& ! [U_126,U_124] :
( ( ! [U_120] :
( ordered_by(U_124,U_126,U_120)
| ~ incident_o(U_120,U_124)
| U_126 = U_120 )
& incident_o(U_126,U_124) )
| ~ start_point(U_126,U_124) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_127,U_125] :
( start_point(U_127,U_125)
| ( ~ ordered_by(U_125,U_127,sK17(U_127,U_125))
& incident_o(sK17(U_127,U_125),U_125)
& U_127 != sK17(U_127,U_125) )
| ~ incident_o(U_127,U_125) )
& ! [U_126,U_124] :
( ( ! [U_120] :
( ordered_by(U_124,U_126,U_120)
| ~ incident_o(U_120,U_124)
| U_126 = U_120 )
& incident_o(U_126,U_124) )
| ~ start_point(U_126,U_124) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_121,sK17(U_127,U_125))],[f_19_3]) ).
fof(f_19_5,plain,
( ! [U_127,U_125] :
( ~ ordered_by(U_125,U_127,sK17(U_127,U_125))
| ~ sP20(U_127,U_125) )
& ! [U_127,U_125] :
( incident_o(sK17(U_127,U_125),U_125)
| ~ sP20(U_127,U_125) )
& ! [U_127,U_125] :
( U_127 != sK17(U_127,U_125)
| ~ sP20(U_127,U_125) )
& ! [U_120,U_126,U_124] :
( ordered_by(U_124,U_126,U_120)
| ~ incident_o(U_120,U_124)
| U_126 = U_120
| ~ sP19(U_120,U_126,U_124) )
& ! [U_120,U_126,U_124] :
( incident_o(U_126,U_124)
| ~ sP19(U_120,U_126,U_124) )
& ! [U_127,U_125] :
( start_point(U_127,U_125)
| sP20(U_127,U_125)
| ~ incident_o(U_127,U_125) )
& ! [U_120,U_126,U_124] :
( sP19(U_120,U_126,U_124)
| ~ start_point(U_126,U_124) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19,sP20])],[f_19_4]) ).
cnf(f_19_6,plain,
( sP19(U_120,U_126,U_124)
| ~ start_point(U_126,U_124) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_7,plain,
( start_point(U_127,U_125)
| sP20(U_127,U_125)
| ~ incident_o(U_127,U_125) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_8,plain,
( incident_o(U_126,U_124)
| ~ sP19(U_120,U_126,U_124) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_9,plain,
( ordered_by(U_124,U_126,U_120)
| ~ incident_o(U_120,U_124)
| U_126 = U_120
| ~ sP19(U_120,U_126,U_124) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_10,plain,
( U_127 != sK17(U_127,U_125)
| ~ sP20(U_127,U_125) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_11,plain,
( incident_o(sK17(U_127,U_125),U_125)
| ~ sP20(U_127,U_125) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_12,plain,
( ~ ordered_by(U_125,U_127,sK17(U_127,U_125))
| ~ sP20(U_127,U_125) ),
inference(clausify,[status(thm)],[f_19_5]) ).
fof(f_20_1,plain,
! [P,O] :
( ( finish_point(P,O)
| ? [Q] :
( ~ ordered_by(O,Q,P)
& incident_o(Q,O)
& P != Q )
| ~ incident_o(P,O) )
& ( ( ! [Q] :
( ordered_by(O,Q,P)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ finish_point(P,O) ) ),
inference(fof_nnf,[status(thm)],[finish_point_defn]) ).
fof(f_20_2,plain,
! [U_131,U_130] :
( ( finish_point(U_131,U_130)
| ? [U_129] :
( ~ ordered_by(U_130,U_129,U_131)
& incident_o(U_129,U_130)
& U_131 != U_129 )
| ~ incident_o(U_131,U_130) )
& ( ( ! [U_128] :
( ordered_by(U_130,U_128,U_131)
| ~ incident_o(U_128,U_130)
| U_131 = U_128 )
& incident_o(U_131,U_130) )
| ~ finish_point(U_131,U_130) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_135,U_133] :
( finish_point(U_135,U_133)
| ? [U_129] :
( ~ ordered_by(U_133,U_129,U_135)
& incident_o(U_129,U_133)
& U_135 != U_129 )
| ~ incident_o(U_135,U_133) )
& ! [U_134,U_132] :
( ( ! [U_128] :
( ordered_by(U_132,U_128,U_134)
| ~ incident_o(U_128,U_132)
| U_134 = U_128 )
& incident_o(U_134,U_132) )
| ~ finish_point(U_134,U_132) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_135,U_133] :
( finish_point(U_135,U_133)
| ( ~ ordered_by(U_133,sK18(U_135,U_133),U_135)
& incident_o(sK18(U_135,U_133),U_133)
& U_135 != sK18(U_135,U_133) )
| ~ incident_o(U_135,U_133) )
& ! [U_134,U_132] :
( ( ! [U_128] :
( ordered_by(U_132,U_128,U_134)
| ~ incident_o(U_128,U_132)
| U_134 = U_128 )
& incident_o(U_134,U_132) )
| ~ finish_point(U_134,U_132) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_129,sK18(U_135,U_133))],[f_20_3]) ).
fof(f_20_5,plain,
( ! [U_135,U_133] :
( ~ ordered_by(U_133,sK18(U_135,U_133),U_135)
| ~ sP22(U_135,U_133) )
& ! [U_135,U_133] :
( incident_o(sK18(U_135,U_133),U_133)
| ~ sP22(U_135,U_133) )
& ! [U_135,U_133] :
( U_135 != sK18(U_135,U_133)
| ~ sP22(U_135,U_133) )
& ! [U_128,U_132,U_134] :
( ordered_by(U_132,U_128,U_134)
| ~ incident_o(U_128,U_132)
| U_134 = U_128
| ~ sP21(U_128,U_132,U_134) )
& ! [U_128,U_132,U_134] :
( incident_o(U_134,U_132)
| ~ sP21(U_128,U_132,U_134) )
& ! [U_135,U_133] :
( finish_point(U_135,U_133)
| sP22(U_135,U_133)
| ~ incident_o(U_135,U_133) )
& ! [U_128,U_132,U_134] :
( sP21(U_128,U_132,U_134)
| ~ finish_point(U_134,U_132) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21,sP22])],[f_20_4]) ).
