TSTP Solution File: GEO111+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO111+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:24:22 EDT 2022
% Result : Theorem 6.33s 6.55s
% Output : CNFRefutation 6.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 211 ( 62 unt; 0 def)
% Number of atoms : 700 ( 92 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 845 ( 356 ~; 274 |; 168 &)
% ( 32 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 28 ( 28 usr; 24 con; 0-4 aty)
% Number of variables : 409 ( 6 sgn 273 !; 45 ?)
% Comments :
%------------------------------------------------------------------------------
fof(part_of_defn,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ) ).
fof(end_point_defn,axiom,
! [P,C] :
( end_point(P,C)
<=> ( incident_c(P,C)
& ! [C1,C2] :
( ( part_of(C1,C)
& part_of(C2,C)
& incident_c(P,C1)
& incident_c(P,C2) )
=> ( part_of(C1,C2)
| part_of(C2,C1) ) ) ) ) ).
fof(inner_point_defn,axiom,
! [P,C] :
( inner_point(P,C)
<=> ( incident_c(P,C)
& ~ end_point(P,C) ) ) ).
fof(between_c_defn,axiom,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
<=> ( P != R
& ? [Cpp] :
( part_of(Cpp,C)
& end_point(P,Cpp)
& end_point(R,Cpp)
& inner_point(Q,Cpp) ) ) ) ).
fof(theorem_3_8_1,conjecture,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> ( incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C)
& P != Q
& Q != R
& P != R ) ) ).
fof(subgoal_0,plain,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> incident_c(P,C) ),
inference(strip,[],[theorem_3_8_1]) ).
fof(subgoal_1,plain,
! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
& incident_c(P,C) )
=> incident_c(Q,C) ),
inference(strip,[],[theorem_3_8_1]) ).
fof(subgoal_2,plain,
! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C) )
=> incident_c(R,C) ),
inference(strip,[],[theorem_3_8_1]) ).
fof(subgoal_3,plain,
! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C) )
=> P != Q ),
inference(strip,[],[theorem_3_8_1]) ).
fof(subgoal_4,plain,
! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C)
& P != Q )
=> Q != R ),
inference(strip,[],[theorem_3_8_1]) ).
fof(subgoal_5,plain,
! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C)
& P != Q
& Q != R )
=> P != R ),
inference(strip,[],[theorem_3_8_1]) ).
fof(negate_0_0,plain,
~ ! [C,P,Q,R] :
( between_c(C,P,Q,R)
=> incident_c(P,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [C,P] :
( ~ end_point(P,C)
<=> ( ~ incident_c(P,C)
| ? [C1,C2] :
( ~ part_of(C1,C2)
& ~ part_of(C2,C1)
& incident_c(P,C1)
& incident_c(P,C2)
& part_of(C1,C)
& part_of(C2,C) ) ) ),
inference(canonicalize,[],[end_point_defn]) ).
fof(normalize_0_1,plain,
! [C,P] :
( ~ end_point(P,C)
<=> ( ~ incident_c(P,C)
| ? [C1,C2] :
( ~ part_of(C1,C2)
& ~ part_of(C2,C1)
& incident_c(P,C1)
& incident_c(P,C2)
& part_of(C1,C)
& part_of(C2,C) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [C,C1,C2,P] :
( ( ~ end_point(P,C)
| incident_c(P,C) )
& ( ~ incident_c(P,C)
| ~ part_of(skolemFOFtoCNF_C1(C,P),skolemFOFtoCNF_C2(C,P))
| end_point(P,C) )
& ( ~ incident_c(P,C)
| ~ part_of(skolemFOFtoCNF_C2(C,P),skolemFOFtoCNF_C1(C,P))
| end_point(P,C) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| incident_c(P,skolemFOFtoCNF_C1(C,P)) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| incident_c(P,skolemFOFtoCNF_C2(C,P)) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| part_of(skolemFOFtoCNF_C1(C,P),C) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| part_of(skolemFOFtoCNF_C2(C,P),C) )
& ( ~ end_point(P,C)
| ~ incident_c(P,C1)
| ~ incident_c(P,C2)
| ~ part_of(C1,C)
| ~ part_of(C2,C)
| part_of(C1,C2)
| part_of(C2,C1) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [C,P] :
( ~ end_point(P,C)
| incident_c(P,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [C,P] :
( ~ incident_c(P,C)
& ? [Q,R] : between_c(C,P,Q,R) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ incident_c(skolemFOFtoCNF_P_4,skolemFOFtoCNF_C_1)
& ? [Q,R] : between_c(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,Q,R) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [Q,R] : between_c(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,Q,R),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
between_c(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(canonicalize,[],[between_c_defn]) ).
