TSTP Solution File: GEO568+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO568+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 05:27:24 EDT 2022
% Result : Theorem 62.94s 63.12s
% Output : CNFRefutation 62.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 29
% Syntax : Number of formulae : 306 ( 111 unt; 0 def)
% Number of atoms : 627 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 553 ( 232 ~; 227 |; 63 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 774 ( 70 sgn 403 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ) ).
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,C)
& coll(A,B,D) )
=> coll(C,D,A) ) ).
fof(ruleD7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ) ).
fof(ruleD8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ) ).
fof(ruleD11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ) ).
fof(ruleD12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,B)
& cong(O,A,O,C) )
=> circle(O,A,B,C) ) ).
fof(ruleD13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,B)
& cong(O,A,O,C)
& cong(O,A,O,D) )
=> cyclic(A,B,C,D) ) ).
fof(ruleD14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ) ).
fof(ruleD15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ) ).
fof(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ) ).
fof(ruleD17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,D)
& cyclic(A,B,C,E) )
=> cyclic(B,C,D,E) ) ).
fof(ruleD19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ) ).
fof(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ) ).
fof(ruleD24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ) ).
fof(ruleD39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ) ).
fof(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ) ).
fof(ruleD41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ) ).
fof(ruleD52,axiom,
! [A,B,C,M] :
( ( perp(A,B,B,C)
& midp(M,A,C) )
=> cong(A,M,B,M) ) ).
fof(ruleD53,axiom,
! [A,B,C,O] :
( ( circle(O,A,B,C)
& coll(O,A,C) )
=> perp(A,B,B,C) ) ).
fof(ruleD56,axiom,
! [A,B,P,Q] :
( ( cong(A,P,B,P)
& cong(A,Q,B,Q) )
=> perp(A,B,P,Q) ) ).
fof(ruleD57,axiom,
! [A,B,P,Q] :
( ( cong(A,P,B,P)
& cong(A,Q,B,Q)
& cyclic(A,B,P,Q) )
=> perp(P,A,A,Q) ) ).
fof(ruleD64,axiom,
! [A,B,C,D,M] :
( ( midp(M,A,B)
& para(A,C,B,D)
& para(A,D,B,C) )
=> midp(M,C,D) ) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ) ).
fof(ruleD67,axiom,
! [A,B,C] :
( ( cong(A,B,A,C)
& coll(A,B,C) )
=> midp(A,B,C) ) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ) ).
fof(ruleD69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ) ).
fof(ruleX7,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( midp(M,A,B)
& midp(N,C,D)
& coll(C,A,B)
& coll(D,A,B) )
=> midp(P,A,Q) ) ).
fof(exemplo6GDDFULL214030,conjecture,
! [A,B,C,O,D,E,MIDPNT1,MIDPNT2,MIDPNT3] :
( ( midp(MIDPNT1,A,B)
& perp(A,B,MIDPNT1,O)
& midp(MIDPNT2,A,C)
& perp(A,C,MIDPNT2,O)
& midp(MIDPNT3,B,C)
& perp(B,C,MIDPNT3,O)
& perp(D,C,A,B)
& coll(D,A,B)
& perp(E,B,A,C)
& coll(E,A,C) )
=> perp(A,O,D,E) ) ).
fof(subgoal_0,plain,
! [A,B,C,O,D,E,MIDPNT1,MIDPNT2,MIDPNT3] :
( ( midp(MIDPNT1,A,B)
& perp(A,B,MIDPNT1,O)
& midp(MIDPNT2,A,C)
& perp(A,C,MIDPNT2,O)
& midp(MIDPNT3,B,C)
& perp(B,C,MIDPNT3,O)
& perp(D,C,A,B)
& coll(D,A,B)
& perp(E,B,A,C)
& coll(E,A,C) )
=> perp(A,O,D,E) ),
inference(strip,[],[exemplo6GDDFULL214030]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,O,D,E,MIDPNT1,MIDPNT2,MIDPNT3] :
( ( midp(MIDPNT1,A,B)
& perp(A,B,MIDPNT1,O)
& midp(MIDPNT2,A,C)
& perp(A,C,MIDPNT2,O)
& midp(MIDPNT3,B,C)
& perp(B,C,MIDPNT3,O)
& perp(D,C,A,B)
& coll(D,A,B)
& perp(E,B,A,C)
& coll(E,A,C) )
=> perp(A,O,D,E) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D,E,MIDPNT1,MIDPNT2,MIDPNT3,O] :
( ~ perp(A,O,D,E)
& coll(D,A,B)
& coll(E,A,C)
& midp(MIDPNT1,A,B)
& midp(MIDPNT2,A,C)
& midp(MIDPNT3,B,C)
& perp(A,B,MIDPNT1,O)
& perp(A,C,MIDPNT2,O)
& perp(B,C,MIDPNT3,O)
& perp(D,C,A,B)
& perp(E,B,A,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
& coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& coll(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& midp(skolemFOFtoCNF_MIDPNT3,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& perp(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_O_2)
& perp(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_O_2)
& perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_MIDPNT3,skolemFOFtoCNF_O_2)
& perp(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& perp(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,P,Q] :
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| perp(A,B,P,Q) ),
inference(canonicalize,[],[ruleD56]) ).
fof(normalize_0_4,plain,
! [A,B,P,Q] :
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| perp(A,B,P,Q) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,M] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(canonicalize,[],[ruleD52]) ).
fof(normalize_0_6,plain,
! [A,B,C,M] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,P,Q] :
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(canonicalize,[],[ruleD57]) ).
fof(normalize_0_8,plain,
! [A,B,P,Q] :
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C,D,E] :
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[ruleD17]) ).
fof(normalize_0_10,plain,
! [A,B,C,D,E] :
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[ruleD14]) ).
fof(normalize_0_12,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[ruleD15]) ).
fof(normalize_0_14,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[ruleD16]) ).
fof(normalize_0_16,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B,C,D,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,B,C,D) ),
inference(canonicalize,[],[ruleD13]) ).