cnf(f_20_6,plain,
( sP21(U_128,U_132,U_134)
| ~ finish_point(U_134,U_132) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_7,plain,
( finish_point(U_135,U_133)
| sP22(U_135,U_133)
| ~ incident_o(U_135,U_133) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_8,plain,
( incident_o(U_134,U_132)
| ~ sP21(U_128,U_132,U_134) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_9,plain,
( ordered_by(U_132,U_128,U_134)
| ~ incident_o(U_128,U_132)
| U_134 = U_128
| ~ sP21(U_128,U_132,U_134) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_10,plain,
( U_135 != sK18(U_135,U_133)
| ~ sP22(U_135,U_133) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_11,plain,
( incident_o(sK18(U_135,U_133),U_133)
| ~ sP22(U_135,U_133) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_12,plain,
( ~ ordered_by(U_133,sK18(U_135,U_133),U_135)
| ~ sP22(U_135,U_133) ),
inference(clausify,[status(thm)],[f_20_5]) ).
fof(f_21_1,plain,
! [O,P,Q] :
( ( incident_o(Q,O)
& incident_o(P,O) )
| ~ ordered_by(O,P,Q) ),
inference(fof_nnf,[status(thm)],[o1]) ).
fof(f_21_2,plain,
! [U_138,U_137,U_136] :
( ( incident_o(U_136,U_138)
& incident_o(U_137,U_138) )
| ~ ordered_by(U_138,U_137,U_136) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_136,U_137,U_138] :
( incident_o(U_136,U_138)
| ~ sP23(U_136,U_137,U_138) )
& ! [U_136,U_137,U_138] :
( incident_o(U_137,U_138)
| ~ sP23(U_136,U_137,U_138) )
& ! [U_136,U_137,U_138] :
( sP23(U_136,U_137,U_138)
| ~ ordered_by(U_138,U_137,U_136) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_21_2]) ).
cnf(f_21_4,plain,
( sP23(U_136,U_137,U_138)
| ~ ordered_by(U_138,U_137,U_136) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( incident_o(U_137,U_138)
| ~ sP23(U_136,U_137,U_138) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_6,plain,
( incident_o(U_136,U_138)
| ~ sP23(U_136,U_137,U_138) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [O] :
? [C] :
( ! [P] :
( ( incident_o(P,O)
| ~ incident_c(P,C) )
& ( incident_c(P,C)
| ~ incident_o(P,O) ) )
& open(C) ),
inference(fof_nnf,[status(thm)],[o2]) ).
fof(f_22_2,plain,
! [U_141] :
? [U_140] :
( ! [U_139] :
( ( incident_o(U_139,U_141)
| ~ incident_c(U_139,U_140) )
& ( incident_c(U_139,U_140)
| ~ incident_o(U_139,U_141) ) )
& open(U_140) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_141] :
? [U_140] :
( ! [U_143] :
( incident_o(U_143,U_141)
| ~ incident_c(U_143,U_140) )
& ! [U_142] :
( incident_c(U_142,U_140)
| ~ incident_o(U_142,U_141) )
& open(U_140) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
! [U_141] :
( ! [U_143] :
( incident_o(U_143,U_141)
| ~ incident_c(U_143,sK19(U_141)) )
& ! [U_142] :
( incident_c(U_142,sK19(U_141))
| ~ incident_o(U_142,U_141) )
& open(sK19(U_141)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_140,sK19(U_141))],[f_22_3]) ).
fof(f_22_5,plain,
( ! [U_141,U_143] :
( incident_o(U_143,U_141)
| ~ incident_c(U_143,sK19(U_141)) )
& ! [U_141,U_142] :
( incident_c(U_142,sK19(U_141))
| ~ incident_o(U_142,U_141) )
& ! [U_141] : open(sK19(U_141)) ),
inference(definitional_conversion,[status(esa)],[f_22_4]) ).
cnf(f_22_6,plain,
open(sK19(U_141)),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_7,plain,
( incident_c(U_142,sK19(U_141))
| ~ incident_o(U_142,U_141) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_8,plain,
( incident_o(U_143,U_141)
| ~ incident_c(U_143,sK19(U_141)) ),
inference(clausify,[status(thm)],[f_22_5]) ).
fof(f_23_1,plain,
! [P,Q,R,O] :
( ( between_o(O,P,Q,R)
| ! [C] :
( ~ between_c(C,P,Q,R)
| ? [P] :
( ( ~ incident_o(P,O)
& incident_c(P,C) )
| ( ~ incident_c(P,C)
& incident_o(P,O) ) ) ) )
& ( ? [C] :
( between_c(C,P,Q,R)
& ! [P] :
( ( incident_o(P,O)
| ~ incident_c(P,C) )
& ( incident_c(P,C)
| ~ incident_o(P,O) ) ) )
| ~ between_o(O,P,Q,R) ) ),
inference(fof_nnf,[status(thm)],[o3]) ).
fof(f_23_2,plain,
! [U_151,U_150,U_149,U_148] :
( ( between_o(U_148,U_151,U_150,U_149)
| ! [U_147] :
( ~ between_c(U_147,U_151,U_150,U_149)
| ? [U_146] :
( ( ~ incident_o(U_146,U_148)
& incident_c(U_146,U_147) )
| ( ~ incident_c(U_146,U_147)
& incident_o(U_146,U_148) ) ) ) )
& ( ? [U_145] :
( between_c(U_145,U_151,U_150,U_149)
& ! [U_144] :
( ( incident_o(U_144,U_148)
| ~ incident_c(U_144,U_145) )
& ( incident_c(U_144,U_145)
| ~ incident_o(U_144,U_148) ) ) )
| ~ between_o(U_148,U_151,U_150,U_149) ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_163,U_161,U_159,U_157] :
( between_o(U_157,U_163,U_161,U_159)
| ! [U_147] :
( ~ between_c(U_147,U_163,U_161,U_159)
| ? [U_155] :
( ~ incident_o(U_155,U_157)
& incident_c(U_155,U_147) )
| ? [U_154] :
( ~ incident_c(U_154,U_147)
& incident_o(U_154,U_157) ) ) )
& ! [U_162,U_160,U_158,U_156] :
( ? [U_145] :
( between_c(U_145,U_162,U_160,U_158)
& ! [U_153] :
( incident_o(U_153,U_156)
| ~ incident_c(U_153,U_145) )
& ! [U_152] :
( incident_c(U_152,U_145)
| ~ incident_o(U_152,U_156) ) )
| ~ between_o(U_156,U_162,U_160,U_158) ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_163,U_161,U_159,U_157] :
( between_o(U_157,U_163,U_161,U_159)
| ! [U_147] :
( ~ between_c(U_147,U_163,U_161,U_159)
| ? [U_155] :
( ~ incident_o(U_155,U_157)
& incident_c(U_155,U_147) )
| ? [U_154] :
( ~ incident_c(U_154,U_147)
& incident_o(U_154,U_157) ) ) )
& ! [U_162,U_160,U_158,U_156] :
( ( between_c(sK20(U_162,U_160,U_158,U_156),U_162,U_160,U_158)
& ! [U_153] :
( incident_o(U_153,U_156)
| ~ incident_c(U_153,sK20(U_162,U_160,U_158,U_156)) )
& ! [U_152] :
( incident_c(U_152,sK20(U_162,U_160,U_158,U_156))
| ~ incident_o(U_152,U_156) ) )
| ~ between_o(U_156,U_162,U_160,U_158) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_145,sK20(U_162,U_160,U_158,U_156))],[f_23_3]) ).
