TSTP Solution File: GEO638+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO638+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 05:27:59 EDT 2022
% Result : Theorem 76.19s 76.38s
% Output : CNFRefutation 76.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 96
% Number of leaves : 28
% Syntax : Number of formulae : 411 ( 176 unt; 0 def)
% Number of atoms : 797 ( 0 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 677 ( 291 ~; 286 |; 70 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 945 ( 159 sgn 408 !; 23 ?)
% 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(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(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(ruleX10,axiom,
! [A,B,C,H] :
? [P,Q] :
( ( perp(A,H,B,C)
& perp(B,H,A,C) )
=> ( coll(P,C,B)
& perp(A,P,C,B)
& coll(Q,C,A)
& perp(B,Q,C,A) ) ) ).
fof(exemplo6GDDFULL81109104,conjecture,
! [A,B,E,G,D,C,F,H,NWPNT1,NWPNT2,NWPNT3] :
( ( midp(E,A,B)
& circle(E,A,NWPNT1,NWPNT2)
& circle(E,A,G,NWPNT3)
& perp(E,G,G,D)
& para(A,D,C,B)
& coll(C,G,D)
& midp(F,C,D)
& perp(H,F,A,B)
& coll(H,A,B) )
=> perp(C,H,D,H) ) ).
fof(subgoal_0,plain,
! [A,B,E,G,D,C,F,H,NWPNT1,NWPNT2,NWPNT3] :
( ( midp(E,A,B)
& circle(E,A,NWPNT1,NWPNT2)
& circle(E,A,G,NWPNT3)
& perp(E,G,G,D)
& para(A,D,C,B)
& coll(C,G,D)
& midp(F,C,D)
& perp(H,F,A,B)
& coll(H,A,B) )
=> perp(C,H,D,H) ),
inference(strip,[],[exemplo6GDDFULL81109104]) ).
fof(negate_0_0,plain,
~ ! [A,B,E,G,D,C,F,H,NWPNT1,NWPNT2,NWPNT3] :
( ( midp(E,A,B)
& circle(E,A,NWPNT1,NWPNT2)
& circle(E,A,G,NWPNT3)
& perp(E,G,G,D)
& para(A,D,C,B)
& coll(C,G,D)
& midp(F,C,D)
& perp(H,F,A,B)
& coll(H,A,B) )
=> perp(C,H,D,H) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D,E,F,G,H] :
( ~ perp(C,H,D,H)
& coll(C,G,D)
& coll(H,A,B)
& midp(E,A,B)
& midp(F,C,D)
& para(A,D,C,B)
& perp(E,G,G,D)
& perp(H,F,A,B)
& ? [NWPNT3] : circle(E,A,G,NWPNT3)
& ? [NWPNT1,NWPNT2] : circle(E,A,NWPNT1,NWPNT2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_D,skolemFOFtoCNF_H)
& coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_D)
& coll(skolemFOFtoCNF_H,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& midp(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D)
& para(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
& perp(skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_D)
& perp(skolemFOFtoCNF_H,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& ? [NWPNT3] : circle(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_G,NWPNT3)
& ? [NWPNT1,NWPNT2] : circle(skolemFOFtoCNF_E,skolemFOFtoCNF_A,NWPNT1,NWPNT2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_D,skolemFOFtoCNF_H),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_4,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,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_6,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[ruleD2]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[ruleD1]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD66]) ).
fof(normalize_0_15,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,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_17,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_16]) ).
fof(normalize_0_18,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_17]) ).
fof(normalize_0_19,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_20,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_19]) ).
fof(normalize_0_21,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_22,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_21]) ).
fof(normalize_0_23,plain,
midp(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_24,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[ruleD11]) ).
fof(normalize_0_25,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[ruleD68]) ).
fof(normalize_0_27,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,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_29,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
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,[],[ruleD40]) ).
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] :
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(clausify,[],[normalize_0_31]) ).
fof(normalize_0_33,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_34,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_33]) ).
fof(normalize_0_35,plain,
coll(skolemFOFtoCNF_H,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_36,plain,
perp(skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_37,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_38,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
! [A,B,C,H] :
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| ? [P,Q] :
( coll(P,C,B)
& coll(Q,C,A)
& perp(A,P,C,B)
& perp(B,Q,C,A) ) ),
inference(canonicalize,[],[ruleX10]) ).
fof(normalize_0_40,plain,
! [A,B,C,H] :
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| ? [P,Q] :
( coll(P,C,B)
& coll(Q,C,A)
& perp(A,P,C,B)
& perp(B,Q,C,A) ) ),
inference(specialize,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [A,B,C,H] :
( ( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_P_3(A,B,C),C,B) )
& ( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_Q_1(A,B,C),C,A) )
& ( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| perp(A,skolemFOFtoCNF_P_3(A,B,C),C,B) )
& ( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| perp(B,skolemFOFtoCNF_Q_1(A,B,C),C,A) ) ),
inference(clausify,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
! [A,B,C,H] :
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_P_3(A,B,C),C,B) ),
inference(conjunct,[],[normalize_0_41]) ).
fof(normalize_0_43,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_44,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[ruleD23]) ).
fof(normalize_0_46,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(specialize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[ruleD24]) ).
fof(normalize_0_48,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(specialize,[],[normalize_0_47]) ).
fof(normalize_0_49,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_50,plain,
! [A,B,C,M] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(specialize,[],[normalize_0_49]) ).
fof(normalize_0_51,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_52,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_51]) ).
fof(normalize_0_53,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[ruleD14]) ).
fof(normalize_0_54,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(specialize,[],[normalize_0_53]) ).
fof(normalize_0_55,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[ruleD15]) ).
fof(normalize_0_56,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(specialize,[],[normalize_0_55]) ).
fof(normalize_0_57,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[ruleD16]) ).
fof(normalize_0_58,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(specialize,[],[normalize_0_57]) ).