fof(normalize_0_18,plain,
! [A,B,C,D,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,B,C,D) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[ruleD68]) ).
fof(normalize_0_20,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B,C,D] :
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ! [M] : ~ midp(M,A,B)
| ! [N] : ~ midp(N,C,D)
| ! [Q] :
? [P] : midp(P,A,Q) ),
inference(canonicalize,[],[ruleX7]) ).
fof(normalize_0_22,plain,
! [A,B,C,D] :
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ! [M] : ~ midp(M,A,B)
| ! [N] : ~ midp(N,C,D)
| ! [Q] :
? [P] : midp(P,A,Q) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B,C,D,M,N,Q] :
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P_1(A,Q),A,Q) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[ruleD1]) ).
fof(normalize_0_25,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[ruleD2]) ).
fof(normalize_0_27,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD66]) ).
fof(normalize_0_29,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q] : ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[ruleD39]) ).
fof(normalize_0_31,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q] : ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [A,B,C,D,P,Q] :
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(clausify,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[ruleD41]) ).
fof(normalize_0_34,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(specialize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_36,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[ruleD11]) ).
fof(normalize_0_37,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(specialize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
! [A,B,C,D] :
( ~ para(A,B,C,D)
| ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[ruleD40]) ).
fof(normalize_0_39,plain,
! [A,B,C,D] :
( ~ para(A,B,C,D)
| ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q) ),
inference(specialize,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [A,B,C,D,P,Q] :
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(clausify,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [A,B,C,D,P,Q,U,V] :
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[ruleD19]) ).
fof(normalize_0_42,plain,
! [A,B,C,D,P,Q,U,V] :
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(specialize,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [A,B,C,D,M] :
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[ruleD64]) ).
fof(normalize_0_44,plain,
! [A,B,C,D,M] :
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[ruleD67]) ).
fof(normalize_0_46,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(specialize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_48,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_49,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_48]) ).
fof(normalize_0_50,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_51,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_50]) ).
fof(normalize_0_52,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[ruleD12]) ).
fof(normalize_0_53,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(specialize,[],[normalize_0_52]) ).
fof(normalize_0_54,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[ruleD53]) ).
fof(normalize_0_55,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(specialize,[],[normalize_0_54]) ).
fof(normalize_0_56,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_57,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_56]) ).
fof(normalize_0_58,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD69]) ).
fof(normalize_0_59,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_58]) ).
fof(normalize_0_60,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[ruleD23]) ).
fof(normalize_0_61,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(specialize,[],[normalize_0_60]) ).
fof(normalize_0_62,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[ruleD24]) ).
fof(normalize_0_63,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(specialize,[],[normalize_0_62]) ).
cnf(refute_0_0,plain,
~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| perp(A,B,P,Q) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ midp(M,X_4672,X_4672)
| ~ perp(X_4672,X_4671,X_4671,X_4672)
| cong(X_4672,M,X_4671,M) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_4672)),bind(B,$fot(X_4671)),bind(C,$fot(X_4672))]]) ).
cnf(refute_0_4,plain,
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ cong(X_4669,X_4670,X_4669,X_4670)
| ~ cyclic(X_4669,X_4669,X_4670,X_4670)
| perp(X_4670,X_4669,X_4669,X_4670) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_4669)),bind(B,$fot(X_4669)),bind(P,$fot(X_4670)),bind(Q,$fot(X_4670))]]) ).
cnf(refute_0_6,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ cyclic(X_4667,X_4667,X_4667,X_4668)
| cyclic(X_4667,X_4667,X_4668,X_4668) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_4667)),bind(B,$fot(X_4667)),bind(C,$fot(X_4667)),bind(D,$fot(X_4668)),bind(E,$fot(X_4668))]]) ).
cnf(refute_0_8,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
( ~ cyclic(X_4665,X_4665,X_4666,X_4665)
| cyclic(X_4665,X_4665,X_4665,X_4666) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_4665)),bind(B,$fot(X_4665)),bind(C,$fot(X_4666)),bind(D,$fot(X_4665))]]) ).
cnf(refute_0_10,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_11,plain,
( ~ cyclic(X_4663,X_4664,X_4663,X_4663)
| cyclic(X_4663,X_4663,X_4664,X_4663) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_4663)),bind(B,$fot(X_4664)),bind(C,$fot(X_4663)),bind(D,$fot(X_4663))]]) ).
cnf(refute_0_12,plain,
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_13,plain,
( ~ cyclic(X_4662,X_4661,X_4661,X_4661)
| cyclic(X_4661,X_4662,X_4661,X_4661) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_4662)),bind(B,$fot(X_4661)),bind(C,$fot(X_4661)),bind(D,$fot(X_4661))]]) ).
cnf(refute_0_14,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_15,plain,
( ~ cong(skolemFOFtoCNF_P_1(X_4660,X_4659),X_4660,skolemFOFtoCNF_P_1(X_4660,X_4659),X_4659)
| cyclic(X_4660,X_4659,X_4659,X_4659) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_4660)),bind(B,$fot(X_4659)),bind(C,$fot(X_4659)),bind(D,$fot(X_4659)),bind(O,$fot(skolemFOFtoCNF_P_1(X_4660,X_4659)))]]) ).
cnf(refute_0_16,plain,
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_17,plain,
( ~ midp(skolemFOFtoCNF_P_1(X_3803,X_3802),X_3803,X_3802)
| cong(skolemFOFtoCNF_P_1(X_3803,X_3802),X_3803,skolemFOFtoCNF_P_1(X_3803,X_3802),X_3802) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_P_1(X_3803,X_3802))),bind(B,$fot(X_3803)),bind(C,$fot(X_3802))]]) ).
cnf(refute_0_18,plain,
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P_1(A,Q),A,Q) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_19,plain,
( ~ coll(D,D,D)
| ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(D)),bind(B,$fot(D)),bind(C,$fot(D)),bind(M,$fot(N))]]) ).