fof(f_23_5,plain,
( ! [U_163,U_161,U_159,U_157] :
( between_o(U_157,U_163,U_161,U_159)
| ! [U_147] :
( ~ between_c(U_147,U_163,U_161,U_159)
| ? [U_155] :
( ~ incident_o(U_155,U_157)
& incident_c(U_155,U_147) )
| ( ~ incident_c(sK21(U_163,U_161,U_159,U_157,U_147),U_147)
& incident_o(sK21(U_163,U_161,U_159,U_157,U_147),U_157) ) ) )
& ! [U_162,U_160,U_158,U_156] :
( ( between_c(sK20(U_162,U_160,U_158,U_156),U_162,U_160,U_158)
& ! [U_153] :
( incident_o(U_153,U_156)
| ~ incident_c(U_153,sK20(U_162,U_160,U_158,U_156)) )
& ! [U_152] :
( incident_c(U_152,sK20(U_162,U_160,U_158,U_156))
| ~ incident_o(U_152,U_156) ) )
| ~ between_o(U_156,U_162,U_160,U_158) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_154,sK21(U_163,U_161,U_159,U_157,U_147))],[f_23_4]) ).
fof(f_23_6,plain,
( ! [U_163,U_161,U_159,U_157] :
( between_o(U_157,U_163,U_161,U_159)
| ! [U_147] :
( ~ between_c(U_147,U_163,U_161,U_159)
| ( ~ incident_o(sK22(U_163,U_161,U_159,U_157,U_147),U_157)
& incident_c(sK22(U_163,U_161,U_159,U_157,U_147),U_147) )
| ( ~ incident_c(sK21(U_163,U_161,U_159,U_157,U_147),U_147)
& incident_o(sK21(U_163,U_161,U_159,U_157,U_147),U_157) ) ) )
& ! [U_162,U_160,U_158,U_156] :
( ( between_c(sK20(U_162,U_160,U_158,U_156),U_162,U_160,U_158)
& ! [U_153] :
( incident_o(U_153,U_156)
| ~ incident_c(U_153,sK20(U_162,U_160,U_158,U_156)) )
& ! [U_152] :
( incident_c(U_152,sK20(U_162,U_160,U_158,U_156))
| ~ incident_o(U_152,U_156) ) )
| ~ between_o(U_156,U_162,U_160,U_158) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_155,sK22(U_163,U_161,U_159,U_157,U_147))],[f_23_5]) ).
fof(f_23_7,plain,
( ! [U_147,U_163,U_161,U_157,U_159] :
( ~ incident_o(sK22(U_163,U_161,U_159,U_157,U_147),U_157)
| ~ sP26(U_147,U_163,U_161,U_157,U_159) )
& ! [U_147,U_163,U_161,U_157,U_159] :
( incident_c(sK22(U_163,U_161,U_159,U_157,U_147),U_147)
| ~ sP26(U_147,U_163,U_161,U_157,U_159) )
& ! [U_147,U_163,U_161,U_157,U_159] :
( ~ incident_c(sK21(U_163,U_161,U_159,U_157,U_147),U_147)
| ~ sP25(U_147,U_163,U_161,U_157,U_159) )
& ! [U_147,U_163,U_161,U_157,U_159] :
( incident_o(sK21(U_163,U_161,U_159,U_157,U_147),U_157)
| ~ sP25(U_147,U_163,U_161,U_157,U_159) )
& ! [U_158,U_162,U_152,U_153,U_160,U_156] :
( between_c(sK20(U_162,U_160,U_158,U_156),U_162,U_160,U_158)
| ~ sP24(U_158,U_162,U_152,U_153,U_160,U_156) )
& ! [U_158,U_162,U_152,U_153,U_160,U_156] :
( incident_o(U_153,U_156)
| ~ incident_c(U_153,sK20(U_162,U_160,U_158,U_156))
| ~ sP24(U_158,U_162,U_152,U_153,U_160,U_156) )
& ! [U_158,U_162,U_152,U_153,U_160,U_156] :
( incident_c(U_152,sK20(U_162,U_160,U_158,U_156))
| ~ incident_o(U_152,U_156)
| ~ sP24(U_158,U_162,U_152,U_153,U_160,U_156) )
& ! [U_147,U_163,U_161,U_157,U_159] :
( between_o(U_157,U_163,U_161,U_159)
| ~ between_c(U_147,U_163,U_161,U_159)
| sP26(U_147,U_163,U_161,U_157,U_159)
| sP25(U_147,U_163,U_161,U_157,U_159) )
& ! [U_158,U_162,U_152,U_153,U_160,U_156] :
( sP24(U_158,U_162,U_152,U_153,U_160,U_156)
| ~ between_o(U_156,U_162,U_160,U_158) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24,sP25,sP26])],[f_23_6]) ).
cnf(f_23_8,plain,
( sP24(U_158,U_162,U_152,U_153,U_160,U_156)
| ~ between_o(U_156,U_162,U_160,U_158) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_9,plain,
( between_o(U_157,U_163,U_161,U_159)
| ~ between_c(U_147,U_163,U_161,U_159)
| sP26(U_147,U_163,U_161,U_157,U_159)
| sP25(U_147,U_163,U_161,U_157,U_159) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_10,plain,
( incident_c(U_152,sK20(U_162,U_160,U_158,U_156))
| ~ incident_o(U_152,U_156)
| ~ sP24(U_158,U_162,U_152,U_153,U_160,U_156) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_11,plain,
( incident_o(U_153,U_156)
| ~ incident_c(U_153,sK20(U_162,U_160,U_158,U_156))
| ~ sP24(U_158,U_162,U_152,U_153,U_160,U_156) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_12,plain,
( between_c(sK20(U_162,U_160,U_158,U_156),U_162,U_160,U_158)
| ~ sP24(U_158,U_162,U_152,U_153,U_160,U_156) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_13,plain,
( incident_o(sK21(U_163,U_161,U_159,U_157,U_147),U_157)
| ~ sP25(U_147,U_163,U_161,U_157,U_159) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_14,plain,
( ~ incident_c(sK21(U_163,U_161,U_159,U_157,U_147),U_147)
| ~ sP25(U_147,U_163,U_161,U_157,U_159) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_15,plain,
( incident_c(sK22(U_163,U_161,U_159,U_157,U_147),U_147)
| ~ sP26(U_147,U_163,U_161,U_157,U_159) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_16,plain,
( ~ incident_o(sK22(U_163,U_161,U_159,U_157,U_147),U_157)
| ~ sP26(U_147,U_163,U_161,U_157,U_159) ),
inference(clausify,[status(thm)],[f_23_7]) ).