fof(normalize_0_9,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [C,Cpp,P,Q,R] :
( ( P != R
| ~ between_c(C,P,Q,R) )
& ( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) )
& ( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C)
| P = R
| between_c(C,P,Q,R) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_13,plain,
! [C,C1] :
( ~ part_of(C1,C)
<=> ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) ),
inference(canonicalize,[],[part_of_defn]) ).
fof(normalize_0_14,plain,
! [C,C1] :
( ~ part_of(C1,C)
<=> ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [C,C1,P] :
( ( ~ incident_c(skolemFOFtoCNF_P(C,C1),C)
| part_of(C1,C) )
& ( incident_c(skolemFOFtoCNF_P(C,C1),C1)
| part_of(C1,C) )
& ( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [C,C1,P] :
( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
~ incident_c(skolemFOFtoCNF_P_4,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ end_point(P,C)
| incident_c(P,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ end_point(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R))
| incident_c(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R)) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R))),bind(P,$fot(skolemFOFtoCNF_P_4))]]) ).
cnf(refute_0_2,plain,
between_c(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_4,plain,
( ~ between_c(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R)
| end_point(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R)) ),
inference(subst,[],[refute_0_3:[bind(C,$fot(skolemFOFtoCNF_C_1)),bind(P,$fot(skolemFOFtoCNF_P_4)),bind(Q,$fot(skolemFOFtoCNF_Q_3)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_5,plain,
end_point(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R)),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
incident_c(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R)),
inference(resolve,[$cnf( end_point(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R)) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_8,plain,
( ~ between_c(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R)
| part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(skolemFOFtoCNF_C_1)),bind(P,$fot(skolemFOFtoCNF_P_4)),bind(Q,$fot(skolemFOFtoCNF_Q_3)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_9,plain,
part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R) )],[refute_0_2,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_11,plain,
( ~ incident_c(X_826,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R))
| ~ part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R),skolemFOFtoCNF_C_1)
| incident_c(X_826,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_10:[bind(C,$fot(skolemFOFtoCNF_C_1)),bind(C1,$fot(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R))),bind(P,$fot(X_826))]]) ).
cnf(refute_0_12,plain,
( ~ incident_c(X_826,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R))
| incident_c(X_826,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R),skolemFOFtoCNF_C_1) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ incident_c(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R))
| incident_c(skolemFOFtoCNF_P_4,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_12:[bind(X_826,$fot(skolemFOFtoCNF_P_4))]]) ).
cnf(refute_0_14,plain,
incident_c(skolemFOFtoCNF_P_4,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_R)) )],[refute_0_6,refute_0_13]) ).
cnf(refute_0_15,plain,
~ incident_c(skolemFOFtoCNF_P_4,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P_4,skolemFOFtoCNF_C_1) )],[refute_0_14,refute_0_15]) ).
fof(negate_1_0,plain,
~ ! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
& incident_c(P,C) )
=> incident_c(Q,C) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [C,P,Q] :
( ~ incident_c(Q,C)
& incident_c(P,C)
& ? [R] : between_c(C,P,Q,R) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ incident_c(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_C_2)
& incident_c(skolemFOFtoCNF_P_5,skolemFOFtoCNF_C_2)
& ? [R] : between_c(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,R) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [R] : between_c(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,R),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
between_c(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(canonicalize,[],[between_c_defn]) ).
fof(normalize_1_5,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [C,Cpp,P,Q,R] :
( ( P != R
| ~ between_c(C,P,Q,R) )
& ( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) )
& ( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C)
| P = R
| between_c(C,P,Q,R) ) ),
inference(clausify,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [C,C1] :
( ~ part_of(C1,C)
<=> ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) ),
inference(canonicalize,[],[part_of_defn]) ).
fof(normalize_1_9,plain,
! [C,C1] :
( ~ part_of(C1,C)
<=> ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [C,C1,P] :
( ( ~ incident_c(skolemFOFtoCNF_P(C,C1),C)
| part_of(C1,C) )
& ( incident_c(skolemFOFtoCNF_P(C,C1),C1)
| part_of(C1,C) )
& ( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ) ),
inference(clausify,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [C,C1,P] :
( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [C,P] :
( ~ inner_point(P,C)
<=> ( ~ incident_c(P,C)
| end_point(P,C) ) ),
inference(canonicalize,[],[inner_point_defn]) ).
fof(normalize_1_13,plain,
! [C,P] :
( ~ inner_point(P,C)
<=> ( ~ incident_c(P,C)
| end_point(P,C) ) ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [C,P] :
( ( ~ end_point(P,C)
| ~ inner_point(P,C) )
& ( ~ inner_point(P,C)
| incident_c(P,C) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| inner_point(P,C) ) ),
inference(clausify,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [C,P] :
( ~ inner_point(P,C)
| incident_c(P,C) ),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_17,plain,
~ incident_c(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
between_c(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_2,plain,
( ~ between_c(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1)
| part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1),skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_1:[bind(C,$fot(skolemFOFtoCNF_C_2)),bind(P,$fot(skolemFOFtoCNF_P_5)),bind(Q,$fot(skolemFOFtoCNF_Q_4)),bind(R,$fot(skolemFOFtoCNF_R_1))]]) ).