fof(normalize_0_59,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_60,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_59]) ).
fof(normalize_0_61,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_60]) ).
fof(normalize_0_62,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_63,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_62]) ).
fof(normalize_0_64,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[ruleD67]) ).
fof(normalize_0_65,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(specialize,[],[normalize_0_64]) ).
fof(normalize_0_66,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_D,skolemFOFtoCNF_H),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ perp(X_20073,X_20074,X_20074,X_20075)
| perp(X_20073,X_20074,X_20075,X_20074) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_20073)),bind(B,$fot(X_20074)),bind(C,$fot(X_20074)),bind(D,$fot(X_20075))]]) ).
cnf(refute_0_3,plain,
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ coll(X_2693,skolemFOFtoCNF_C_1,C)
| ~ coll(X_2693,skolemFOFtoCNF_C_1,X_2694)
| coll(C,X_2694,X_2693) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2693)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_2694))]]) ).
cnf(refute_0_6,plain,
( ~ coll(X_2635,skolemFOFtoCNF_D,C)
| ~ coll(X_2635,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1)
| coll(C,skolemFOFtoCNF_C_1,X_2635) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2635)),bind(B,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_7,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ coll(skolemFOFtoCNF_D,X_2634,skolemFOFtoCNF_C_1)
| coll(X_2634,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_2634)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_9,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_10,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_12,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_D) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) )],[refute_0_12,refute_0_9]) ).
cnf(refute_0_14,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2620)
| ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_D,X_2620,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_2620))]]) ).
cnf(refute_0_15,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2620)
| coll(skolemFOFtoCNF_D,X_2620,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_17,plain,
( ~ coll(X_486,X_485,X_486)
| coll(X_486,X_486,X_485) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_486)),bind(B,$fot(X_485)),bind(C,$fot(X_486))]]) ).
cnf(refute_0_18,plain,
( ~ coll(X_483,X_484,X_484)
| coll(X_484,X_483,X_484) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_483)),bind(B,$fot(X_484)),bind(C,$fot(X_484))]]) ).
cnf(refute_0_19,plain,
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_20,plain,
( ~ para(X_478,X_479,X_478,X_479)
| coll(X_478,X_479,X_479) ),
inference(subst,[],[refute_0_19:[bind(A,$fot(X_478)),bind(B,$fot(X_479)),bind(C,$fot(X_479))]]) ).
cnf(refute_0_21,plain,
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_22,plain,
( ~ eqangle(X_476,X_477,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_476,X_477,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(X_476,X_477,X_476,X_477) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(X_476)),bind(B,$fot(X_477)),bind(C,$fot(X_476)),bind(D,$fot(X_477)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_23,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_24,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_23:[bind(A,$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_25,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_22]) ).
cnf(refute_0_26,plain,
( ~ cong(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_E,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_27,plain,
midp(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_28,plain,
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_29,plain,
( ~ midp(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| midp(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_28:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(M,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_30,plain,
midp(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_27,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_32,plain,
( ~ midp(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_E,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_33,plain,
cong(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_E,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_30,refute_0_32]) ).
cnf(refute_0_34,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_E,skolemFOFtoCNF_A) )],[refute_0_33,refute_0_26]) ).
cnf(refute_0_35,plain,
cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_34,refute_0_24]) ).
cnf(refute_0_36,plain,
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_37,plain,
( ~ cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_36:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_38,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_35,refute_0_37]) ).
cnf(refute_0_39,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_21:[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_40,plain,
para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_42,plain,
( ~ para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154) ),
inference(subst,[],[refute_0_41:[bind(A,$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,$fot(X_154))]]) ).
cnf(refute_0_43,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_40,refute_0_42]) ).
cnf(refute_0_44,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_474,X_475,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_474,X_475),
inference(subst,[],[refute_0_43:[bind(X_153,$fot(X_474)),bind(X_154,$fot(X_475))]]) ).
cnf(refute_0_45,plain,
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_46,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_474,X_475,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_474,X_475)
| eqangle(X_474,X_475,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_474,X_475,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_45:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(X_474)),bind(D,$fot(X_475)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A)),bind(U,$fot(X_474)),bind(V,$fot(X_475))]]) ).
cnf(refute_0_47,plain,
eqangle(X_474,X_475,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_474,X_475,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_474,X_475,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_474,X_475) )],[refute_0_44,refute_0_46]) ).
cnf(refute_0_48,plain,
eqangle(X_476,X_477,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_476,X_477,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_47:[bind(X_474,$fot(X_476)),bind(X_475,$fot(X_477))]]) ).
cnf(refute_0_49,plain,
para(X_476,X_477,X_476,X_477),
inference(resolve,[$cnf( eqangle(X_476,X_477,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_476,X_477,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_48,refute_0_22]) ).
cnf(refute_0_50,plain,
para(X_478,X_479,X_478,X_479),
inference(subst,[],[refute_0_49:[bind(X_476,$fot(X_478)),bind(X_477,$fot(X_479))]]) ).
cnf(refute_0_51,plain,
coll(X_478,X_479,X_479),
inference(resolve,[$cnf( para(X_478,X_479,X_478,X_479) )],[refute_0_50,refute_0_20]) ).
cnf(refute_0_52,plain,
coll(X_483,X_484,X_484),
inference(subst,[],[refute_0_51:[bind(X_478,$fot(X_483)),bind(X_479,$fot(X_484))]]) ).
cnf(refute_0_53,plain,
coll(X_484,X_483,X_484),
inference(resolve,[$cnf( coll(X_483,X_484,X_484) )],[refute_0_52,refute_0_18]) ).
cnf(refute_0_54,plain,
coll(X_486,X_485,X_486),
inference(subst,[],[refute_0_53:[bind(X_483,$fot(X_485)),bind(X_484,$fot(X_486))]]) ).
cnf(refute_0_55,plain,
coll(X_486,X_486,X_485),
inference(resolve,[$cnf( coll(X_486,X_485,X_486) )],[refute_0_54,refute_0_17]) ).