fof(f_24_1,plain,
! [O] :
? [P] : start_point(P,O),
inference(fof_nnf,[status(thm)],[o4]) ).
fof(f_24_2,plain,
! [U_165] :
? [U_164] : start_point(U_164,U_165),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_165] : start_point(sK23(U_165),U_165),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_164,sK23(U_165))],[f_24_2]) ).
fof(f_24_4,plain,
! [U_165] : start_point(sK23(U_165),U_165),
inference(definitional_conversion,[status(esa)],[f_24_3]) ).
cnf(f_24_5,plain,
start_point(sK23(U_165),U_165),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
! [P,Q,C] :
( ? [O] :
( ordered_by(O,P,Q)
& ! [R] :
( ( incident_o(R,O)
| ~ incident_c(R,C) )
& ( incident_c(R,C)
| ~ incident_o(R,O) ) ) )
| ~ incident_c(Q,C)
| ~ incident_c(P,C)
| P = Q
| ~ open(C) ),
inference(fof_nnf,[status(thm)],[o5]) ).
fof(f_25_2,plain,
! [U_170,U_169,U_168] :
( ? [U_167] :
( ordered_by(U_167,U_170,U_169)
& ! [U_166] :
( ( incident_o(U_166,U_167)
| ~ incident_c(U_166,U_168) )
& ( incident_c(U_166,U_168)
| ~ incident_o(U_166,U_167) ) ) )
| ~ incident_c(U_169,U_168)
| ~ incident_c(U_170,U_168)
| U_170 = U_169
| ~ open(U_168) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_170,U_169,U_168] :
( ? [U_167] :
( ordered_by(U_167,U_170,U_169)
& ! [U_172] :
( incident_o(U_172,U_167)
| ~ incident_c(U_172,U_168) )
& ! [U_171] :
( incident_c(U_171,U_168)
| ~ incident_o(U_171,U_167) ) )
| ~ incident_c(U_169,U_168)
| ~ incident_c(U_170,U_168)
| U_170 = U_169
| ~ open(U_168) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
! [U_170,U_169,U_168] :
( ( ordered_by(sK24(U_170,U_169,U_168),U_170,U_169)
& ! [U_172] :
( incident_o(U_172,sK24(U_170,U_169,U_168))
| ~ incident_c(U_172,U_168) )
& ! [U_171] :
( incident_c(U_171,U_168)
| ~ incident_o(U_171,sK24(U_170,U_169,U_168)) ) )
| ~ incident_c(U_169,U_168)
| ~ incident_c(U_170,U_168)
| U_170 = U_169
| ~ open(U_168) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_167,sK24(U_170,U_169,U_168))],[f_25_3]) ).
fof(f_25_5,plain,
( ! [U_171,U_169,U_172,U_170,U_168] :
( ordered_by(sK24(U_170,U_169,U_168),U_170,U_169)
| ~ sP27(U_171,U_169,U_172,U_170,U_168) )
& ! [U_171,U_169,U_172,U_170,U_168] :
( incident_o(U_172,sK24(U_170,U_169,U_168))
| ~ incident_c(U_172,U_168)
| ~ sP27(U_171,U_169,U_172,U_170,U_168) )
& ! [U_171,U_169,U_172,U_170,U_168] :
( incident_c(U_171,U_168)
| ~ incident_o(U_171,sK24(U_170,U_169,U_168))
| ~ sP27(U_171,U_169,U_172,U_170,U_168) )
& ! [U_171,U_169,U_172,U_170,U_168] :
( sP27(U_171,U_169,U_172,U_170,U_168)
| ~ incident_c(U_169,U_168)
| ~ incident_c(U_170,U_168)
| U_170 = U_169
| ~ open(U_168) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_25_4]) ).
cnf(f_25_6,plain,
( sP27(U_171,U_169,U_172,U_170,U_168)
| ~ incident_c(U_169,U_168)
| ~ incident_c(U_170,U_168)
| U_170 = U_169
| ~ open(U_168) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_7,plain,
( incident_c(U_171,U_168)
| ~ incident_o(U_171,sK24(U_170,U_169,U_168))
| ~ sP27(U_171,U_169,U_172,U_170,U_168) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_8,plain,
( incident_o(U_172,sK24(U_170,U_169,U_168))
| ~ incident_c(U_172,U_168)
| ~ sP27(U_171,U_169,U_172,U_170,U_168) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_9,plain,
( ordered_by(sK24(U_170,U_169,U_168),U_170,U_169)
| ~ sP27(U_171,U_169,U_172,U_170,U_168) ),
inference(clausify,[status(thm)],[f_25_5]) ).
fof(f_26_1,plain,
! [O1,O2] :
( O1 = O2
| ? [P,Q] :
( ( ~ ordered_by(O1,P,Q)
& ordered_by(O2,P,Q) )
| ( ~ ordered_by(O2,P,Q)
& ordered_by(O1,P,Q) ) ) ),
inference(fof_nnf,[status(thm)],[o6]) ).
fof(f_26_2,plain,
! [U_176,U_175] :
( U_176 = U_175
| ? [U_174,U_173] :
( ( ~ ordered_by(U_176,U_174,U_173)
& ordered_by(U_175,U_174,U_173) )
| ( ~ ordered_by(U_175,U_174,U_173)
& ordered_by(U_176,U_174,U_173) ) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_176,U_175] :
( U_176 = U_175
| ? [U_180,U_178] :
( ~ ordered_by(U_176,U_180,U_178)
& ordered_by(U_175,U_180,U_178) )
| ? [U_179,U_177] :
( ~ ordered_by(U_175,U_179,U_177)
& ordered_by(U_176,U_179,U_177) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
! [U_176,U_175] :
( U_176 = U_175
| ? [U_180,U_178] :
( ~ ordered_by(U_176,U_180,U_178)
& ordered_by(U_175,U_180,U_178) )
| ? [U_177] :
( ~ ordered_by(U_175,sK25(U_176,U_175),U_177)
& ordered_by(U_176,sK25(U_176,U_175),U_177) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_179,sK25(U_176,U_175))],[f_26_3]) ).