cnf(refute_1_3,plain,
part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1),skolemFOFtoCNF_C_2),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_5,plain,
( ~ incident_c(X_1435,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1))
| ~ part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1),skolemFOFtoCNF_C_2)
| incident_c(X_1435,skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_4:[bind(C,$fot(skolemFOFtoCNF_C_2)),bind(C1,$fot(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1))),bind(P,$fot(X_1435))]]) ).
cnf(refute_1_6,plain,
( ~ incident_c(X_1435,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1))
| incident_c(X_1435,skolemFOFtoCNF_C_2) ),
inference(resolve,[$cnf( part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1),skolemFOFtoCNF_C_2) )],[refute_1_3,refute_1_5]) ).
cnf(refute_1_7,plain,
( ~ incident_c(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1))
| incident_c(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_6:[bind(X_1435,$fot(skolemFOFtoCNF_Q_4))]]) ).
cnf(refute_1_8,plain,
( ~ inner_point(P,C)
| incident_c(P,C) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_9,plain,
( ~ inner_point(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1))
| incident_c(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1)) ),
inference(subst,[],[refute_1_8:[bind(C,$fot(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1))),bind(P,$fot(skolemFOFtoCNF_Q_4))]]) ).
cnf(refute_1_10,plain,
( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_11,plain,
( ~ between_c(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1)
| inner_point(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1)) ),
inference(subst,[],[refute_1_10:[bind(C,$fot(skolemFOFtoCNF_C_2)),bind(P,$fot(skolemFOFtoCNF_P_5)),bind(Q,$fot(skolemFOFtoCNF_Q_4)),bind(R,$fot(skolemFOFtoCNF_R_1))]]) ).
cnf(refute_1_12,plain,
inner_point(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1)),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1) )],[refute_1_0,refute_1_11]) ).
cnf(refute_1_13,plain,
incident_c(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1)),
inference(resolve,[$cnf( inner_point(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1)) )],[refute_1_12,refute_1_9]) ).
cnf(refute_1_14,plain,
incident_c(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_C_2),
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_2,skolemFOFtoCNF_P_5,skolemFOFtoCNF_Q_4,skolemFOFtoCNF_R_1)) )],[refute_1_13,refute_1_7]) ).
cnf(refute_1_15,plain,
~ incident_c(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_16,plain,
$false,
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_Q_4,skolemFOFtoCNF_C_2) )],[refute_1_14,refute_1_15]) ).
fof(negate_2_0,plain,
~ ! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C) )
=> incident_c(R,C) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
! [C,P] :
( ~ end_point(P,C)
<=> ( ~ incident_c(P,C)
| ? [C1,C2] :
( ~ part_of(C1,C2)
& ~ part_of(C2,C1)
& incident_c(P,C1)
& incident_c(P,C2)
& part_of(C1,C)
& part_of(C2,C) ) ) ),
inference(canonicalize,[],[end_point_defn]) ).
fof(normalize_2_1,plain,
! [C,P] :
( ~ end_point(P,C)
<=> ( ~ incident_c(P,C)
| ? [C1,C2] :
( ~ part_of(C1,C2)
& ~ part_of(C2,C1)
& incident_c(P,C1)
& incident_c(P,C2)
& part_of(C1,C)
& part_of(C2,C) ) ) ),
inference(specialize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
! [C,C1,C2,P] :
( ( ~ end_point(P,C)
| incident_c(P,C) )
& ( ~ incident_c(P,C)
| ~ part_of(skolemFOFtoCNF_C1(C,P),skolemFOFtoCNF_C2(C,P))
| end_point(P,C) )
& ( ~ incident_c(P,C)
| ~ part_of(skolemFOFtoCNF_C2(C,P),skolemFOFtoCNF_C1(C,P))
| end_point(P,C) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| incident_c(P,skolemFOFtoCNF_C1(C,P)) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| incident_c(P,skolemFOFtoCNF_C2(C,P)) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| part_of(skolemFOFtoCNF_C1(C,P),C) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| part_of(skolemFOFtoCNF_C2(C,P),C) )
& ( ~ end_point(P,C)
| ~ incident_c(P,C1)
| ~ incident_c(P,C2)
| ~ part_of(C1,C)
| ~ part_of(C2,C)
| part_of(C1,C2)
| part_of(C2,C1) ) ),
inference(clausify,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [C,P] :
( ~ end_point(P,C)
| incident_c(P,C) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
? [C,P,Q,R] :
( ~ incident_c(R,C)
& between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_5,plain,
( ~ incident_c(skolemFOFtoCNF_R_2,skolemFOFtoCNF_C_3)
& between_c(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2)
& incident_c(skolemFOFtoCNF_P_6,skolemFOFtoCNF_C_3)
& incident_c(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_C_3) ),
inference(skolemize,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
between_c(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2),
inference(conjunct,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(canonicalize,[],[between_c_defn]) ).