cnf(refute_0_56,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2620),
inference(subst,[],[refute_0_55:[bind(X_485,$fot(X_2620)),bind(X_486,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_57,plain,
coll(skolemFOFtoCNF_D,X_2620,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2620) )],[refute_0_56,refute_0_15]) ).
cnf(refute_0_58,plain,
coll(skolemFOFtoCNF_D,X_2634,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_57:[bind(X_2620,$fot(X_2634))]]) ).
cnf(refute_0_59,plain,
coll(X_2634,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,X_2634,skolemFOFtoCNF_C_1) )],[refute_0_58,refute_0_8]) ).
cnf(refute_0_60,plain,
coll(X_2635,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_59:[bind(X_2634,$fot(X_2635))]]) ).
cnf(refute_0_61,plain,
( ~ coll(X_2635,skolemFOFtoCNF_D,C)
| coll(C,skolemFOFtoCNF_C_1,X_2635) ),
inference(resolve,[$cnf( coll(X_2635,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) )],[refute_0_60,refute_0_6]) ).
cnf(refute_0_62,plain,
( ~ coll(X_483,X_484,X_484)
| coll(X_484,X_484,X_483) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_483)),bind(B,$fot(X_484)),bind(C,$fot(X_484)),bind(D,$fot(X_484))]]) ).
cnf(refute_0_63,plain,
coll(X_484,X_484,X_483),
inference(resolve,[$cnf( coll(X_483,X_484,X_484) )],[refute_0_52,refute_0_62]) ).
cnf(refute_0_64,plain,
coll(X_2618,X_2618,X_2619),
inference(subst,[],[refute_0_63:[bind(X_483,$fot(X_2619)),bind(X_484,$fot(X_2618))]]) ).
cnf(refute_0_65,plain,
( ~ coll(X_2618,X_2618,X_2619)
| ~ coll(X_2618,X_2618,X_2620)
| coll(X_2619,X_2620,X_2618) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2618)),bind(B,$fot(X_2618)),bind(C,$fot(X_2619)),bind(D,$fot(X_2620))]]) ).
cnf(refute_0_66,plain,
( ~ coll(X_2618,X_2618,X_2620)
| coll(X_2619,X_2620,X_2618) ),
inference(resolve,[$cnf( coll(X_2618,X_2618,X_2619) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
coll(X_2618,X_2618,X_2620),
inference(subst,[],[refute_0_55:[bind(X_485,$fot(X_2620)),bind(X_486,$fot(X_2618))]]) ).
cnf(refute_0_68,plain,
coll(X_2619,X_2620,X_2618),
inference(resolve,[$cnf( coll(X_2618,X_2618,X_2620) )],[refute_0_67,refute_0_66]) ).
cnf(refute_0_69,plain,
coll(X_2635,skolemFOFtoCNF_D,C),
inference(subst,[],[refute_0_68:[bind(X_2618,$fot(C)),bind(X_2619,$fot(X_2635)),bind(X_2620,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_70,plain,
coll(C,skolemFOFtoCNF_C_1,X_2635),
inference(resolve,[$cnf( coll(X_2635,skolemFOFtoCNF_D,C) )],[refute_0_69,refute_0_61]) ).
cnf(refute_0_71,plain,
coll(X_2693,skolemFOFtoCNF_C_1,X_2694),
inference(subst,[],[refute_0_70:[bind(C,$fot(X_2693)),bind(X_2635,$fot(X_2694))]]) ).
cnf(refute_0_72,plain,
( ~ coll(X_2693,skolemFOFtoCNF_C_1,C)
| coll(C,X_2694,X_2693) ),
inference(resolve,[$cnf( coll(X_2693,skolemFOFtoCNF_C_1,X_2694) )],[refute_0_71,refute_0_5]) ).
cnf(refute_0_73,plain,
( ~ coll(X_2669,skolemFOFtoCNF_G,C)
| ~ coll(X_2669,skolemFOFtoCNF_G,X_2670)
| coll(C,X_2670,X_2669) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2669)),bind(B,$fot(skolemFOFtoCNF_G)),bind(D,$fot(X_2670))]]) ).
cnf(refute_0_74,plain,
( ~ coll(X_2668,skolemFOFtoCNF_C_1,C)
| ~ coll(X_2668,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G)
| coll(C,skolemFOFtoCNF_G,X_2668) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2668)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_75,plain,
( ~ coll(skolemFOFtoCNF_C_1,X_2667,skolemFOFtoCNF_G)
| coll(X_2667,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(X_2667)),bind(C,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_76,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_77,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_D) )],[refute_0_10,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_79,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_G) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_2620)
| ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,X_2620,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_2620))]]) ).
cnf(refute_0_81,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_2620)
| coll(skolemFOFtoCNF_C_1,X_2620,skolemFOFtoCNF_G) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_C_1) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_2620),
inference(subst,[],[refute_0_55:[bind(X_485,$fot(X_2620)),bind(X_486,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_83,plain,
coll(skolemFOFtoCNF_C_1,X_2620,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_2620) )],[refute_0_82,refute_0_81]) ).
cnf(refute_0_84,plain,
coll(skolemFOFtoCNF_C_1,X_2667,skolemFOFtoCNF_G),
inference(subst,[],[refute_0_83:[bind(X_2620,$fot(X_2667))]]) ).
cnf(refute_0_85,plain,
coll(X_2667,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,X_2667,skolemFOFtoCNF_G) )],[refute_0_84,refute_0_75]) ).
cnf(refute_0_86,plain,
coll(X_2668,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G),
inference(subst,[],[refute_0_85:[bind(X_2667,$fot(X_2668))]]) ).
cnf(refute_0_87,plain,
( ~ coll(X_2668,skolemFOFtoCNF_C_1,C)
| coll(C,skolemFOFtoCNF_G,X_2668) ),
inference(resolve,[$cnf( coll(X_2668,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G) )],[refute_0_86,refute_0_74]) ).