cnf(refute_0_20,plain,
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_21,plain,
( ~ coll(X_577,X_576,X_577)
| coll(X_577,X_577,X_576) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(X_577)),bind(B,$fot(X_576)),bind(C,$fot(X_577))]]) ).
cnf(refute_0_22,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_23,plain,
( ~ coll(X_574,X_575,X_575)
| coll(X_575,X_574,X_575) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_574)),bind(B,$fot(X_575)),bind(C,$fot(X_575))]]) ).
cnf(refute_0_24,plain,
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_25,plain,
( ~ para(X_569,X_570,X_569,X_570)
| coll(X_569,X_570,X_570) ),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_569)),bind(B,$fot(X_570)),bind(C,$fot(X_570))]]) ).
cnf(refute_0_26,plain,
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_27,plain,
( ~ eqangle(X_567,X_568,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_567,X_568,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(X_567,X_568,X_567,X_568) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_567)),bind(B,$fot(X_568)),bind(C,$fot(X_567)),bind(D,$fot(X_568)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_28,plain,
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_29,plain,
( ~ cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_28:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_30,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(E,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_31,plain,
( ~ cong(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_MIDPNT1))]]) ).
cnf(refute_0_32,plain,
midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_33,plain,
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_34,plain,
( ~ midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(M,$fot(skolemFOFtoCNF_MIDPNT1))]]) ).
cnf(refute_0_35,plain,
midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_32,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_MIDPNT1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_37,plain,
cong(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A) )],[refute_0_37,refute_0_31]) ).
cnf(refute_0_39,plain,
cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_38,refute_0_30]) ).
cnf(refute_0_40,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_39,refute_0_29]) ).
cnf(refute_0_41,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_42,plain,
para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_44,plain,
( ~ para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154) ),
inference(subst,[],[refute_0_43:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(P,$fot(X_153)),bind(Q,$fot(X_154))]]) ).
cnf(refute_0_45,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_42,refute_0_44]) ).
cnf(refute_0_46,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_565,X_566,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_565,X_566),
inference(subst,[],[refute_0_45:[bind(X_153,$fot(X_565)),bind(X_154,$fot(X_566))]]) ).
cnf(refute_0_47,plain,
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_48,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_565,X_566,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_565,X_566)
| eqangle(X_565,X_566,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_565,X_566,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_47:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(X_565)),bind(D,$fot(X_566)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A)),bind(U,$fot(X_565)),bind(V,$fot(X_566))]]) ).
cnf(refute_0_49,plain,
eqangle(X_565,X_566,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_565,X_566,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_565,X_566,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_565,X_566) )],[refute_0_46,refute_0_48]) ).
cnf(refute_0_50,plain,
eqangle(X_567,X_568,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_567,X_568,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_49:[bind(X_565,$fot(X_567)),bind(X_566,$fot(X_568))]]) ).
cnf(refute_0_51,plain,
para(X_567,X_568,X_567,X_568),
inference(resolve,[$cnf( eqangle(X_567,X_568,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_567,X_568,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_50,refute_0_27]) ).
cnf(refute_0_52,plain,
para(X_569,X_570,X_569,X_570),
inference(subst,[],[refute_0_51:[bind(X_567,$fot(X_569)),bind(X_568,$fot(X_570))]]) ).
cnf(refute_0_53,plain,
coll(X_569,X_570,X_570),
inference(resolve,[$cnf( para(X_569,X_570,X_569,X_570) )],[refute_0_52,refute_0_25]) ).
cnf(refute_0_54,plain,
coll(X_574,X_575,X_575),
inference(subst,[],[refute_0_53:[bind(X_569,$fot(X_574)),bind(X_570,$fot(X_575))]]) ).
cnf(refute_0_55,plain,
coll(X_575,X_574,X_575),
inference(resolve,[$cnf( coll(X_574,X_575,X_575) )],[refute_0_54,refute_0_23]) ).
cnf(refute_0_56,plain,
coll(X_577,X_576,X_577),
inference(subst,[],[refute_0_55:[bind(X_574,$fot(X_576)),bind(X_575,$fot(X_577))]]) ).
cnf(refute_0_57,plain,
coll(X_577,X_577,X_576),
inference(resolve,[$cnf( coll(X_577,X_576,X_577) )],[refute_0_56,refute_0_21]) ).
cnf(refute_0_58,plain,
coll(D,D,D),
inference(subst,[],[refute_0_57:[bind(X_576,$fot(D)),bind(X_577,$fot(D))]]) ).
cnf(refute_0_59,plain,
( ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(resolve,[$cnf( coll(D,D,D) )],[refute_0_58,refute_0_19]) ).
cnf(refute_0_60,plain,
( ~ midp(skolemFOFtoCNF_A,X_3696,X_3696)
| midp(skolemFOFtoCNF_P_1(X_3696,Q),X_3696,Q) ),
inference(subst,[],[refute_0_59:[bind(D,$fot(X_3696)),bind(N,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_61,plain,
para(X_3643,X_3644,X_3643,X_3644),
inference(subst,[],[refute_0_51:[bind(X_567,$fot(X_3643)),bind(X_568,$fot(X_3644))]]) ).
cnf(refute_0_62,plain,
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_63,plain,
( ~ midp(X_3645,X_3643,X_3643)
| ~ para(X_3643,X_3644,X_3643,X_3644)
| midp(X_3645,X_3644,X_3644) ),
inference(subst,[],[refute_0_62:[bind(A,$fot(X_3643)),bind(B,$fot(X_3643)),bind(C,$fot(X_3644)),bind(D,$fot(X_3644)),bind(M,$fot(X_3645))]]) ).