fof(normalize_2_8,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(specialize,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
! [C,Cpp,P,Q,R] :
( ( P != R
| ~ between_c(C,P,Q,R) )
& ( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) )
& ( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C)
| P = R
| between_c(C,P,Q,R) ) ),
inference(clausify,[],[normalize_2_8]) ).
fof(normalize_2_10,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(conjunct,[],[normalize_2_9]) ).
fof(normalize_2_11,plain,
! [C,C1] :
( ~ part_of(C1,C)
<=> ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) ),
inference(canonicalize,[],[part_of_defn]) ).
fof(normalize_2_12,plain,
! [C,C1] :
( ~ part_of(C1,C)
<=> ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) ) ),
inference(specialize,[],[normalize_2_11]) ).
fof(normalize_2_13,plain,
! [C,C1,P] :
( ( ~ incident_c(skolemFOFtoCNF_P(C,C1),C)
| part_of(C1,C) )
& ( incident_c(skolemFOFtoCNF_P(C,C1),C1)
| part_of(C1,C) )
& ( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ) ),
inference(clausify,[],[normalize_2_12]) ).
fof(normalize_2_14,plain,
! [C,C1,P] :
( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ),
inference(conjunct,[],[normalize_2_13]) ).
fof(normalize_2_15,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) ),
inference(conjunct,[],[normalize_2_9]) ).
fof(normalize_2_16,plain,
~ incident_c(skolemFOFtoCNF_R_2,skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_2_5]) ).
cnf(refute_2_0,plain,
( ~ end_point(P,C)
| incident_c(P,C) ),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
( ~ end_point(skolemFOFtoCNF_R_2,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2))
| incident_c(skolemFOFtoCNF_R_2,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2)) ),
inference(subst,[],[refute_2_0:[bind(C,$fot(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2))),bind(P,$fot(skolemFOFtoCNF_R_2))]]) ).
cnf(refute_2_2,plain,
between_c(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_3,plain,
( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(canonicalize,[],[normalize_2_10]) ).
cnf(refute_2_4,plain,
( ~ between_c(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2)
| end_point(skolemFOFtoCNF_R_2,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2)) ),
inference(subst,[],[refute_2_3:[bind(C,$fot(skolemFOFtoCNF_C_3)),bind(P,$fot(skolemFOFtoCNF_P_6)),bind(Q,$fot(skolemFOFtoCNF_Q_5)),bind(R,$fot(skolemFOFtoCNF_R_2))]]) ).
cnf(refute_2_5,plain,
end_point(skolemFOFtoCNF_R_2,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2)),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2) )],[refute_2_2,refute_2_4]) ).
cnf(refute_2_6,plain,
incident_c(skolemFOFtoCNF_R_2,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2)),
inference(resolve,[$cnf( end_point(skolemFOFtoCNF_R_2,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2)) )],[refute_2_5,refute_2_1]) ).
cnf(refute_2_7,plain,
( ~ incident_c(P,C1)
| ~ part_of(C1,C)
| incident_c(P,C) ),
inference(canonicalize,[],[normalize_2_14]) ).
cnf(refute_2_8,plain,
( ~ incident_c(P,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2))
| ~ part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2),skolemFOFtoCNF_C_3)
| incident_c(P,skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_2_7:[bind(C,$fot(skolemFOFtoCNF_C_3)),bind(C1,$fot(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2)))]]) ).
cnf(refute_2_9,plain,
( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) ),
inference(canonicalize,[],[normalize_2_15]) ).
cnf(refute_2_10,plain,
( ~ between_c(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2)
| part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2),skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_2_9:[bind(C,$fot(skolemFOFtoCNF_C_3)),bind(P,$fot(skolemFOFtoCNF_P_6)),bind(Q,$fot(skolemFOFtoCNF_Q_5)),bind(R,$fot(skolemFOFtoCNF_R_2))]]) ).
cnf(refute_2_11,plain,
part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2),skolemFOFtoCNF_C_3),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2) )],[refute_2_2,refute_2_10]) ).
cnf(refute_2_12,plain,
( ~ incident_c(P,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2))
| incident_c(P,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( part_of(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2),skolemFOFtoCNF_C_3) )],[refute_2_11,refute_2_8]) ).
cnf(refute_2_13,plain,
( ~ incident_c(skolemFOFtoCNF_R_2,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2))
| incident_c(skolemFOFtoCNF_R_2,skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_2_12:[bind(P,$fot(skolemFOFtoCNF_R_2))]]) ).