fof(f_26_5,plain,
! [U_176,U_175] :
( U_176 = U_175
| ? [U_180,U_178] :
( ~ ordered_by(U_176,U_180,U_178)
& ordered_by(U_175,U_180,U_178) )
| ( ~ ordered_by(U_175,sK25(U_176,U_175),sK26(U_176,U_175))
& ordered_by(U_176,sK25(U_176,U_175),sK26(U_176,U_175)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_177,sK26(U_176,U_175))],[f_26_4]) ).
fof(f_26_6,plain,
! [U_176,U_175] :
( U_176 = U_175
| ? [U_178] :
( ~ ordered_by(U_176,sK27(U_176,U_175),U_178)
& ordered_by(U_175,sK27(U_176,U_175),U_178) )
| ( ~ ordered_by(U_175,sK25(U_176,U_175),sK26(U_176,U_175))
& ordered_by(U_176,sK25(U_176,U_175),sK26(U_176,U_175)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_180,sK27(U_176,U_175))],[f_26_5]) ).
fof(f_26_7,plain,
! [U_176,U_175] :
( U_176 = U_175
| ( ~ ordered_by(U_176,sK27(U_176,U_175),sK28(U_176,U_175))
& ordered_by(U_175,sK27(U_176,U_175),sK28(U_176,U_175)) )
| ( ~ ordered_by(U_175,sK25(U_176,U_175),sK26(U_176,U_175))
& ordered_by(U_176,sK25(U_176,U_175),sK26(U_176,U_175)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_178,sK28(U_176,U_175))],[f_26_6]) ).
fof(f_26_8,plain,
( ! [U_175,U_176] :
( ~ ordered_by(U_176,sK27(U_176,U_175),sK28(U_176,U_175))
| ~ sP29(U_175,U_176) )
& ! [U_175,U_176] :
( ordered_by(U_175,sK27(U_176,U_175),sK28(U_176,U_175))
| ~ sP29(U_175,U_176) )
& ! [U_175,U_176] :
( ~ ordered_by(U_175,sK25(U_176,U_175),sK26(U_176,U_175))
| ~ sP28(U_175,U_176) )
& ! [U_175,U_176] :
( ordered_by(U_176,sK25(U_176,U_175),sK26(U_176,U_175))
| ~ sP28(U_175,U_176) )
& ! [U_175,U_176] :
( U_176 = U_175
| sP29(U_175,U_176)
| sP28(U_175,U_176) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28,sP29])],[f_26_7]) ).
cnf(f_26_9,plain,
( U_176 = U_175
| sP29(U_175,U_176)
| sP28(U_175,U_176) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_10,plain,
( ordered_by(U_176,sK25(U_176,U_175),sK26(U_176,U_175))
| ~ sP28(U_175,U_176) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_11,plain,
( ~ ordered_by(U_175,sK25(U_176,U_175),sK26(U_176,U_175))
| ~ sP28(U_175,U_176) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_12,plain,
( ordered_by(U_175,sK27(U_176,U_175),sK28(U_176,U_175))
| ~ sP29(U_175,U_176) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_13,plain,
( ~ ordered_by(U_176,sK27(U_176,U_175),sK28(U_176,U_175))
| ~ sP29(U_175,U_176) ),
inference(clausify,[status(thm)],[f_26_8]) ).
fof(f_27_1,plain,
! [C,O] :
( ( C = underlying_curve(O)
| ? [P] :
( ( ~ incident_o(P,O)
& incident_c(P,C) )
| ( ~ incident_c(P,C)
& incident_o(P,O) ) ) )
& ( ! [P] :
( ( incident_o(P,O)
| ~ incident_c(P,C) )
& ( incident_c(P,C)
| ~ incident_o(P,O) ) )
| C != underlying_curve(O) ) ),
inference(fof_nnf,[status(thm)],[underlying_curve_defn]) ).
fof(f_27_2,plain,
! [U_184,U_183] :
( ( U_184 = underlying_curve(U_183)
| ? [U_182] :
( ( ~ incident_o(U_182,U_183)
& incident_c(U_182,U_184) )
| ( ~ incident_c(U_182,U_184)
& incident_o(U_182,U_183) ) ) )
& ( ! [U_181] :
( ( incident_o(U_181,U_183)
| ~ incident_c(U_181,U_184) )
& ( incident_c(U_181,U_184)
| ~ incident_o(U_181,U_183) ) )
| U_184 != underlying_curve(U_183) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_192,U_190] :
( U_192 = underlying_curve(U_190)
| ? [U_188] :
( ~ incident_o(U_188,U_190)
& incident_c(U_188,U_192) )
| ? [U_187] :
( ~ incident_c(U_187,U_192)
& incident_o(U_187,U_190) ) )
& ! [U_191,U_189] :
( ( ! [U_186] :
( incident_o(U_186,U_189)
| ~ incident_c(U_186,U_191) )
& ! [U_185] :
( incident_c(U_185,U_191)
| ~ incident_o(U_185,U_189) ) )
| U_191 != underlying_curve(U_189) ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_192,U_190] :
( U_192 = underlying_curve(U_190)
| ? [U_188] :
( ~ incident_o(U_188,U_190)
& incident_c(U_188,U_192) )
| ( ~ incident_c(sK29(U_192,U_190),U_192)
& incident_o(sK29(U_192,U_190),U_190) ) )
& ! [U_191,U_189] :
( ( ! [U_186] :
( incident_o(U_186,U_189)
| ~ incident_c(U_186,U_191) )
& ! [U_185] :
( incident_c(U_185,U_191)
| ~ incident_o(U_185,U_189) ) )
| U_191 != underlying_curve(U_189) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_187,sK29(U_192,U_190))],[f_27_3]) ).
fof(f_27_5,plain,
( ! [U_192,U_190] :
( U_192 = underlying_curve(U_190)
| ( ~ incident_o(sK30(U_192,U_190),U_190)
& incident_c(sK30(U_192,U_190),U_192) )
| ( ~ incident_c(sK29(U_192,U_190),U_192)
& incident_o(sK29(U_192,U_190),U_190) ) )
& ! [U_191,U_189] :
( ( ! [U_186] :
( incident_o(U_186,U_189)
| ~ incident_c(U_186,U_191) )
& ! [U_185] :
( incident_c(U_185,U_191)
| ~ incident_o(U_185,U_189) ) )
| U_191 != underlying_curve(U_189) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_188,sK30(U_192,U_190))],[f_27_4]) ).