cnf(refute_0_88,plain,
( ~ coll(X_2661,skolemFOFtoCNF_A,C)
| ~ coll(X_2661,skolemFOFtoCNF_A,X_2662)
| coll(C,X_2662,X_2661) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2661)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_2662))]]) ).
cnf(refute_0_89,plain,
( ~ coll(X_2645,skolemFOFtoCNF_B_1,C)
| ~ coll(X_2645,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| coll(C,skolemFOFtoCNF_A,X_2645) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2645)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_90,plain,
( ~ coll(skolemFOFtoCNF_B_1,X_2629,skolemFOFtoCNF_A)
| coll(X_2629,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_2629)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_91,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_H)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_92,plain,
coll(skolemFOFtoCNF_H,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_93,plain,
( ~ coll(skolemFOFtoCNF_H,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_H)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_94,plain,
coll(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_H,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( ~ coll(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_H)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_96,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_A) )],[refute_0_96,refute_0_91]) ).
cnf(refute_0_98,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_2620)
| ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,X_2620,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_2620))]]) ).
cnf(refute_0_99,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_2620)
| coll(skolemFOFtoCNF_B_1,X_2620,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_2620),
inference(subst,[],[refute_0_55:[bind(X_485,$fot(X_2620)),bind(X_486,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_101,plain,
coll(skolemFOFtoCNF_B_1,X_2620,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_2620) )],[refute_0_100,refute_0_99]) ).
cnf(refute_0_102,plain,
coll(skolemFOFtoCNF_B_1,X_2629,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_101:[bind(X_2620,$fot(X_2629))]]) ).
cnf(refute_0_103,plain,
coll(X_2629,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,X_2629,skolemFOFtoCNF_A) )],[refute_0_102,refute_0_90]) ).
cnf(refute_0_104,plain,
coll(X_2645,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_103:[bind(X_2629,$fot(X_2645))]]) ).
cnf(refute_0_105,plain,
( ~ coll(X_2645,skolemFOFtoCNF_B_1,C)
| coll(C,skolemFOFtoCNF_A,X_2645) ),
inference(resolve,[$cnf( coll(X_2645,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_104,refute_0_89]) ).
cnf(refute_0_106,plain,
coll(X_2645,skolemFOFtoCNF_B_1,C),
inference(subst,[],[refute_0_68:[bind(X_2618,$fot(C)),bind(X_2619,$fot(X_2645)),bind(X_2620,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_107,plain,
coll(C,skolemFOFtoCNF_A,X_2645),
inference(resolve,[$cnf( coll(X_2645,skolemFOFtoCNF_B_1,C) )],[refute_0_106,refute_0_105]) ).
cnf(refute_0_108,plain,
coll(X_2661,skolemFOFtoCNF_A,X_2662),
inference(subst,[],[refute_0_107:[bind(C,$fot(X_2661)),bind(X_2645,$fot(X_2662))]]) ).
cnf(refute_0_109,plain,
( ~ coll(X_2661,skolemFOFtoCNF_A,C)
| coll(C,X_2662,X_2661) ),
inference(resolve,[$cnf( coll(X_2661,skolemFOFtoCNF_A,X_2662) )],[refute_0_108,refute_0_88]) ).
cnf(refute_0_110,plain,
( ~ coll(X_2659,skolemFOFtoCNF_E,C)
| ~ coll(X_2659,skolemFOFtoCNF_E,X_2660)
| coll(C,X_2660,X_2659) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2659)),bind(B,$fot(skolemFOFtoCNF_E)),bind(D,$fot(X_2660))]]) ).
cnf(refute_0_111,plain,
( ~ coll(X_2641,skolemFOFtoCNF_G,C)
| ~ coll(X_2641,skolemFOFtoCNF_G,skolemFOFtoCNF_E)
| coll(C,skolemFOFtoCNF_E,X_2641) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2641)),bind(B,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_112,plain,
( ~ coll(skolemFOFtoCNF_G,X_2640,skolemFOFtoCNF_E)
| coll(X_2640,skolemFOFtoCNF_G,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(X_2640)),bind(C,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_113,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E)
| coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_114,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P_3(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E),skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E))),bind(C,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_115,plain,
( ~ coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E),skolemFOFtoCNF_E,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P_3(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E),skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E))),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_116,plain,
( ~ perp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G)
| perp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_117,plain,
perp(skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_118,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_119,plain,
( ~ perp(skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_D)
| perp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_118:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_120,plain,
perp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_D) )],[refute_0_117,refute_0_119]) ).
cnf(refute_0_121,plain,
perp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G) )],[refute_0_120,refute_0_116]) ).
cnf(refute_0_122,plain,
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_P_3(A,B,C),C,B) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_123,plain,
( ~ perp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E)
| coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E),skolemFOFtoCNF_E,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_122:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_E)),bind(H,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_124,plain,
coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E),skolemFOFtoCNF_E,skolemFOFtoCNF_G),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E) )],[refute_0_121,refute_0_123]) ).
cnf(refute_0_125,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P_3(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E),skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E),skolemFOFtoCNF_E,skolemFOFtoCNF_G) )],[refute_0_124,refute_0_115]) ).
cnf(refute_0_126,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P_3(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E),skolemFOFtoCNF_G) )],[refute_0_125,refute_0_114]) ).
cnf(refute_0_127,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E) )],[refute_0_126,refute_0_113]) ).
cnf(refute_0_128,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_2620)
| ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_G,X_2620,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_G)),bind(D,$fot(X_2620))]]) ).
cnf(refute_0_129,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_2620)
| coll(skolemFOFtoCNF_G,X_2620,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_G) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_2620),
inference(subst,[],[refute_0_55:[bind(X_485,$fot(X_2620)),bind(X_486,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_131,plain,
coll(skolemFOFtoCNF_G,X_2620,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_2620) )],[refute_0_130,refute_0_129]) ).