cnf(refute_2_14,plain,
incident_c(skolemFOFtoCNF_R_2,skolemFOFtoCNF_C_3),
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_R_2,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_3,skolemFOFtoCNF_P_6,skolemFOFtoCNF_Q_5,skolemFOFtoCNF_R_2)) )],[refute_2_6,refute_2_13]) ).
cnf(refute_2_15,plain,
~ incident_c(skolemFOFtoCNF_R_2,skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_2_16]) ).
cnf(refute_2_16,plain,
$false,
inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_R_2,skolemFOFtoCNF_C_3) )],[refute_2_14,refute_2_15]) ).
fof(negate_3_0,plain,
~ ! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C) )
=> P != Q ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
! [C,P] :
( ~ inner_point(P,C)
<=> ( ~ incident_c(P,C)
| end_point(P,C) ) ),
inference(canonicalize,[],[inner_point_defn]) ).
fof(normalize_3_1,plain,
! [C,P] :
( ~ inner_point(P,C)
<=> ( ~ incident_c(P,C)
| end_point(P,C) ) ),
inference(specialize,[],[normalize_3_0]) ).
fof(normalize_3_2,plain,
! [C,P] :
( ( ~ end_point(P,C)
| ~ inner_point(P,C) )
& ( ~ inner_point(P,C)
| incident_c(P,C) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| inner_point(P,C) ) ),
inference(clausify,[],[normalize_3_1]) ).
fof(normalize_3_3,plain,
! [C,P] :
( ~ end_point(P,C)
| ~ inner_point(P,C) ),
inference(conjunct,[],[normalize_3_2]) ).
fof(normalize_3_4,plain,
? [C,P,Q,R] :
( P = Q
& between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_5,plain,
( skolemFOFtoCNF_P_7 = skolemFOFtoCNF_Q_6
& between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_6,skolemFOFtoCNF_R_3)
& incident_c(skolemFOFtoCNF_P_7,skolemFOFtoCNF_C_4)
& incident_c(skolemFOFtoCNF_Q_6,skolemFOFtoCNF_C_4)
& incident_c(skolemFOFtoCNF_R_3,skolemFOFtoCNF_C_4) ),
inference(skolemize,[],[normalize_3_4]) ).
fof(normalize_3_6,plain,
between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_6,skolemFOFtoCNF_R_3),
inference(conjunct,[],[normalize_3_5]) ).
fof(normalize_3_7,plain,
skolemFOFtoCNF_P_7 = skolemFOFtoCNF_Q_6,
inference(conjunct,[],[normalize_3_5]) ).
fof(normalize_3_8,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(canonicalize,[],[between_c_defn]) ).
fof(normalize_3_9,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(specialize,[],[normalize_3_8]) ).
fof(normalize_3_10,plain,
! [C,Cpp,P,Q,R] :
( ( P != R
| ~ between_c(C,P,Q,R) )
& ( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) )
& ( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C)
| P = R
| between_c(C,P,Q,R) ) ),
inference(clausify,[],[normalize_3_9]) ).
fof(normalize_3_11,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(conjunct,[],[normalize_3_10]) ).
fof(normalize_3_12,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(conjunct,[],[normalize_3_10]) ).
cnf(refute_3_0,plain,
( ~ end_point(P,C)
| ~ inner_point(P,C) ),
inference(canonicalize,[],[normalize_3_3]) ).
cnf(refute_3_1,plain,
( ~ end_point(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3))
| ~ inner_point(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3)) ),
inference(subst,[],[refute_3_0:[bind(C,$fot(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3))),bind(P,$fot(skolemFOFtoCNF_P_7))]]) ).
cnf(refute_3_2,plain,
between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_6,skolemFOFtoCNF_R_3),
inference(canonicalize,[],[normalize_3_6]) ).
cnf(refute_3_3,plain,
skolemFOFtoCNF_P_7 = skolemFOFtoCNF_Q_6,
inference(canonicalize,[],[normalize_3_7]) ).
cnf(refute_3_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_3_5,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_3_6,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_3_4,refute_3_5]) ).
cnf(refute_3_7,plain,
( skolemFOFtoCNF_P_7 != skolemFOFtoCNF_Q_6
| skolemFOFtoCNF_Q_6 = skolemFOFtoCNF_P_7 ),
inference(subst,[],[refute_3_6:[bind(X,$fot(skolemFOFtoCNF_P_7)),bind(Y,$fot(skolemFOFtoCNF_Q_6))]]) ).
cnf(refute_3_8,plain,
skolemFOFtoCNF_Q_6 = skolemFOFtoCNF_P_7,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_6) )],[refute_3_3,refute_3_7]) ).
cnf(refute_3_9,plain,
( skolemFOFtoCNF_Q_6 != skolemFOFtoCNF_P_7
| ~ between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_6,skolemFOFtoCNF_R_3)
| between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3) ),
introduced(tautology,[equality,[$cnf( between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_6,skolemFOFtoCNF_R_3) ),[2],$fot(skolemFOFtoCNF_P_7)]]) ).