fof(f_27_6,plain,
( ! [U_190,U_192] :
( ~ incident_o(sK30(U_192,U_190),U_190)
| ~ sP32(U_190,U_192) )
& ! [U_190,U_192] :
( incident_c(sK30(U_192,U_190),U_192)
| ~ sP32(U_190,U_192) )
& ! [U_190,U_192] :
( ~ incident_c(sK29(U_192,U_190),U_192)
| ~ sP31(U_190,U_192) )
& ! [U_190,U_192] :
( incident_o(sK29(U_192,U_190),U_190)
| ~ sP31(U_190,U_192) )
& ! [U_189,U_191,U_185,U_186] :
( incident_o(U_186,U_189)
| ~ incident_c(U_186,U_191)
| ~ sP30(U_189,U_191,U_185,U_186) )
& ! [U_189,U_191,U_185,U_186] :
( incident_c(U_185,U_191)
| ~ incident_o(U_185,U_189)
| ~ sP30(U_189,U_191,U_185,U_186) )
& ! [U_190,U_192] :
( U_192 = underlying_curve(U_190)
| sP32(U_190,U_192)
| sP31(U_190,U_192) )
& ! [U_189,U_191,U_185,U_186] :
( sP30(U_189,U_191,U_185,U_186)
| U_191 != underlying_curve(U_189) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30,sP31,sP32])],[f_27_5]) ).
cnf(f_27_7,plain,
( sP30(U_189,U_191,U_185,U_186)
| U_191 != underlying_curve(U_189) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_8,plain,
( U_192 = underlying_curve(U_190)
| sP32(U_190,U_192)
| sP31(U_190,U_192) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_9,plain,
( incident_c(U_185,U_191)
| ~ incident_o(U_185,U_189)
| ~ sP30(U_189,U_191,U_185,U_186) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_10,plain,
( incident_o(U_186,U_189)
| ~ incident_c(U_186,U_191)
| ~ sP30(U_189,U_191,U_185,U_186) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_11,plain,
( incident_o(sK29(U_192,U_190),U_190)
| ~ sP31(U_190,U_192) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_12,plain,
( ~ incident_c(sK29(U_192,U_190),U_192)
| ~ sP31(U_190,U_192) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_13,plain,
( incident_c(sK30(U_192,U_190),U_192)
| ~ sP32(U_190,U_192) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_14,plain,
( ~ incident_o(sK30(U_192,U_190),U_190)
| ~ sP32(U_190,U_192) ),
inference(clausify,[status(thm)],[f_27_6]) ).
fof(f_28_1,plain,
! [X,Y,P] :
( ( connect(X,Y,P)
| ~ once(at_the_same_time(at(X,P),at(Y,P))) )
& ( once(at_the_same_time(at(X,P),at(Y,P)))
| ~ connect(X,Y,P) ) ),
inference(fof_nnf,[status(thm)],[connect_defn]) ).
fof(f_28_2,plain,
! [U_195,U_194,U_193] :
( ( connect(U_195,U_194,U_193)
| ~ once(at_the_same_time(at(U_195,U_193),at(U_194,U_193))) )
& ( once(at_the_same_time(at(U_195,U_193),at(U_194,U_193)))
| ~ connect(U_195,U_194,U_193) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_201,U_199,U_197] :
( connect(U_201,U_199,U_197)
| ~ once(at_the_same_time(at(U_201,U_197),at(U_199,U_197))) )
& ! [U_200,U_198,U_196] :
( once(at_the_same_time(at(U_200,U_196),at(U_198,U_196)))
| ~ connect(U_200,U_198,U_196) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_199,U_197,U_201] :
( connect(U_201,U_199,U_197)
| ~ once(at_the_same_time(at(U_201,U_197),at(U_199,U_197))) )
& ! [U_196,U_198,U_200] :
( once(at_the_same_time(at(U_200,U_196),at(U_198,U_196)))
| ~ connect(U_200,U_198,U_196) ) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
( once(at_the_same_time(at(U_200,U_196),at(U_198,U_196)))
| ~ connect(U_200,U_198,U_196) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
( connect(U_201,U_199,U_197)
| ~ once(at_the_same_time(at(U_201,U_197),at(U_199,U_197))) ),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [A,B] :
( ( once(at_the_same_time(A,B))
| ~ once(at_the_same_time(B,A)) )
& ( once(at_the_same_time(B,A))
| ~ once(at_the_same_time(A,B)) ) ),
inference(fof_nnf,[status(thm)],[symmetry_of_at_the_same_time]) ).
fof(f_29_2,plain,
! [U_203,U_202] :
( ( once(at_the_same_time(U_203,U_202))
| ~ once(at_the_same_time(U_202,U_203)) )
& ( once(at_the_same_time(U_202,U_203))
| ~ once(at_the_same_time(U_203,U_202)) ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_207,U_205] :
( once(at_the_same_time(U_207,U_205))
| ~ once(at_the_same_time(U_205,U_207)) )
& ! [U_206,U_204] :
( once(at_the_same_time(U_204,U_206))
| ~ once(at_the_same_time(U_206,U_204)) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_205,U_207] :
( once(at_the_same_time(U_207,U_205))
| ~ once(at_the_same_time(U_205,U_207)) )
& ! [U_206,U_204] :
( once(at_the_same_time(U_204,U_206))
| ~ once(at_the_same_time(U_206,U_204)) ) ),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
( once(at_the_same_time(U_204,U_206))
| ~ once(at_the_same_time(U_206,U_204)) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( once(at_the_same_time(U_207,U_205))
| ~ once(at_the_same_time(U_205,U_207)) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [A,B,C] :
( ( once(at_the_same_time(at_the_same_time(A,B),C))
| ~ once(at_the_same_time(A,at_the_same_time(B,C))) )
& ( once(at_the_same_time(A,at_the_same_time(B,C)))
| ~ once(at_the_same_time(at_the_same_time(A,B),C)) ) ),
inference(fof_nnf,[status(thm)],[assciativity_of_at_the_same_time]) ).