cnf(refute_0_132,plain,
coll(skolemFOFtoCNF_G,X_2640,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_131:[bind(X_2620,$fot(X_2640))]]) ).
cnf(refute_0_133,plain,
coll(X_2640,skolemFOFtoCNF_G,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,X_2640,skolemFOFtoCNF_E) )],[refute_0_132,refute_0_112]) ).
cnf(refute_0_134,plain,
coll(X_2641,skolemFOFtoCNF_G,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_133:[bind(X_2640,$fot(X_2641))]]) ).
cnf(refute_0_135,plain,
( ~ coll(X_2641,skolemFOFtoCNF_G,C)
| coll(C,skolemFOFtoCNF_E,X_2641) ),
inference(resolve,[$cnf( coll(X_2641,skolemFOFtoCNF_G,skolemFOFtoCNF_E) )],[refute_0_134,refute_0_111]) ).
cnf(refute_0_136,plain,
coll(X_2641,skolemFOFtoCNF_G,C),
inference(subst,[],[refute_0_68:[bind(X_2618,$fot(C)),bind(X_2619,$fot(X_2641)),bind(X_2620,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_137,plain,
coll(C,skolemFOFtoCNF_E,X_2641),
inference(resolve,[$cnf( coll(X_2641,skolemFOFtoCNF_G,C) )],[refute_0_136,refute_0_135]) ).
cnf(refute_0_138,plain,
coll(X_2659,skolemFOFtoCNF_E,X_2660),
inference(subst,[],[refute_0_137:[bind(C,$fot(X_2659)),bind(X_2641,$fot(X_2660))]]) ).
cnf(refute_0_139,plain,
( ~ coll(X_2659,skolemFOFtoCNF_E,C)
| coll(C,X_2660,X_2659) ),
inference(resolve,[$cnf( coll(X_2659,skolemFOFtoCNF_E,X_2660) )],[refute_0_138,refute_0_110]) ).
cnf(refute_0_140,plain,
( ~ coll(X_2652,skolemFOFtoCNF_D,C)
| ~ coll(X_2652,skolemFOFtoCNF_D,X_2653)
| coll(C,X_2653,X_2652) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2652)),bind(B,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_2653))]]) ).
cnf(refute_0_141,plain,
( ~ coll(X_2650,X_2651,skolemFOFtoCNF_D)
| coll(X_2650,skolemFOFtoCNF_D,X_2651) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_2650)),bind(B,$fot(X_2651)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_142,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,C)
| ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,X_2649)
| coll(C,X_2649,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_2649))]]) ).
cnf(refute_0_143,plain,
( ~ coll(skolemFOFtoCNF_D,X_2634,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,X_2634) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_2634)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_144,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,X_2634),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,X_2634,skolemFOFtoCNF_C_1) )],[refute_0_58,refute_0_143]) ).
cnf(refute_0_145,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,X_2649),
inference(subst,[],[refute_0_144:[bind(X_2634,$fot(X_2649))]]) ).
cnf(refute_0_146,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,C)
| coll(C,X_2649,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,X_2649) )],[refute_0_145,refute_0_142]) ).
cnf(refute_0_147,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,C),
inference(subst,[],[refute_0_68:[bind(X_2618,$fot(C)),bind(X_2619,$fot(skolemFOFtoCNF_D)),bind(X_2620,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_148,plain,
coll(C,X_2649,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,C) )],[refute_0_147,refute_0_146]) ).
cnf(refute_0_149,plain,
coll(X_2650,X_2651,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_148:[bind(C,$fot(X_2650)),bind(X_2649,$fot(X_2651))]]) ).
cnf(refute_0_150,plain,
coll(X_2650,skolemFOFtoCNF_D,X_2651),
inference(resolve,[$cnf( coll(X_2650,X_2651,skolemFOFtoCNF_D) )],[refute_0_149,refute_0_141]) ).
cnf(refute_0_151,plain,
coll(X_2652,skolemFOFtoCNF_D,X_2653),
inference(subst,[],[refute_0_150:[bind(X_2650,$fot(X_2652)),bind(X_2651,$fot(X_2653))]]) ).
cnf(refute_0_152,plain,
( ~ coll(X_2652,skolemFOFtoCNF_D,C)
| coll(C,X_2653,X_2652) ),
inference(resolve,[$cnf( coll(X_2652,skolemFOFtoCNF_D,X_2653) )],[refute_0_151,refute_0_140]) ).
cnf(refute_0_153,plain,
coll(X_2652,skolemFOFtoCNF_D,C),
inference(subst,[],[refute_0_68:[bind(X_2618,$fot(C)),bind(X_2619,$fot(X_2652)),bind(X_2620,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_154,plain,
coll(C,X_2653,X_2652),
inference(resolve,[$cnf( coll(X_2652,skolemFOFtoCNF_D,C) )],[refute_0_153,refute_0_152]) ).
cnf(refute_0_155,plain,
coll(X_2659,skolemFOFtoCNF_E,C),
inference(subst,[],[refute_0_154:[bind(C,$fot(X_2659)),bind(X_2652,$fot(C)),bind(X_2653,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_156,plain,
coll(C,X_2660,X_2659),
inference(resolve,[$cnf( coll(X_2659,skolemFOFtoCNF_E,C) )],[refute_0_155,refute_0_139]) ).
cnf(refute_0_157,plain,
coll(X_2661,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_156:[bind(C,$fot(X_2661)),bind(X_2659,$fot(C)),bind(X_2660,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_158,plain,
coll(C,X_2662,X_2661),
inference(resolve,[$cnf( coll(X_2661,skolemFOFtoCNF_A,C) )],[refute_0_157,refute_0_109]) ).