cnf(refute_3_10,plain,
( ~ between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_6,skolemFOFtoCNF_R_3)
| between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Q_6,skolemFOFtoCNF_P_7) )],[refute_3_8,refute_3_9]) ).
cnf(refute_3_11,plain,
between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_6,skolemFOFtoCNF_R_3) )],[refute_3_2,refute_3_10]) ).
cnf(refute_3_12,plain,
( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(canonicalize,[],[normalize_3_11]) ).
cnf(refute_3_13,plain,
( ~ between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3)
| inner_point(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3)) ),
inference(subst,[],[refute_3_12:[bind(C,$fot(skolemFOFtoCNF_C_4)),bind(P,$fot(skolemFOFtoCNF_P_7)),bind(Q,$fot(skolemFOFtoCNF_P_7)),bind(R,$fot(skolemFOFtoCNF_R_3))]]) ).
cnf(refute_3_14,plain,
inner_point(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3)),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3) )],[refute_3_11,refute_3_13]) ).
cnf(refute_3_15,plain,
~ end_point(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3)),
inference(resolve,[$cnf( inner_point(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3)) )],[refute_3_14,refute_3_1]) ).
cnf(refute_3_16,plain,
( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(canonicalize,[],[normalize_3_12]) ).
cnf(refute_3_17,plain,
( ~ between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3)
| end_point(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3)) ),
inference(subst,[],[refute_3_16:[bind(C,$fot(skolemFOFtoCNF_C_4)),bind(P,$fot(skolemFOFtoCNF_P_7)),bind(Q,$fot(skolemFOFtoCNF_P_7)),bind(R,$fot(skolemFOFtoCNF_R_3))]]) ).
cnf(refute_3_18,plain,
end_point(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3)),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3) )],[refute_3_11,refute_3_17]) ).
cnf(refute_3_19,plain,
$false,
inference(resolve,[$cnf( end_point(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_4,skolemFOFtoCNF_P_7,skolemFOFtoCNF_P_7,skolemFOFtoCNF_R_3)) )],[refute_3_18,refute_3_15]) ).
fof(negate_4_0,plain,
~ ! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C)
& P != Q )
=> Q != R ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
? [C,P,Q,R] :
( P != Q
& Q = R
& between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C) ),
inference(canonicalize,[],[negate_4_0]) ).
fof(normalize_4_1,plain,
( skolemFOFtoCNF_P_8 != skolemFOFtoCNF_Q_7
& skolemFOFtoCNF_Q_7 = skolemFOFtoCNF_R_4
& between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_4)
& incident_c(skolemFOFtoCNF_P_8,skolemFOFtoCNF_C_5)
& incident_c(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_C_5)
& incident_c(skolemFOFtoCNF_R_4,skolemFOFtoCNF_C_5) ),
inference(skolemize,[],[normalize_4_0]) ).
fof(normalize_4_2,plain,
between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_4),
inference(conjunct,[],[normalize_4_1]) ).
fof(normalize_4_3,plain,
skolemFOFtoCNF_Q_7 = skolemFOFtoCNF_R_4,
inference(conjunct,[],[normalize_4_1]) ).
fof(normalize_4_4,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(canonicalize,[],[between_c_defn]) ).
fof(normalize_4_5,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(specialize,[],[normalize_4_4]) ).
fof(normalize_4_6,plain,
! [C,Cpp,P,Q,R] :
( ( P != R
| ~ between_c(C,P,Q,R) )
& ( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) )
& ( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C)
| P = R
| between_c(C,P,Q,R) ) ),
inference(clausify,[],[normalize_4_5]) ).
fof(normalize_4_7,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(conjunct,[],[normalize_4_6]) ).
fof(normalize_4_8,plain,
! [C,P] :
( ~ inner_point(P,C)
<=> ( ~ incident_c(P,C)
| end_point(P,C) ) ),
inference(canonicalize,[],[inner_point_defn]) ).
fof(normalize_4_9,plain,
! [C,P] :
( ~ inner_point(P,C)
<=> ( ~ incident_c(P,C)
| end_point(P,C) ) ),
inference(specialize,[],[normalize_4_8]) ).
fof(normalize_4_10,plain,
! [C,P] :
( ( ~ end_point(P,C)
| ~ inner_point(P,C) )
& ( ~ inner_point(P,C)
| incident_c(P,C) )
& ( ~ incident_c(P,C)
| end_point(P,C)
| inner_point(P,C) ) ),
inference(clausify,[],[normalize_4_9]) ).
fof(normalize_4_11,plain,
! [C,P] :
( ~ end_point(P,C)
| ~ inner_point(P,C) ),
inference(conjunct,[],[normalize_4_10]) ).
