%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO112+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:39:31 AM UTC 2026
% Result : Theorem 8.25s 13.54s
% Output : Proof 8.40s
% 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(theorem_3_8_2,conjecture,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> between_c(C,R,Q,P) ),
file('theBenchmark.p',theorem_3_8_2) ).
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]) ).
cnf(f_1_5,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_4]) ).
cnf(f_1_6,plain,
( incident_c(sK1(U_7,U_5),U_5)
| part_of(U_5,U_7) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( ~ incident_c(sK1(U_7,U_5),U_7)
| part_of(U_5,U_7) ),
inference(clausify,[status(thm)],[f_1_4]) ).
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]) ).
cnf(f_2_6,plain,
( 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(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_7,plain,
( ~ incident_c(U_14,U_19)
| incident_c(U_14,U_21)
| U_21 != sum(U_19,U_17) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_8,plain,
( ~ incident_c(U_14,U_17)
| incident_c(U_14,U_21)
| U_21 != sum(U_19,U_17) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_9,plain,
( 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_22)
| U_22 = sum(U_20,U_18) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_10,plain,
( ~ incident_c(sK3(U_22,U_20,U_18),U_22)
| incident_c(sK2(U_22,U_20,U_18),U_22)
| U_22 = sum(U_20,U_18) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_11,plain,
( ~ incident_c(sK2(U_22,U_20,U_18),U_20)
| incident_c(sK3(U_22,U_20,U_18),U_18)
| incident_c(sK3(U_22,U_20,U_18),U_20)
| U_22 = sum(U_20,U_18) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_12,plain,
( ~ incident_c(sK2(U_22,U_20,U_18),U_18)
| incident_c(sK3(U_22,U_20,U_18),U_18)
| incident_c(sK3(U_22,U_20,U_18),U_20)
| U_22 = sum(U_20,U_18) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_13,plain,
( ~ incident_c(sK2(U_22,U_20,U_18),U_20)
| ~ incident_c(sK3(U_22,U_20,U_18),U_22)
| U_22 = sum(U_20,U_18) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_14,plain,
( ~ incident_c(sK2(U_22,U_20,U_18),U_18)
| ~ incident_c(sK3(U_22,U_20,U_18),U_22)
| U_22 = sum(U_20,U_18) ),
inference(clausify,[status(thm)],[f_2_5]) ).
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]) ).
cnf(f_3_6,plain,
( incident_c(U_31,U_29)
| ~ end_point(U_31,U_29) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,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)
| ~ end_point(U_31,U_29) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( part_of(sK4(U_32,U_30),U_30)
| ~ incident_c(U_32,U_30)
| end_point(U_32,U_30) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( part_of(sK5(U_32,U_30),U_30)
| ~ incident_c(U_32,U_30)
| end_point(U_32,U_30) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( incident_c(U_32,sK4(U_32,U_30))
| ~ incident_c(U_32,U_30)
| end_point(U_32,U_30) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( incident_c(U_32,sK5(U_32,U_30))
| ~ incident_c(U_32,U_30)
| end_point(U_32,U_30) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_12,plain,
( ~ part_of(sK4(U_32,U_30),sK5(U_32,U_30))
| ~ incident_c(U_32,U_30)
| end_point(U_32,U_30) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_13,plain,
( ~ part_of(sK5(U_32,U_30),sK4(U_32,U_30))
| ~ incident_c(U_32,U_30)
| end_point(U_32,U_30) ),
inference(clausify,[status(thm)],[f_3_5]) ).
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]) ).
cnf(f_4_4,plain,
( incident_c(U_37,U_35)
| ~ inner_point(U_37,U_35) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ end_point(U_37,U_35)
| ~ inner_point(U_37,U_35) ),
inference(clausify,[status(thm)],[f_4_3]) ).
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_3]) ).
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]) ).
cnf(f_5_5,plain,
( incident_c(U_48,U_46)
| ~ meet(U_48,U_46,U_44) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( incident_c(U_48,U_44)
| ~ meet(U_48,U_46,U_44) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( end_point(U_39,U_46)
| ~ incident_c(U_39,U_44)
| ~ incident_c(U_39,U_46)
| ~ meet(U_48,U_46,U_44) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_8,plain,
( end_point(U_39,U_44)
| ~ incident_c(U_39,U_44)
| ~ incident_c(U_39,U_46)
| ~ meet(U_48,U_46,U_44) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_9,plain,
( incident_c(sK6(U_49,U_47,U_45),U_47)
| ~ incident_c(U_49,U_45)
| ~ incident_c(U_49,U_47)
| meet(U_49,U_47,U_45) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_10,plain,
( incident_c(sK6(U_49,U_47,U_45),U_45)
| ~ incident_c(U_49,U_45)
| ~ incident_c(U_49,U_47)
| meet(U_49,U_47,U_45) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_11,plain,
( ~ end_point(sK6(U_49,U_47,U_45),U_45)
| ~ end_point(sK6(U_49,U_47,U_45),U_47)
| ~ incident_c(U_49,U_45)
| ~ incident_c(U_49,U_47)
| meet(U_49,U_47,U_45) ),
inference(clausify,[status(thm)],[f_5_4]) ).
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]) ).
cnf(f_6_5,plain,
( ~ end_point(U_50,U_53)
| ~ closed(U_53) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( closed(U_54)
| end_point(sK7(U_54),U_54) ),
inference(clausify,[status(thm)],[f_6_4]) ).
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]) ).
cnf(f_7_5,plain,
( end_point(sK8(U_58),U_58)
| ~ open(U_58) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( open(U_59)
| ~ end_point(U_56,U_59) ),
inference(clausify,[status(thm)],[f_7_4]) ).