cnf(refute_0_64,plain,
( ~ midp(X_3645,X_3643,X_3643)
| midp(X_3645,X_3644,X_3644) ),
inference(resolve,[$cnf( para(X_3643,X_3644,X_3643,X_3644) )],[refute_0_61,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ midp(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2)
| midp(skolemFOFtoCNF_A,X_3644,X_3644) ),
inference(subst,[],[refute_0_64:[bind(X_3643,$fot(skolemFOFtoCNF_MIDPNT2)),bind(X_3645,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_66,plain,
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_67,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2)
| ~ cong(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2)
| midp(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2) ),
inference(subst,[],[refute_0_66:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_MIDPNT2)),bind(C,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_68,plain,
midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_69,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_49]) ).
cnf(refute_0_70,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_69:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_71,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_72,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_71:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_73,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[normalize_0_53]) ).
cnf(refute_0_74,plain,
( ~ cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A)
| circle(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_73:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_75,plain,
( ~ midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
| midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(M,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_76,plain,
midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) )],[refute_0_68,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_MIDPNT2)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_78,plain,
cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
circle(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A) )],[refute_0_78,refute_0_74]) ).
cnf(refute_0_80,plain,
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_81,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_82,plain,
( ~ coll(X_3591,skolemFOFtoCNF_MIDPNT1,C)
| ~ coll(X_3591,skolemFOFtoCNF_MIDPNT1,X_3592)
| coll(C,X_3592,X_3591) ),
inference(subst,[],[refute_0_81:[bind(A,$fot(X_3591)),bind(B,$fot(skolemFOFtoCNF_MIDPNT1)),bind(D,$fot(X_3592))]]) ).
cnf(refute_0_83,plain,
( ~ coll(X_3572,skolemFOFtoCNF_B_1,C)
| ~ coll(X_3572,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1)
| coll(C,skolemFOFtoCNF_MIDPNT1,X_3572) ),
inference(subst,[],[refute_0_81:[bind(A,$fot(X_3572)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_MIDPNT1))]]) ).
cnf(refute_0_84,plain,
( ~ coll(skolemFOFtoCNF_MIDPNT1,X_3527,C)
| ~ coll(skolemFOFtoCNF_MIDPNT1,X_3527,skolemFOFtoCNF_B_1)
| coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1) ),
inference(subst,[],[refute_0_81:[bind(A,$fot(skolemFOFtoCNF_MIDPNT1)),bind(B,$fot(X_3527)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_85,plain,
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_59]) ).
cnf(refute_0_86,plain,
( ~ midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_85:[bind(A,$fot(skolemFOFtoCNF_MIDPNT1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_87,plain,
coll(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_32,refute_0_86]) ).
cnf(refute_0_88,plain,
( ~ coll(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1) ),
inference(subst,[],[refute_0_81:[bind(A,$fot(skolemFOFtoCNF_MIDPNT1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_89,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_MIDPNT1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_3526)
| ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1)
| coll(skolemFOFtoCNF_MIDPNT1,X_3526,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_81:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_MIDPNT1)),bind(D,$fot(X_3526))]]) ).
cnf(refute_0_91,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_3526)
| coll(skolemFOFtoCNF_MIDPNT1,X_3526,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_3526),
inference(subst,[],[refute_0_57:[bind(X_576,$fot(X_3526)),bind(X_577,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_93,plain,
coll(skolemFOFtoCNF_MIDPNT1,X_3526,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_3526) )],[refute_0_92,refute_0_91]) ).
cnf(refute_0_94,plain,
coll(skolemFOFtoCNF_MIDPNT1,X_3527,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_93:[bind(X_3526,$fot(X_3527))]]) ).
cnf(refute_0_95,plain,
( ~ coll(skolemFOFtoCNF_MIDPNT1,X_3527,C)
| coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_MIDPNT1,X_3527,skolemFOFtoCNF_B_1) )],[refute_0_94,refute_0_84]) ).
cnf(refute_0_96,plain,
( ~ coll(X_574,X_575,X_575)
| coll(X_575,X_575,X_574) ),
inference(subst,[],[refute_0_81:[bind(A,$fot(X_574)),bind(B,$fot(X_575)),bind(C,$fot(X_575)),bind(D,$fot(X_575))]]) ).
cnf(refute_0_97,plain,
coll(X_575,X_575,X_574),
inference(resolve,[$cnf( coll(X_574,X_575,X_575) )],[refute_0_54,refute_0_96]) ).
cnf(refute_0_98,plain,
coll(X_3524,X_3524,X_3525),
inference(subst,[],[refute_0_97:[bind(X_574,$fot(X_3525)),bind(X_575,$fot(X_3524))]]) ).
cnf(refute_0_99,plain,
( ~ coll(X_3524,X_3524,X_3525)
| ~ coll(X_3524,X_3524,X_3526)
| coll(X_3525,X_3526,X_3524) ),
inference(subst,[],[refute_0_81:[bind(A,$fot(X_3524)),bind(B,$fot(X_3524)),bind(C,$fot(X_3525)),bind(D,$fot(X_3526))]]) ).
cnf(refute_0_100,plain,
( ~ coll(X_3524,X_3524,X_3526)
| coll(X_3525,X_3526,X_3524) ),
inference(resolve,[$cnf( coll(X_3524,X_3524,X_3525) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
coll(X_3524,X_3524,X_3526),
inference(subst,[],[refute_0_57:[bind(X_576,$fot(X_3526)),bind(X_577,$fot(X_3524))]]) ).
cnf(refute_0_102,plain,
coll(X_3525,X_3526,X_3524),
inference(resolve,[$cnf( coll(X_3524,X_3524,X_3526) )],[refute_0_101,refute_0_100]) ).
cnf(refute_0_103,plain,
coll(skolemFOFtoCNF_MIDPNT1,X_3527,C),
inference(subst,[],[refute_0_102:[bind(X_3524,$fot(C)),bind(X_3525,$fot(skolemFOFtoCNF_MIDPNT1)),bind(X_3526,$fot(X_3527))]]) ).
cnf(refute_0_104,plain,
coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_MIDPNT1,X_3527,C) )],[refute_0_103,refute_0_95]) ).