fof(normalize_4_12,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(conjunct,[],[normalize_4_6]) ).
cnf(refute_4_0,plain,
between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_4),
inference(canonicalize,[],[normalize_4_2]) ).
cnf(refute_4_1,plain,
skolemFOFtoCNF_Q_7 = skolemFOFtoCNF_R_4,
inference(canonicalize,[],[normalize_4_3]) ).
cnf(refute_4_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_4_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_4_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_4_2,refute_4_3]) ).
cnf(refute_4_5,plain,
( skolemFOFtoCNF_Q_7 != skolemFOFtoCNF_R_4
| skolemFOFtoCNF_R_4 = skolemFOFtoCNF_Q_7 ),
inference(subst,[],[refute_4_4:[bind(X,$fot(skolemFOFtoCNF_Q_7)),bind(Y,$fot(skolemFOFtoCNF_R_4))]]) ).
cnf(refute_4_6,plain,
skolemFOFtoCNF_R_4 = skolemFOFtoCNF_Q_7,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_4) )],[refute_4_1,refute_4_5]) ).
cnf(refute_4_7,plain,
( skolemFOFtoCNF_R_4 != skolemFOFtoCNF_Q_7
| ~ between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_4)
| between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7) ),
introduced(tautology,[equality,[$cnf( between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_4) ),[3],$fot(skolemFOFtoCNF_Q_7)]]) ).
cnf(refute_4_8,plain,
( ~ between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_4)
| between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_R_4,skolemFOFtoCNF_Q_7) )],[refute_4_6,refute_4_7]) ).
cnf(refute_4_9,plain,
between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_4) )],[refute_4_0,refute_4_8]) ).
cnf(refute_4_10,plain,
( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(canonicalize,[],[normalize_4_7]) ).
cnf(refute_4_11,plain,
( ~ between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7)
| end_point(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7)) ),
inference(subst,[],[refute_4_10:[bind(C,$fot(skolemFOFtoCNF_C_5)),bind(P,$fot(skolemFOFtoCNF_P_8)),bind(Q,$fot(skolemFOFtoCNF_Q_7)),bind(R,$fot(skolemFOFtoCNF_Q_7))]]) ).
cnf(refute_4_12,plain,
end_point(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7)),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7) )],[refute_4_9,refute_4_11]) ).
cnf(refute_4_13,plain,
( ~ end_point(P,C)
| ~ inner_point(P,C) ),
inference(canonicalize,[],[normalize_4_11]) ).
cnf(refute_4_14,plain,
( ~ end_point(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7))
| ~ inner_point(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7)) ),
inference(subst,[],[refute_4_13:[bind(C,$fot(skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7))),bind(P,$fot(skolemFOFtoCNF_Q_7))]]) ).
cnf(refute_4_15,plain,
( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) ),
inference(canonicalize,[],[normalize_4_12]) ).
cnf(refute_4_16,plain,
( ~ between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7)
| inner_point(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7)) ),
inference(subst,[],[refute_4_15:[bind(C,$fot(skolemFOFtoCNF_C_5)),bind(P,$fot(skolemFOFtoCNF_P_8)),bind(Q,$fot(skolemFOFtoCNF_Q_7)),bind(R,$fot(skolemFOFtoCNF_Q_7))]]) ).
cnf(refute_4_17,plain,
inner_point(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7)),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7) )],[refute_4_9,refute_4_16]) ).
cnf(refute_4_18,plain,
~ end_point(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7)),
inference(resolve,[$cnf( inner_point(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7)) )],[refute_4_17,refute_4_14]) ).
cnf(refute_4_19,plain,
$false,
inference(resolve,[$cnf( end_point(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Cpp(skolemFOFtoCNF_C_5,skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_7,skolemFOFtoCNF_Q_7)) )],[refute_4_12,refute_4_18]) ).
fof(negate_5_0,plain,
~ ! [C,P,Q,R] :
( ( between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C)
& P != Q
& Q != R )
=> P != R ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
? [C,P,Q,R] :
( P != Q
& Q != R
& P = R
& between_c(C,P,Q,R)
& incident_c(P,C)
& incident_c(Q,C)
& incident_c(R,C) ),
inference(canonicalize,[],[negate_5_0]) ).
fof(normalize_5_1,plain,
( skolemFOFtoCNF_P_9 != skolemFOFtoCNF_Q_8
& skolemFOFtoCNF_Q_8 != skolemFOFtoCNF_R_5
& skolemFOFtoCNF_P_9 = skolemFOFtoCNF_R_5
& between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_R_5)
& incident_c(skolemFOFtoCNF_P_9,skolemFOFtoCNF_C_6)
& incident_c(skolemFOFtoCNF_Q_8,skolemFOFtoCNF_C_6)
& incident_c(skolemFOFtoCNF_R_5,skolemFOFtoCNF_C_6) ),
inference(skolemize,[],[normalize_5_0]) ).