cnf(refute_0_159,plain,
coll(X_2668,skolemFOFtoCNF_C_1,C),
inference(subst,[],[refute_0_158:[bind(C,$fot(X_2668)),bind(X_2661,$fot(C)),bind(X_2662,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_160,plain,
coll(C,skolemFOFtoCNF_G,X_2668),
inference(resolve,[$cnf( coll(X_2668,skolemFOFtoCNF_C_1,C) )],[refute_0_159,refute_0_87]) ).
cnf(refute_0_161,plain,
coll(X_2669,skolemFOFtoCNF_G,X_2670),
inference(subst,[],[refute_0_160:[bind(C,$fot(X_2669)),bind(X_2668,$fot(X_2670))]]) ).
cnf(refute_0_162,plain,
( ~ coll(X_2669,skolemFOFtoCNF_G,C)
| coll(C,X_2670,X_2669) ),
inference(resolve,[$cnf( coll(X_2669,skolemFOFtoCNF_G,X_2670) )],[refute_0_161,refute_0_73]) ).
cnf(refute_0_163,plain,
coll(X_2669,skolemFOFtoCNF_G,C),
inference(subst,[],[refute_0_158:[bind(C,$fot(X_2669)),bind(X_2661,$fot(C)),bind(X_2662,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_164,plain,
coll(C,X_2670,X_2669),
inference(resolve,[$cnf( coll(X_2669,skolemFOFtoCNF_G,C) )],[refute_0_163,refute_0_162]) ).
cnf(refute_0_165,plain,
coll(X_2693,skolemFOFtoCNF_C_1,C),
inference(subst,[],[refute_0_164:[bind(C,$fot(X_2693)),bind(X_2669,$fot(C)),bind(X_2670,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_166,plain,
coll(C,X_2694,X_2693),
inference(resolve,[$cnf( coll(X_2693,skolemFOFtoCNF_C_1,C) )],[refute_0_165,refute_0_72]) ).
cnf(refute_0_167,plain,
coll(O,A,C),
inference(subst,[],[refute_0_166:[bind(C,$fot(O)),bind(X_2693,$fot(C)),bind(X_2694,$fot(A))]]) ).
cnf(refute_0_168,plain,
( ~ circle(O,A,B,C)
| perp(A,B,B,C) ),
inference(resolve,[$cnf( coll(O,A,C) )],[refute_0_167,refute_0_3]) ).
cnf(refute_0_169,plain,
( ~ circle(X_20072,X_20069,X_20070,X_20071)
| perp(X_20069,X_20070,X_20070,X_20071) ),
inference(subst,[],[refute_0_168:[bind(A,$fot(X_20069)),bind(B,$fot(X_20070)),bind(C,$fot(X_20071)),bind(O,$fot(X_20072))]]) ).
cnf(refute_0_170,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_171,plain,
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_172,plain,
( ~ cong(X_6214,X_6215,X_6216,X_6214)
| cong(X_6214,X_6215,X_6214,X_6216) ),
inference(subst,[],[refute_0_171:[bind(A,$fot(X_6214)),bind(B,$fot(X_6215)),bind(C,$fot(X_6216)),bind(D,$fot(X_6214))]]) ).
cnf(refute_0_173,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_174,plain,
( ~ cong(X_6193,X_6191,X_6191,X_6192)
| cong(X_6191,X_6192,X_6193,X_6191) ),
inference(subst,[],[refute_0_173:[bind(A,$fot(X_6193)),bind(B,$fot(X_6191)),bind(C,$fot(X_6191)),bind(D,$fot(X_6192))]]) ).
cnf(refute_0_175,plain,
( ~ cong(X_6190,X_6188,X_6189,X_6188)
| cong(X_6190,X_6188,X_6188,X_6189) ),
inference(subst,[],[refute_0_171:[bind(A,$fot(X_6190)),bind(B,$fot(X_6188)),bind(C,$fot(X_6189)),bind(D,$fot(X_6188))]]) ).
cnf(refute_0_176,plain,
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_177,plain,
( ~ midp(M,X_6171,X_6171)
| ~ perp(X_6171,X_6170,X_6170,X_6171)
| cong(X_6171,M,X_6170,M) ),
inference(subst,[],[refute_0_176:[bind(A,$fot(X_6171)),bind(B,$fot(X_6170)),bind(C,$fot(X_6171))]]) ).
cnf(refute_0_178,plain,
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_179,plain,
( ~ cong(X_6168,X_6169,X_6168,X_6169)
| ~ cyclic(X_6168,X_6168,X_6169,X_6169)
| perp(X_6169,X_6168,X_6168,X_6169) ),
inference(subst,[],[refute_0_178:[bind(A,$fot(X_6168)),bind(B,$fot(X_6168)),bind(P,$fot(X_6169)),bind(Q,$fot(X_6169))]]) ).
cnf(refute_0_180,plain,
( ~ cyclic(X_6166,X_6166,X_6166,X_6167)
| cyclic(X_6166,X_6166,X_6167,X_6167) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_6166)),bind(B,$fot(X_6166)),bind(C,$fot(X_6166)),bind(D,$fot(X_6167)),bind(E,$fot(X_6167))]]) ).
cnf(refute_0_181,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_182,plain,
( ~ cyclic(X_6164,X_6164,X_6165,X_6164)
| cyclic(X_6164,X_6164,X_6164,X_6165) ),
inference(subst,[],[refute_0_181:[bind(A,$fot(X_6164)),bind(B,$fot(X_6164)),bind(C,$fot(X_6165)),bind(D,$fot(X_6164))]]) ).
cnf(refute_0_183,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[normalize_0_56]) ).
cnf(refute_0_184,plain,
( ~ cyclic(X_6162,X_6163,X_6162,X_6162)
| cyclic(X_6162,X_6162,X_6163,X_6162) ),
inference(subst,[],[refute_0_183:[bind(A,$fot(X_6162)),bind(B,$fot(X_6163)),bind(C,$fot(X_6162)),bind(D,$fot(X_6162))]]) ).