cnf(refute_0_105,plain,
coll(X_3572,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1),
inference(subst,[],[refute_0_104:[bind(C,$fot(X_3572))]]) ).
cnf(refute_0_106,plain,
( ~ coll(X_3572,skolemFOFtoCNF_B_1,C)
| coll(C,skolemFOFtoCNF_MIDPNT1,X_3572) ),
inference(resolve,[$cnf( coll(X_3572,skolemFOFtoCNF_B_1,skolemFOFtoCNF_MIDPNT1) )],[refute_0_105,refute_0_83]) ).
cnf(refute_0_107,plain,
coll(X_3572,skolemFOFtoCNF_B_1,C),
inference(subst,[],[refute_0_102:[bind(X_3524,$fot(C)),bind(X_3525,$fot(X_3572)),bind(X_3526,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_108,plain,
coll(C,skolemFOFtoCNF_MIDPNT1,X_3572),
inference(resolve,[$cnf( coll(X_3572,skolemFOFtoCNF_B_1,C) )],[refute_0_107,refute_0_106]) ).
cnf(refute_0_109,plain,
coll(X_3591,skolemFOFtoCNF_MIDPNT1,X_3592),
inference(subst,[],[refute_0_108:[bind(C,$fot(X_3591)),bind(X_3572,$fot(X_3592))]]) ).
cnf(refute_0_110,plain,
( ~ coll(X_3591,skolemFOFtoCNF_MIDPNT1,C)
| coll(C,X_3592,X_3591) ),
inference(resolve,[$cnf( coll(X_3591,skolemFOFtoCNF_MIDPNT1,X_3592) )],[refute_0_109,refute_0_82]) ).
cnf(refute_0_111,plain,
coll(X_3591,skolemFOFtoCNF_MIDPNT1,C),
inference(subst,[],[refute_0_102:[bind(X_3524,$fot(C)),bind(X_3525,$fot(X_3591)),bind(X_3526,$fot(skolemFOFtoCNF_MIDPNT1))]]) ).
cnf(refute_0_112,plain,
coll(C,X_3592,X_3591),
inference(resolve,[$cnf( coll(X_3591,skolemFOFtoCNF_MIDPNT1,C) )],[refute_0_111,refute_0_110]) ).
cnf(refute_0_113,plain,
coll(O,A,C),
inference(subst,[],[refute_0_112:[bind(C,$fot(O)),bind(X_3591,$fot(C)),bind(X_3592,$fot(A))]]) ).
cnf(refute_0_114,plain,
( ~ circle(O,A,B,C)
| perp(A,B,B,C) ),
inference(resolve,[$cnf( coll(O,A,C) )],[refute_0_113,refute_0_80]) ).
cnf(refute_0_115,plain,
( ~ circle(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_114:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_116,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_79,refute_0_115]) ).
cnf(refute_0_117,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_116,refute_0_72]) ).
cnf(refute_0_118,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) )],[refute_0_117,refute_0_70]) ).
cnf(refute_0_119,plain,
( ~ midp(X_3694,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
| ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_A,X_3694,skolemFOFtoCNF_A,X_3694) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(M,$fot(X_3694))]]) ).
cnf(refute_0_120,plain,
( ~ midp(X_3694,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_A,X_3694,skolemFOFtoCNF_A,X_3694) ),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( ~ midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2) ),
inference(subst,[],[refute_0_120:[bind(X_3694,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_122,plain,
cong(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) )],[refute_0_68,refute_0_121]) ).
cnf(refute_0_123,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2)
| midp(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2) )],[refute_0_122,refute_0_67]) ).
cnf(refute_0_124,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2),
inference(subst,[],[refute_0_112:[bind(C,$fot(skolemFOFtoCNF_A)),bind(X_3591,$fot(skolemFOFtoCNF_MIDPNT2)),bind(X_3592,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_125,plain,
midp(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2) )],[refute_0_124,refute_0_123]) ).
cnf(refute_0_126,plain,
midp(skolemFOFtoCNF_A,X_3644,X_3644),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2) )],[refute_0_125,refute_0_65]) ).
cnf(refute_0_127,plain,
midp(skolemFOFtoCNF_A,X_3696,X_3696),
inference(subst,[],[refute_0_126:[bind(X_3644,$fot(X_3696))]]) ).
cnf(refute_0_128,plain,
midp(skolemFOFtoCNF_P_1(X_3696,Q),X_3696,Q),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A,X_3696,X_3696) )],[refute_0_127,refute_0_60]) ).
cnf(refute_0_129,plain,
midp(skolemFOFtoCNF_P_1(X_3803,X_3802),X_3803,X_3802),
inference(subst,[],[refute_0_128:[bind(Q,$fot(X_3802)),bind(X_3696,$fot(X_3803))]]) ).
cnf(refute_0_130,plain,
cong(skolemFOFtoCNF_P_1(X_3803,X_3802),X_3803,skolemFOFtoCNF_P_1(X_3803,X_3802),X_3802),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(X_3803,X_3802),X_3803,X_3802) )],[refute_0_129,refute_0_17]) ).
cnf(refute_0_131,plain,
cong(skolemFOFtoCNF_P_1(X_4660,X_4659),X_4660,skolemFOFtoCNF_P_1(X_4660,X_4659),X_4659),
inference(subst,[],[refute_0_130:[bind(X_3802,$fot(X_4659)),bind(X_3803,$fot(X_4660))]]) ).
cnf(refute_0_132,plain,
cyclic(X_4660,X_4659,X_4659,X_4659),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_P_1(X_4660,X_4659),X_4660,skolemFOFtoCNF_P_1(X_4660,X_4659),X_4659) )],[refute_0_131,refute_0_15]) ).
cnf(refute_0_133,plain,
cyclic(X_4662,X_4661,X_4661,X_4661),
inference(subst,[],[refute_0_132:[bind(X_4659,$fot(X_4661)),bind(X_4660,$fot(X_4662))]]) ).