fof(normalize_5_2,plain,
between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_R_5),
inference(conjunct,[],[normalize_5_1]) ).
fof(normalize_5_3,plain,
skolemFOFtoCNF_P_9 = skolemFOFtoCNF_R_5,
inference(conjunct,[],[normalize_5_1]) ).
fof(normalize_5_4,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(canonicalize,[],[between_c_defn]) ).
fof(normalize_5_5,plain,
! [C,P,Q,R] :
( ~ between_c(C,P,Q,R)
<=> ( P = R
| ! [Cpp] :
( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C) ) ) ),
inference(specialize,[],[normalize_5_4]) ).
fof(normalize_5_6,plain,
! [C,Cpp,P,Q,R] :
( ( P != R
| ~ between_c(C,P,Q,R) )
& ( ~ between_c(C,P,Q,R)
| end_point(P,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| end_point(R,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| inner_point(Q,skolemFOFtoCNF_Cpp(C,P,Q,R)) )
& ( ~ between_c(C,P,Q,R)
| part_of(skolemFOFtoCNF_Cpp(C,P,Q,R),C) )
& ( ~ end_point(P,Cpp)
| ~ end_point(R,Cpp)
| ~ inner_point(Q,Cpp)
| ~ part_of(Cpp,C)
| P = R
| between_c(C,P,Q,R) ) ),
inference(clausify,[],[normalize_5_5]) ).
fof(normalize_5_7,plain,
! [C,P,Q,R] :
( P != R
| ~ between_c(C,P,Q,R) ),
inference(conjunct,[],[normalize_5_6]) ).
cnf(refute_5_0,plain,
between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_R_5),
inference(canonicalize,[],[normalize_5_2]) ).
cnf(refute_5_1,plain,
skolemFOFtoCNF_P_9 = skolemFOFtoCNF_R_5,
inference(canonicalize,[],[normalize_5_3]) ).
cnf(refute_5_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_5_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_5_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_5_2,refute_5_3]) ).
cnf(refute_5_5,plain,
( skolemFOFtoCNF_P_9 != skolemFOFtoCNF_R_5
| skolemFOFtoCNF_R_5 = skolemFOFtoCNF_P_9 ),
inference(subst,[],[refute_5_4:[bind(X,$fot(skolemFOFtoCNF_P_9)),bind(Y,$fot(skolemFOFtoCNF_R_5))]]) ).
cnf(refute_5_6,plain,
skolemFOFtoCNF_R_5 = skolemFOFtoCNF_P_9,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_P_9,skolemFOFtoCNF_R_5) )],[refute_5_1,refute_5_5]) ).
cnf(refute_5_7,plain,
( skolemFOFtoCNF_R_5 != skolemFOFtoCNF_P_9
| ~ between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_R_5)
| between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_P_9) ),
introduced(tautology,[equality,[$cnf( between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_R_5) ),[3],$fot(skolemFOFtoCNF_P_9)]]) ).
cnf(refute_5_8,plain,
( ~ between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_R_5)
| between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_P_9) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_R_5,skolemFOFtoCNF_P_9) )],[refute_5_6,refute_5_7]) ).
cnf(refute_5_9,plain,
between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_P_9),
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_R_5) )],[refute_5_0,refute_5_8]) ).
cnf(refute_5_10,plain,
( P != R
| ~ between_c(C,P,Q,R) ),
inference(canonicalize,[],[normalize_5_7]) ).
cnf(refute_5_11,plain,
( R != R
| ~ between_c(C,R,Q,R) ),
inference(subst,[],[refute_5_10:[bind(P,$fot(R))]]) ).
cnf(refute_5_12,plain,
R = R,
introduced(tautology,[refl,[$fot(R)]]) ).
cnf(refute_5_13,plain,
~ between_c(C,R,Q,R),
inference(resolve,[$cnf( $equal(R,R) )],[refute_5_12,refute_5_11]) ).
cnf(refute_5_14,plain,
~ between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_P_9),
inference(subst,[],[refute_5_13:[bind(C,$fot(skolemFOFtoCNF_C_6)),bind(Q,$fot(skolemFOFtoCNF_Q_8)),bind(R,$fot(skolemFOFtoCNF_P_9))]]) ).
cnf(refute_5_15,plain,
$false,
inference(resolve,[$cnf( between_c(skolemFOFtoCNF_C_6,skolemFOFtoCNF_P_9,skolemFOFtoCNF_Q_8,skolemFOFtoCNF_P_9) )],[refute_5_9,refute_5_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GEO111+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.10 % Command : metis --show proof --show saturation %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Sat Jun 18 18:11:02 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.09/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.33/6.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.33/6.55
% 6.33/6.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.33/6.56
%------------------------------------------------------------------------------