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]) ).
cnf(f_8_3,plain,
( open(U_60)
| U_60 = U_61
| ~ part_of(U_60,U_61) ),
inference(clausify,[status(thm)],[f_8_2]) ).
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]) ).
cnf(f_9_3,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_2]) ).
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]) ).
cnf(f_10_4,plain,
inner_point(sK9(U_68),U_68),
inference(clausify,[status(thm)],[f_10_3]) ).
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]) ).
cnf(f_11_5,plain,
( meet(U_71,sK10(U_72,U_71),sK11(U_72,U_71))
| ~ inner_point(U_71,U_72) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_6,plain,
( U_72 = sum(sK10(U_72,U_71),sK11(U_72,U_71))
| ~ inner_point(U_71,U_72) ),
inference(clausify,[status(thm)],[f_11_4]) ).
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]) ).
cnf(f_12_3,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_2]) ).
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]) ).
cnf(f_13_4,plain,
( end_point(sK12(U_79,U_78),U_79)
| ~ end_point(U_78,U_79) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( U_78 != sK12(U_79,U_78)
| ~ end_point(U_78,U_79) ),
inference(clausify,[status(thm)],[f_13_3]) ).
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]) ).
cnf(f_14_4,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_3]) ).
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]) ).
cnf(f_15_4,plain,
( sK13(U_88,U_87) = sum(U_88,U_87)
| ~ meet(U_85,U_88,U_87) ),
inference(clausify,[status(thm)],[f_15_3]) ).
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]) ).
cnf(f_16_6,plain,
( incident_c(sK15(U_91,U_90),U_90)
| incident_c(sK14(U_91,U_90),U_91)
| U_91 = U_90 ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_7,plain,
( ~ incident_c(sK15(U_91,U_90),U_91)
| incident_c(sK14(U_91,U_90),U_91)
| U_91 = U_90 ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_8,plain,
( incident_c(sK15(U_91,U_90),U_90)
| ~ incident_c(sK14(U_91,U_90),U_90)
| U_91 = U_90 ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_9,plain,
( ~ incident_c(sK15(U_91,U_90),U_91)
| ~ incident_c(sK14(U_91,U_90),U_90)
| U_91 = U_90 ),
inference(clausify,[status(thm)],[f_16_5]) ).
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]) ).
cnf(f_17_5,plain,
( U_104 != U_100
| ~ between_c(U_106,U_104,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_6,plain,
( part_of(sK16(U_106,U_104,U_102,U_100),U_106)
| ~ between_c(U_106,U_104,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_7,plain,
( end_point(U_104,sK16(U_106,U_104,U_102,U_100))
| ~ between_c(U_106,U_104,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_8,plain,
( end_point(U_100,sK16(U_106,U_104,U_102,U_100))
| ~ between_c(U_106,U_104,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_9,plain,
( inner_point(U_102,sK16(U_106,U_104,U_102,U_100))
| ~ between_c(U_106,U_104,U_102,U_100) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_10,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_4]) ).
fof(f_18_1,negated_conjecture,
~ ! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> between_c(C,R,Q,P) ),
inference(negate,[status(cth)],[theorem_3_8_2]) ).
fof(f_18_2,negated_conjecture,
? [C,P,Q,R] :
( ~ between_c(C,R,Q,P)
& between_c(C,P,Q,R) ),
inference(fof_nnf,[status(thm)],[f_18_1]) ).
fof(f_18_3,negated_conjecture,
? [U_111,U_110,U_109,U_108] :
( ~ between_c(U_111,U_108,U_109,U_110)
& between_c(U_111,U_110,U_109,U_108) ),
inference(variable_rename,[status(thm)],[f_18_2]) ).
fof(f_18_4,negated_conjecture,
? [U_110,U_109,U_108] :
( ~ between_c(sK17,U_108,U_109,U_110)
& between_c(sK17,U_110,U_109,U_108) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_111,sK17)],[f_18_3]) ).
fof(f_18_5,negated_conjecture,
? [U_109,U_108] :
( ~ between_c(sK17,U_108,U_109,sK18)
& between_c(sK17,sK18,U_109,U_108) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_110,sK18)],[f_18_4]) ).
fof(f_18_6,negated_conjecture,
? [U_108] :
( ~ between_c(sK17,U_108,sK19,sK18)
& between_c(sK17,sK18,sK19,U_108) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_109,sK19)],[f_18_5]) ).
fof(f_18_7,negated_conjecture,
( ~ between_c(sK17,sK20,sK19,sK18)
& between_c(sK17,sK18,sK19,sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_108,sK20)],[f_18_6]) ).
fof(f_18_8,negated_conjecture,
( ~ between_c(sK17,sK20,sK19,sK18)
& between_c(sK17,sK18,sK19,sK20) ),
inference(definitional_conversion,[status(esa)],[f_18_7]) ).
cnf(f_18_9,negated_conjecture,
between_c(sK17,sK18,sK19,sK20),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_10,negated_conjecture,
~ between_c(sK17,sK20,sK19,sK18),
inference(clausify,[status(thm)],[f_18_8]) ).
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,
( 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_6,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_7,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_8,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_9,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_10,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_11,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,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_16,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_17,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_18,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_19,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_20,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_21,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_22,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_23,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_24,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_25,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_26,axiom,
( closed(Eq_y_0)
| ~ closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( open(Eq_y_0)
| ~ open(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO112+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n014.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sat Sep 19 07:26:27 UTC 2026
% 0.10/5.36 % CPUTime :
% 8.25/13.54 % SZS status Theorem for theBenchmark
% 8.25/13.54 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------