cnf(refute_0_134,plain,
cyclic(X_4661,X_4662,X_4661,X_4661),
inference(resolve,[$cnf( cyclic(X_4662,X_4661,X_4661,X_4661) )],[refute_0_133,refute_0_13]) ).
cnf(refute_0_135,plain,
cyclic(X_4663,X_4664,X_4663,X_4663),
inference(subst,[],[refute_0_134:[bind(X_4661,$fot(X_4663)),bind(X_4662,$fot(X_4664))]]) ).
cnf(refute_0_136,plain,
cyclic(X_4663,X_4663,X_4664,X_4663),
inference(resolve,[$cnf( cyclic(X_4663,X_4664,X_4663,X_4663) )],[refute_0_135,refute_0_11]) ).
cnf(refute_0_137,plain,
cyclic(X_4665,X_4665,X_4666,X_4665),
inference(subst,[],[refute_0_136:[bind(X_4663,$fot(X_4665)),bind(X_4664,$fot(X_4666))]]) ).
cnf(refute_0_138,plain,
cyclic(X_4665,X_4665,X_4665,X_4666),
inference(resolve,[$cnf( cyclic(X_4665,X_4665,X_4666,X_4665) )],[refute_0_137,refute_0_9]) ).
cnf(refute_0_139,plain,
cyclic(X_4667,X_4667,X_4667,X_4668),
inference(subst,[],[refute_0_138:[bind(X_4665,$fot(X_4667)),bind(X_4666,$fot(X_4668))]]) ).
cnf(refute_0_140,plain,
cyclic(X_4667,X_4667,X_4668,X_4668),
inference(resolve,[$cnf( cyclic(X_4667,X_4667,X_4667,X_4668) )],[refute_0_139,refute_0_7]) ).
cnf(refute_0_141,plain,
cyclic(X_4669,X_4669,X_4670,X_4670),
inference(subst,[],[refute_0_140:[bind(X_4667,$fot(X_4669)),bind(X_4668,$fot(X_4670))]]) ).
cnf(refute_0_142,plain,
( ~ cong(X_4669,X_4670,X_4669,X_4670)
| perp(X_4670,X_4669,X_4669,X_4670) ),
inference(resolve,[$cnf( cyclic(X_4669,X_4669,X_4670,X_4670) )],[refute_0_141,refute_0_5]) ).
cnf(refute_0_143,plain,
( ~ midp(X_3738,X_3737,X_3737)
| cong(X_3738,X_3737,X_3738,X_3737) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_3738)),bind(B,$fot(X_3737)),bind(C,$fot(X_3737))]]) ).
cnf(refute_0_144,plain,
( ~ midp(X_3715,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(X_3715,X_3644,X_3644) ),
inference(subst,[],[refute_0_64:[bind(X_3643,$fot(skolemFOFtoCNF_A)),bind(X_3645,$fot(X_3715))]]) ).
cnf(refute_0_145,plain,
( ~ coll(X_3714,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| ~ cong(X_3714,skolemFOFtoCNF_A,X_3714,skolemFOFtoCNF_A)
| midp(X_3714,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_66:[bind(A,$fot(X_3714)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_146,plain,
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_61]) ).
cnf(refute_0_147,plain,
( ~ cong(X_3712,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_3712)
| cong(X_3712,skolemFOFtoCNF_A,X_3712,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_146:[bind(A,$fot(X_3712)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_3712))]]) ).
cnf(refute_0_148,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_63]) ).
cnf(refute_0_149,plain,
( ~ cong(skolemFOFtoCNF_A,X_3707,X_3707,skolemFOFtoCNF_A)
| cong(X_3707,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_3707) ),
inference(subst,[],[refute_0_148:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_3707)),bind(C,$fot(X_3707)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_150,plain,
( ~ cong(skolemFOFtoCNF_A,X_3699,skolemFOFtoCNF_A,X_3699)
| cong(skolemFOFtoCNF_A,X_3699,X_3699,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_146:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_3699)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_3699))]]) ).
cnf(refute_0_151,plain,
( ~ midp(skolemFOFtoCNF_A,X_3696,X_3696)
| cong(skolemFOFtoCNF_A,X_3696,skolemFOFtoCNF_A,X_3696) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_3696)),bind(C,$fot(X_3696))]]) ).
cnf(refute_0_152,plain,
cong(skolemFOFtoCNF_A,X_3696,skolemFOFtoCNF_A,X_3696),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A,X_3696,X_3696) )],[refute_0_127,refute_0_151]) ).
cnf(refute_0_153,plain,
cong(skolemFOFtoCNF_A,X_3699,skolemFOFtoCNF_A,X_3699),
inference(subst,[],[refute_0_152:[bind(X_3696,$fot(X_3699))]]) ).
cnf(refute_0_154,plain,
cong(skolemFOFtoCNF_A,X_3699,X_3699,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,X_3699,skolemFOFtoCNF_A,X_3699) )],[refute_0_153,refute_0_150]) ).
cnf(refute_0_155,plain,
cong(skolemFOFtoCNF_A,X_3707,X_3707,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_154:[bind(X_3699,$fot(X_3707))]]) ).
cnf(refute_0_156,plain,
cong(X_3707,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_3707),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,X_3707,X_3707,skolemFOFtoCNF_A) )],[refute_0_155,refute_0_149]) ).
cnf(refute_0_157,plain,
cong(X_3712,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_3712),
inference(subst,[],[refute_0_156:[bind(X_3707,$fot(X_3712))]]) ).
cnf(refute_0_158,plain,
cong(X_3712,skolemFOFtoCNF_A,X_3712,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(X_3712,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_3712) )],[refute_0_157,refute_0_147]) ).
cnf(refute_0_159,plain,
cong(X_3714,skolemFOFtoCNF_A,X_3714,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_158:[bind(X_3712,$fot(X_3714))]]) ).