cnf(refute_0_185,plain,
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_186,plain,
( ~ cyclic(X_6161,X_6160,X_6160,X_6160)
| cyclic(X_6160,X_6161,X_6160,X_6160) ),
inference(subst,[],[refute_0_185:[bind(A,$fot(X_6161)),bind(B,$fot(X_6160)),bind(C,$fot(X_6160)),bind(D,$fot(X_6160))]]) ).
cnf(refute_0_187,plain,
( ~ cong(skolemFOFtoCNF_P_1(X_6159,X_6158),X_6159,skolemFOFtoCNF_P_1(X_6159,X_6158),X_6158)
| cyclic(X_6159,X_6158,X_6158,X_6158) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_6159)),bind(B,$fot(X_6158)),bind(C,$fot(X_6158)),bind(D,$fot(X_6158)),bind(O,$fot(skolemFOFtoCNF_P_1(X_6159,X_6158)))]]) ).
cnf(refute_0_188,plain,
( ~ midp(skolemFOFtoCNF_P_1(X_2799,X_2798),X_2799,X_2798)
| cong(skolemFOFtoCNF_P_1(X_2799,X_2798),X_2799,skolemFOFtoCNF_P_1(X_2799,X_2798),X_2798) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(skolemFOFtoCNF_P_1(X_2799,X_2798))),bind(B,$fot(X_2799)),bind(C,$fot(X_2798))]]) ).
cnf(refute_0_189,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_61]) ).
cnf(refute_0_190,plain,
( ~ coll(X_484,X_484,X_484)
| ~ midp(N,X_484,X_484)
| midp(skolemFOFtoCNF_P_1(X_484,Q),X_484,Q) ),
inference(subst,[],[refute_0_189:[bind(A,$fot(X_484)),bind(B,$fot(X_484)),bind(C,$fot(X_484)),bind(D,$fot(X_484)),bind(M,$fot(N))]]) ).
cnf(refute_0_191,plain,
coll(X_484,X_484,X_484),
inference(subst,[],[refute_0_51:[bind(X_478,$fot(X_484)),bind(X_479,$fot(X_484))]]) ).
cnf(refute_0_192,plain,
( ~ midp(N,X_484,X_484)
| midp(skolemFOFtoCNF_P_1(X_484,Q),X_484,Q) ),
inference(resolve,[$cnf( coll(X_484,X_484,X_484) )],[refute_0_191,refute_0_190]) ).
cnf(refute_0_193,plain,
( ~ midp(skolemFOFtoCNF_F,X_2770,X_2770)
| midp(skolemFOFtoCNF_P_1(X_2770,Q),X_2770,Q) ),
inference(subst,[],[refute_0_192:[bind(N,$fot(skolemFOFtoCNF_F)),bind(X_484,$fot(X_2770))]]) ).
cnf(refute_0_194,plain,
para(X_2723,X_2724,X_2723,X_2724),
inference(subst,[],[refute_0_49:[bind(X_476,$fot(X_2723)),bind(X_477,$fot(X_2724))]]) ).
cnf(refute_0_195,plain,
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[normalize_0_63]) ).
cnf(refute_0_196,plain,
( ~ midp(X_2725,X_2723,X_2723)
| ~ para(X_2723,X_2724,X_2723,X_2724)
| midp(X_2725,X_2724,X_2724) ),
inference(subst,[],[refute_0_195:[bind(A,$fot(X_2723)),bind(B,$fot(X_2723)),bind(C,$fot(X_2724)),bind(D,$fot(X_2724)),bind(M,$fot(X_2725))]]) ).
cnf(refute_0_197,plain,
( ~ midp(X_2725,X_2723,X_2723)
| midp(X_2725,X_2724,X_2724) ),
inference(resolve,[$cnf( para(X_2723,X_2724,X_2723,X_2724) )],[refute_0_194,refute_0_196]) ).
cnf(refute_0_198,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| midp(skolemFOFtoCNF_F,X_2724,X_2724) ),
inference(subst,[],[refute_0_197:[bind(X_2723,$fot(skolemFOFtoCNF_C_1)),bind(X_2725,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_199,plain,
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[normalize_0_65]) ).
cnf(refute_0_200,plain,
( ~ coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| ~ cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1)
| midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_199:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_201,plain,
( ~ cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F)
| cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_171:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_202,plain,
( ~ cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_173:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_F)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_203,plain,
( ~ cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F)
| cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_171:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_204,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D),
inference(canonicalize,[],[normalize_0_66]) ).
cnf(refute_0_205,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1)
| perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_206,plain,
( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_118:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_207,plain,
( ~ cong(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1)
| circle(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_170:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(O,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_208,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D)
| midp(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_28:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(M,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_209,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) )],[refute_0_204,refute_0_208]) ).
cnf(refute_0_210,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_211,plain,
cong(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
circle(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1) )],[refute_0_211,refute_0_207]) ).
cnf(refute_0_213,plain,
( ~ circle(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| perp(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_168:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(O,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_214,plain,
perp(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) )],[refute_0_214,refute_0_206]) ).
cnf(refute_0_216,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) )],[refute_0_215,refute_0_205]) ).
cnf(refute_0_217,plain,
( ~ midp(X_2767,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D)
| ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_C_1,X_2767,skolemFOFtoCNF_C_1,X_2767) ),
inference(subst,[],[refute_0_176:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_D)),bind(M,$fot(X_2767))]]) ).
cnf(refute_0_218,plain,
( ~ midp(X_2767,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_C_1,X_2767,skolemFOFtoCNF_C_1,X_2767) ),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_218:[bind(X_2767,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_220,plain,
cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) )],[refute_0_204,refute_0_219]) ).
cnf(refute_0_221,plain,
cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F) )],[refute_0_220,refute_0_203]) ).
cnf(refute_0_222,plain,
cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1) )],[refute_0_221,refute_0_202]) ).