fof(f_30_2,plain,
! [U_210,U_209,U_208] :
( ( once(at_the_same_time(at_the_same_time(U_210,U_209),U_208))
| ~ once(at_the_same_time(U_210,at_the_same_time(U_209,U_208))) )
& ( once(at_the_same_time(U_210,at_the_same_time(U_209,U_208)))
| ~ once(at_the_same_time(at_the_same_time(U_210,U_209),U_208)) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_216,U_214,U_212] :
( once(at_the_same_time(at_the_same_time(U_216,U_214),U_212))
| ~ once(at_the_same_time(U_216,at_the_same_time(U_214,U_212))) )
& ! [U_215,U_213,U_211] :
( once(at_the_same_time(U_215,at_the_same_time(U_213,U_211)))
| ~ once(at_the_same_time(at_the_same_time(U_215,U_213),U_211)) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_212,U_214,U_216] :
( once(at_the_same_time(at_the_same_time(U_216,U_214),U_212))
| ~ once(at_the_same_time(U_216,at_the_same_time(U_214,U_212))) )
& ! [U_213,U_215,U_211] :
( once(at_the_same_time(U_215,at_the_same_time(U_213,U_211)))
| ~ once(at_the_same_time(at_the_same_time(U_215,U_213),U_211)) ) ),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
( once(at_the_same_time(U_215,at_the_same_time(U_213,U_211)))
| ~ once(at_the_same_time(at_the_same_time(U_215,U_213),U_211)) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
( once(at_the_same_time(at_the_same_time(U_216,U_214),U_212))
| ~ once(at_the_same_time(U_216,at_the_same_time(U_214,U_212))) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
! [A] :
( once(at_the_same_time(A,A))
| ~ once(A) ),
inference(fof_nnf,[status(thm)],[idempotence_of_at_the_same_time]) ).
fof(f_31_2,plain,
! [U_217] :
( once(at_the_same_time(U_217,U_217))
| ~ once(U_217) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_217] :
( once(at_the_same_time(U_217,U_217))
| ~ once(U_217) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( once(at_the_same_time(U_217,U_217))
| ~ once(U_217) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B] :
( ( once(B)
& once(A) )
| ~ once(at_the_same_time(A,B)) ),
inference(fof_nnf,[status(thm)],[conjunction_at_the_same_time]) ).
fof(f_32_2,plain,
! [U_219,U_218] :
( ( once(U_218)
& once(U_219) )
| ~ once(at_the_same_time(U_219,U_218)) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_218,U_219] :
( once(U_218)
| ~ sP33(U_218,U_219) )
& ! [U_218,U_219] :
( once(U_219)
| ~ sP33(U_218,U_219) )
& ! [U_218,U_219] :
( sP33(U_218,U_219)
| ~ once(at_the_same_time(U_219,U_218)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33])],[f_32_2]) ).
cnf(f_32_4,plain,
( sP33(U_218,U_219)
| ~ once(at_the_same_time(U_219,U_218)) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( once(U_219)
| ~ sP33(U_218,U_219) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_6,plain,
( once(U_218)
| ~ sP33(U_218,U_219) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [X,P] :
( ( once(at(X,P))
| ~ incident_o(P,trajectory_of(X)) )
& ( incident_o(P,trajectory_of(X))
| ~ once(at(X,P)) ) ),
inference(fof_nnf,[status(thm)],[at_on_trajectory]) ).
fof(f_33_2,plain,
! [U_221,U_220] :
( ( once(at(U_221,U_220))
| ~ incident_o(U_220,trajectory_of(U_221)) )
& ( incident_o(U_220,trajectory_of(U_221))
| ~ once(at(U_221,U_220)) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_225,U_223] :
( once(at(U_225,U_223))
| ~ incident_o(U_223,trajectory_of(U_225)) )
& ! [U_224,U_222] :
( incident_o(U_222,trajectory_of(U_224))
| ~ once(at(U_224,U_222)) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_223,U_225] :
( once(at(U_225,U_223))
| ~ incident_o(U_223,trajectory_of(U_225)) )
& ! [U_224,U_222] :
( incident_o(U_222,trajectory_of(U_224))
| ~ once(at(U_224,U_222)) ) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( incident_o(U_222,trajectory_of(U_224))
| ~ once(at(U_224,U_222)) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
( once(at(U_225,U_223))
| ~ incident_o(U_223,trajectory_of(U_225)) ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [X] :
? [O] : trajectory_of(X) = O,
inference(fof_nnf,[status(thm)],[trajectories_are_oriented_curves]) ).
fof(f_34_2,plain,
! [U_227] :
? [U_226] : trajectory_of(U_227) = U_226,
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_227] : trajectory_of(U_227) = sK31(U_227),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_226,sK31(U_227))],[f_34_2]) ).
fof(f_34_4,plain,
! [U_227] : trajectory_of(U_227) = sK31(U_227),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
trajectory_of(U_227) = sK31(U_227),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
! [P1,P2,Q1,Q2,X,Y] :
( ~ ordered_by(trajectory_of(Y),Q2,P2)
| ~ ordered_by(trajectory_of(X),P1,Q1)
| ~ once(at_the_same_time(at(X,Q1),at(Y,Q2)))
| ~ once(at_the_same_time(at(X,P1),at(Y,P2))) ),
inference(fof_nnf,[status(thm)],[homogeneous_behaviour]) ).
fof(f_35_2,plain,
! [U_233,U_232,U_231,U_230,U_229,U_228] :
( ~ ordered_by(trajectory_of(U_228),U_230,U_232)
| ~ ordered_by(trajectory_of(U_229),U_233,U_231)
| ~ once(at_the_same_time(at(U_229,U_231),at(U_228,U_230)))
| ~ once(at_the_same_time(at(U_229,U_233),at(U_228,U_232))) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_228,U_229,U_230,U_231,U_232,U_233] :
( ~ ordered_by(trajectory_of(U_228),U_230,U_232)
| ~ ordered_by(trajectory_of(U_229),U_233,U_231)
| ~ once(at_the_same_time(at(U_229,U_231),at(U_228,U_230)))
| ~ once(at_the_same_time(at(U_229,U_233),at(U_228,U_232))) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( ~ ordered_by(trajectory_of(U_228),U_230,U_232)
| ~ ordered_by(trajectory_of(U_229),U_233,U_231)
| ~ once(at_the_same_time(at(U_229,U_231),at(U_228,U_230)))
| ~ once(at_the_same_time(at(U_229,U_233),at(U_228,U_232))) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A] :
( ! [X] :
? [P] : once(at_the_same_time(A,at(X,P)))
| ~ once(A) ),
inference(fof_nnf,[status(thm)],[localization]) ).