cnf(refute_0_160,plain,
( ~ coll(X_3714,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(X_3714,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( cong(X_3714,skolemFOFtoCNF_A,X_3714,skolemFOFtoCNF_A) )],[refute_0_159,refute_0_145]) ).
cnf(refute_0_161,plain,
coll(X_3714,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_112:[bind(C,$fot(X_3714)),bind(X_3591,$fot(skolemFOFtoCNF_A)),bind(X_3592,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_162,plain,
midp(X_3714,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(X_3714,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_161,refute_0_160]) ).
cnf(refute_0_163,plain,
midp(X_3715,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_162:[bind(X_3714,$fot(X_3715))]]) ).
cnf(refute_0_164,plain,
midp(X_3715,X_3644,X_3644),
inference(resolve,[$cnf( midp(X_3715,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_163,refute_0_144]) ).
cnf(refute_0_165,plain,
midp(X_3738,X_3737,X_3737),
inference(subst,[],[refute_0_164:[bind(X_3644,$fot(X_3737)),bind(X_3715,$fot(X_3738))]]) ).
cnf(refute_0_166,plain,
cong(X_3738,X_3737,X_3738,X_3737),
inference(resolve,[$cnf( midp(X_3738,X_3737,X_3737) )],[refute_0_165,refute_0_143]) ).
cnf(refute_0_167,plain,
cong(X_4669,X_4670,X_4669,X_4670),
inference(subst,[],[refute_0_166:[bind(X_3737,$fot(X_4670)),bind(X_3738,$fot(X_4669))]]) ).
cnf(refute_0_168,plain,
perp(X_4670,X_4669,X_4669,X_4670),
inference(resolve,[$cnf( cong(X_4669,X_4670,X_4669,X_4670) )],[refute_0_167,refute_0_142]) ).
cnf(refute_0_169,plain,
perp(X_4672,X_4671,X_4671,X_4672),
inference(subst,[],[refute_0_168:[bind(X_4669,$fot(X_4671)),bind(X_4670,$fot(X_4672))]]) ).
cnf(refute_0_170,plain,
( ~ midp(M,X_4672,X_4672)
| cong(X_4672,M,X_4671,M) ),
inference(resolve,[$cnf( perp(X_4672,X_4671,X_4671,X_4672) )],[refute_0_169,refute_0_3]) ).
cnf(refute_0_171,plain,
( ~ midp(X_3722,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2)
| midp(X_3722,X_3644,X_3644) ),
inference(subst,[],[refute_0_64:[bind(X_3643,$fot(skolemFOFtoCNF_MIDPNT2)),bind(X_3645,$fot(X_3722))]]) ).
cnf(refute_0_172,plain,
( ~ coll(X_3721,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2)
| ~ cong(X_3721,skolemFOFtoCNF_MIDPNT2,X_3721,skolemFOFtoCNF_MIDPNT2)
| midp(X_3721,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2) ),
inference(subst,[],[refute_0_66:[bind(A,$fot(X_3721)),bind(B,$fot(skolemFOFtoCNF_MIDPNT2)),bind(C,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_173,plain,
( ~ cong(X_3720,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2,X_3720)
| cong(X_3720,skolemFOFtoCNF_MIDPNT2,X_3720,skolemFOFtoCNF_MIDPNT2) ),
inference(subst,[],[refute_0_146:[bind(A,$fot(X_3720)),bind(B,$fot(skolemFOFtoCNF_MIDPNT2)),bind(C,$fot(skolemFOFtoCNF_MIDPNT2)),bind(D,$fot(X_3720))]]) ).
cnf(refute_0_174,plain,
( ~ cong(skolemFOFtoCNF_MIDPNT2,X_3716,X_3716,skolemFOFtoCNF_MIDPNT2)
| cong(X_3716,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2,X_3716) ),
inference(subst,[],[refute_0_148:[bind(A,$fot(skolemFOFtoCNF_MIDPNT2)),bind(B,$fot(X_3716)),bind(C,$fot(X_3716)),bind(D,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_175,plain,
( ~ cong(skolemFOFtoCNF_MIDPNT2,X_3705,skolemFOFtoCNF_MIDPNT2,X_3705)
| cong(skolemFOFtoCNF_MIDPNT2,X_3705,X_3705,skolemFOFtoCNF_MIDPNT2) ),
inference(subst,[],[refute_0_146:[bind(A,$fot(skolemFOFtoCNF_MIDPNT2)),bind(B,$fot(X_3705)),bind(C,$fot(skolemFOFtoCNF_MIDPNT2)),bind(D,$fot(X_3705))]]) ).
cnf(refute_0_176,plain,
( ~ midp(skolemFOFtoCNF_MIDPNT2,X_3697,X_3697)
| cong(skolemFOFtoCNF_MIDPNT2,X_3697,skolemFOFtoCNF_MIDPNT2,X_3697) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_MIDPNT2)),bind(B,$fot(X_3697)),bind(C,$fot(X_3697))]]) ).
cnf(refute_0_177,plain,
( ~ midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_MIDPNT2,X_3644,X_3644) ),
inference(subst,[],[refute_0_64:[bind(X_3643,$fot(skolemFOFtoCNF_A)),bind(X_3645,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_178,plain,
( ~ coll(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| ~ cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_66:[bind(A,$fot(skolemFOFtoCNF_MIDPNT2)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_179,plain,
( ~ cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2)
| cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_146:[bind(A,$fot(skolemFOFtoCNF_MIDPNT2)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_180,plain,
( ~ cong(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2) ),
inference(subst,[],[refute_0_148:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_MIDPNT2)),bind(C,$fot(skolemFOFtoCNF_MIDPNT2)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_181,plain,
( ~ cong(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2)
| cong(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_146:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_MIDPNT2)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_182,plain,
cong(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2) )],[refute_0_122,refute_0_181]) ).
cnf(refute_0_183,plain,
cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A) )],[refute_0_182,refute_0_180]) ).
cnf(refute_0_184,plain,
cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2) )],[refute_0_183,refute_0_179]) ).
cnf(refute_0_185,plain,
( ~ coll(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A) )],[refute_0_184,refute_0_178]) ).
cnf(refute_0_186,plain,
coll(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_112:[bind(C,$fot(skolemFOFtoCNF_MIDPNT2)),bind(X_3591,$fot(skolemFOFtoCNF_A)),bind(X_3592,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_187,plain,
midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_186,refute_0_185]) ).
cnf(refute_0_188,plain,
midp(skolemFOFtoCNF_MIDPNT2,X_3644,X_3644),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_187,refute_0_177]) ).
cnf(refute_0_189,plain,
midp(skolemFOFtoCNF_MIDPNT2,X_3697,X_3697),
inference(subst,[],[refute_0_188:[bind(X_3644,$fot(X_3697))]]) ).
cnf(refute_0_190,plain,
cong(skolemFOFtoCNF_MIDPNT2,X_3697,skolemFOFtoCNF_MIDPNT2,X_3697),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_MIDPNT2,X_3697,X_3697) )],[refute_0_189,refute_0_176]) ).
cnf(refute_0_191,plain,
cong(skolemFOFtoCNF_MIDPNT2,X_3705,skolemFOFtoCNF_MIDPNT2,X_3705),
inference(subst,[],[refute_0_190:[bind(X_3697,$fot(X_3705))]]) ).
cnf(refute_0_192,plain,
cong(skolemFOFtoCNF_MIDPNT2,X_3705,X_3705,skolemFOFtoCNF_MIDPNT2),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_MIDPNT2,X_3705,skolemFOFtoCNF_MIDPNT2,X_3705) )],[refute_0_191,refute_0_175]) ).
cnf(refute_0_193,plain,
cong(skolemFOFtoCNF_MIDPNT2,X_3716,X_3716,skolemFOFtoCNF_MIDPNT2),
inference(subst,[],[refute_0_192:[bind(X_3705,$fot(X_3716))]]) ).
cnf(refute_0_194,plain,
cong(X_3716,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2,X_3716),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_MIDPNT2,X_3716,X_3716,skolemFOFtoCNF_MIDPNT2) )],[refute_0_193,refute_0_174]) ).
cnf(refute_0_195,plain,
cong(X_3720,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2,X_3720),
inference(subst,[],[refute_0_194:[bind(X_3716,$fot(X_3720))]]) ).
cnf(refute_0_196,plain,
cong(X_3720,skolemFOFtoCNF_MIDPNT2,X_3720,skolemFOFtoCNF_MIDPNT2),
inference(resolve,[$cnf( cong(X_3720,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2,X_3720) )],[refute_0_195,refute_0_173]) ).
cnf(refute_0_197,plain,
cong(X_3721,skolemFOFtoCNF_MIDPNT2,X_3721,skolemFOFtoCNF_MIDPNT2),
inference(subst,[],[refute_0_196:[bind(X_3720,$fot(X_3721))]]) ).
cnf(refute_0_198,plain,
( ~ coll(X_3721,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2)
| midp(X_3721,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2) ),
inference(resolve,[$cnf( cong(X_3721,skolemFOFtoCNF_MIDPNT2,X_3721,skolemFOFtoCNF_MIDPNT2) )],[refute_0_197,refute_0_172]) ).
cnf(refute_0_199,plain,
coll(X_3721,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2),
inference(subst,[],[refute_0_112:[bind(C,$fot(X_3721)),bind(X_3591,$fot(skolemFOFtoCNF_MIDPNT2)),bind(X_3592,$fot(skolemFOFtoCNF_MIDPNT2))]]) ).
cnf(refute_0_200,plain,
midp(X_3721,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2),
inference(resolve,[$cnf( coll(X_3721,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2) )],[refute_0_199,refute_0_198]) ).
cnf(refute_0_201,plain,
midp(X_3722,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2),
inference(subst,[],[refute_0_200:[bind(X_3721,$fot(X_3722))]]) ).
cnf(refute_0_202,plain,
midp(X_3722,X_3644,X_3644),
inference(resolve,[$cnf( midp(X_3722,skolemFOFtoCNF_MIDPNT2,skolemFOFtoCNF_MIDPNT2) )],[refute_0_201,refute_0_171]) ).
cnf(refute_0_203,plain,
midp(M,X_4672,X_4672),
inference(subst,[],[refute_0_202:[bind(X_3644,$fot(X_4672)),bind(X_3722,$fot(M))]]) ).
cnf(refute_0_204,plain,
cong(X_4672,M,X_4671,M),
inference(resolve,[$cnf( midp(M,X_4672,X_4672) )],[refute_0_203,refute_0_170]) ).
cnf(refute_0_205,plain,
cong(A,P,B,P),
inference(subst,[],[refute_0_204:[bind(M,$fot(P)),bind(X_4671,$fot(B)),bind(X_4672,$fot(A))]]) ).
cnf(refute_0_206,plain,
( ~ cong(A,Q,B,Q)
| perp(A,B,P,Q) ),
inference(resolve,[$cnf( cong(A,P,B,P) )],[refute_0_205,refute_0_1]) ).
cnf(refute_0_207,plain,
cong(A,Q,B,Q),
inference(subst,[],[refute_0_204:[bind(M,$fot(Q)),bind(X_4671,$fot(B)),bind(X_4672,$fot(A))]]) ).
cnf(refute_0_208,plain,
perp(A,B,P,Q),
inference(resolve,[$cnf( cong(A,Q,B,Q) )],[refute_0_207,refute_0_206]) ).
cnf(refute_0_209,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_208:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(P,$fot(skolemFOFtoCNF_D)),bind(Q,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_210,plain,
$false,
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_209,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO568+1 : TPTP v8.1.0. Released v7.5.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 10:15:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 62.94/63.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.94/63.12
% 62.94/63.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 62.94/63.14
%------------------------------------------------------------------------------