fof(f_36_2,plain,
! [U_236] :
( ! [U_235] :
? [U_234] : once(at_the_same_time(U_236,at(U_235,U_234)))
| ~ once(U_236) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_236] :
( ! [U_235] : once(at_the_same_time(U_236,at(U_235,sK32(U_236,U_235))))
| ~ once(U_236) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_234,sK32(U_236,U_235))],[f_36_2]) ).
fof(f_36_4,plain,
! [U_235,U_236] :
( once(at_the_same_time(U_236,at(U_235,sK32(U_236,U_235))))
| ~ once(U_236) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
( once(at_the_same_time(U_236,at(U_235,sK32(U_236,U_235))))
| ~ once(U_236) ),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,negated_conjecture,
~ ! [P,X,Y] :
( connect(X,Y,P)
=> ( incident_o(P,trajectory_of(Y))
& incident_o(P,trajectory_of(X)) ) ),
inference(negate,[status(cth)],[t13]) ).
fof(f_37_2,negated_conjecture,
? [P,X,Y] :
( ( ~ incident_o(P,trajectory_of(Y))
| ~ incident_o(P,trajectory_of(X)) )
& connect(X,Y,P) ),
inference(fof_nnf,[status(thm)],[f_37_1]) ).
fof(f_37_3,negated_conjecture,
? [U_239,U_238,U_237] :
( ( ~ incident_o(U_239,trajectory_of(U_237))
| ~ incident_o(U_239,trajectory_of(U_238)) )
& connect(U_238,U_237,U_239) ),
inference(variable_rename,[status(thm)],[f_37_2]) ).
fof(f_37_4,negated_conjecture,
? [U_238,U_237] :
( ( ~ incident_o(sK33,trajectory_of(U_237))
| ~ incident_o(sK33,trajectory_of(U_238)) )
& connect(U_238,U_237,sK33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_239,sK33)],[f_37_3]) ).
fof(f_37_5,negated_conjecture,
? [U_237] :
( ( ~ incident_o(sK33,trajectory_of(U_237))
| ~ incident_o(sK33,trajectory_of(sK34)) )
& connect(sK34,U_237,sK33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_238,sK34)],[f_37_4]) ).
fof(f_37_6,negated_conjecture,
( ( ~ incident_o(sK33,trajectory_of(sK35))
| ~ incident_o(sK33,trajectory_of(sK34)) )
& connect(sK34,sK35,sK33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_237,sK35)],[f_37_5]) ).
fof(f_37_7,negated_conjecture,
( ( ~ incident_o(sK33,trajectory_of(sK35))
| ~ incident_o(sK33,trajectory_of(sK34)) )
& connect(sK34,sK35,sK33) ),
inference(definitional_conversion,[status(esa)],[f_37_6]) ).
cnf(f_37_8,negated_conjecture,
connect(sK34,sK35,sK33),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_9,negated_conjecture,
( ~ incident_o(sK33,trajectory_of(sK35))
| ~ incident_o(sK33,trajectory_of(sK34)) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( sum(Eq_x_0,Eq_x_1) = sum(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( underlying_curve(Eq_x_0) = underlying_curve(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( at(Eq_x_0,Eq_x_1) = at(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( at_the_same_time(Eq_x_0,Eq_x_1) = at_the_same_time(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( trajectory_of(Eq_x_0) = trajectory_of(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK15(Eq_x_0,Eq_x_1) = sK15(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_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_functions]) ).
cnf(equality_25,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_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_functions]) ).
cnf(equality_29,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| 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_functions]) ).
cnf(equality_30,axiom,
( sK22(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK22(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| 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_functions]) ).
cnf(equality_31,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( sK25(Eq_x_0,Eq_x_1) = sK25(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( sK26(Eq_x_0,Eq_x_1) = sK26(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK27(Eq_x_0,Eq_x_1) = sK27(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK28(Eq_x_0,Eq_x_1) = sK28(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( part_of(Eq_y_0,Eq_y_1)
| ~ part_of(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( incident_c(Eq_y_0,Eq_y_1)
| ~ incident_c(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,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_44,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(equality_45,axiom,
( meet(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ meet(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(equality_46,axiom,
( closed(Eq_y_0)
| ~ closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( open(Eq_y_0)
| ~ open(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( between_c(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ between_c(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(equality_49,axiom,
( between_o(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ between_o(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(equality_50,axiom,
( ordered_by(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ ordered_by(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(equality_51,axiom,
( start_point(Eq_y_0,Eq_y_1)
| ~ start_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_52,axiom,
( incident_o(Eq_y_0,Eq_y_1)
| ~ incident_o(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( finish_point(Eq_y_0,Eq_y_1)
| ~ finish_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_54,axiom,
( connect(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ connect(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(equality_55,axiom,
( once(Eq_y_0)
| ~ once(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(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(equality_58,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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(equality_59,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(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(equality_60,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(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(equality_61,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP5(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(equality_62,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( sP7(Eq_y_0,Eq_y_1)
| ~ sP7(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_64,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(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(equality_65,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP9(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(equality_66,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP10(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(equality_67,axiom,
( sP11(Eq_y_0,Eq_y_1)
| ~ sP11(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_68,axiom,
( sP12(Eq_y_0,Eq_y_1)
| ~ sP12(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_69,axiom,
( sP13(Eq_y_0,Eq_y_1)
| ~ sP13(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_70,axiom,
( sP14(Eq_y_0,Eq_y_1)
| ~ sP14(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_71,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP15(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(equality_72,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP16(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(equality_73,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP17(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(equality_74,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP18(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(equality_75,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP19(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(equality_76,axiom,
( sP20(Eq_y_0,Eq_y_1)
| ~ sP20(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_77,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP21(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(equality_78,axiom,
( sP22(Eq_y_0,Eq_y_1)
| ~ sP22(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_79,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP23(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(equality_80,axiom,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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(equality_81,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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(equality_82,axiom,
( sP26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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(equality_83,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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(equality_84,axiom,
( sP28(Eq_y_0,Eq_y_1)
| ~ sP28(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_85,axiom,
( sP29(Eq_y_0,Eq_y_1)
| ~ sP29(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_86,axiom,
( sP30(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP30(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(equality_87,axiom,
( sP31(Eq_y_0,Eq_y_1)
| ~ sP31(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_88,axiom,
( sP32(Eq_y_0,Eq_y_1)
| ~ sP32(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_89,axiom,
( sP33(Eq_y_0,Eq_y_1)
| ~ sP33(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO147+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 07:35:50 UTC 2026
% 0.13/0.36 % CPUTime :
% 30.37/30.60 % SZS status Theorem for theBenchmark
% 30.37/30.60 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------