cnf(refute_0_223,plain,
cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F) )],[refute_0_222,refute_0_201]) ).
cnf(refute_0_224,plain,
( ~ coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1) )],[refute_0_223,refute_0_200]) ).
cnf(refute_0_225,plain,
coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_166:[bind(C,$fot(skolemFOFtoCNF_F)),bind(X_2693,$fot(skolemFOFtoCNF_C_1)),bind(X_2694,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_226,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) )],[refute_0_225,refute_0_224]) ).
cnf(refute_0_227,plain,
midp(skolemFOFtoCNF_F,X_2724,X_2724),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) )],[refute_0_226,refute_0_198]) ).
cnf(refute_0_228,plain,
midp(skolemFOFtoCNF_F,X_2770,X_2770),
inference(subst,[],[refute_0_227:[bind(X_2724,$fot(X_2770))]]) ).
cnf(refute_0_229,plain,
midp(skolemFOFtoCNF_P_1(X_2770,Q),X_2770,Q),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,X_2770,X_2770) )],[refute_0_228,refute_0_193]) ).
cnf(refute_0_230,plain,
midp(skolemFOFtoCNF_P_1(X_2799,X_2798),X_2799,X_2798),
inference(subst,[],[refute_0_229:[bind(Q,$fot(X_2798)),bind(X_2770,$fot(X_2799))]]) ).
cnf(refute_0_231,plain,
cong(skolemFOFtoCNF_P_1(X_2799,X_2798),X_2799,skolemFOFtoCNF_P_1(X_2799,X_2798),X_2798),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(X_2799,X_2798),X_2799,X_2798) )],[refute_0_230,refute_0_188]) ).
cnf(refute_0_232,plain,
cong(skolemFOFtoCNF_P_1(X_6159,X_6158),X_6159,skolemFOFtoCNF_P_1(X_6159,X_6158),X_6158),
inference(subst,[],[refute_0_231:[bind(X_2798,$fot(X_6158)),bind(X_2799,$fot(X_6159))]]) ).
cnf(refute_0_233,plain,
cyclic(X_6159,X_6158,X_6158,X_6158),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_P_1(X_6159,X_6158),X_6159,skolemFOFtoCNF_P_1(X_6159,X_6158),X_6158) )],[refute_0_232,refute_0_187]) ).
cnf(refute_0_234,plain,
cyclic(X_6161,X_6160,X_6160,X_6160),
inference(subst,[],[refute_0_233:[bind(X_6158,$fot(X_6160)),bind(X_6159,$fot(X_6161))]]) ).
cnf(refute_0_235,plain,
cyclic(X_6160,X_6161,X_6160,X_6160),
inference(resolve,[$cnf( cyclic(X_6161,X_6160,X_6160,X_6160) )],[refute_0_234,refute_0_186]) ).
cnf(refute_0_236,plain,
cyclic(X_6162,X_6163,X_6162,X_6162),
inference(subst,[],[refute_0_235:[bind(X_6160,$fot(X_6162)),bind(X_6161,$fot(X_6163))]]) ).
cnf(refute_0_237,plain,
cyclic(X_6162,X_6162,X_6163,X_6162),
inference(resolve,[$cnf( cyclic(X_6162,X_6163,X_6162,X_6162) )],[refute_0_236,refute_0_184]) ).
cnf(refute_0_238,plain,
cyclic(X_6164,X_6164,X_6165,X_6164),
inference(subst,[],[refute_0_237:[bind(X_6162,$fot(X_6164)),bind(X_6163,$fot(X_6165))]]) ).
cnf(refute_0_239,plain,
cyclic(X_6164,X_6164,X_6164,X_6165),
inference(resolve,[$cnf( cyclic(X_6164,X_6164,X_6165,X_6164) )],[refute_0_238,refute_0_182]) ).
cnf(refute_0_240,plain,
cyclic(X_6166,X_6166,X_6166,X_6167),
inference(subst,[],[refute_0_239:[bind(X_6164,$fot(X_6166)),bind(X_6165,$fot(X_6167))]]) ).
cnf(refute_0_241,plain,
cyclic(X_6166,X_6166,X_6167,X_6167),
inference(resolve,[$cnf( cyclic(X_6166,X_6166,X_6166,X_6167) )],[refute_0_240,refute_0_180]) ).
cnf(refute_0_242,plain,
cyclic(X_6168,X_6168,X_6169,X_6169),
inference(subst,[],[refute_0_241:[bind(X_6166,$fot(X_6168)),bind(X_6167,$fot(X_6169))]]) ).
cnf(refute_0_243,plain,
( ~ cong(X_6168,X_6169,X_6168,X_6169)
| perp(X_6169,X_6168,X_6168,X_6169) ),
inference(resolve,[$cnf( cyclic(X_6168,X_6168,X_6169,X_6169) )],[refute_0_242,refute_0_179]) ).
cnf(refute_0_244,plain,
( ~ midp(X_2804,X_2803,X_2803)
| cong(X_2804,X_2803,X_2804,X_2803) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(X_2804)),bind(B,$fot(X_2803)),bind(C,$fot(X_2803))]]) ).
cnf(refute_0_245,plain,
( ~ midp(X_2785,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| midp(X_2785,X_2724,X_2724) ),
inference(subst,[],[refute_0_197:[bind(X_2723,$fot(skolemFOFtoCNF_C_1)),bind(X_2725,$fot(X_2785))]]) ).
cnf(refute_0_246,plain,
( ~ coll(X_2784,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| ~ cong(X_2784,skolemFOFtoCNF_C_1,X_2784,skolemFOFtoCNF_C_1)
| midp(X_2784,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_199:[bind(A,$fot(X_2784)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_247,plain,
( ~ cong(X_2782,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2782)
| cong(X_2782,skolemFOFtoCNF_C_1,X_2782,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_171:[bind(A,$fot(X_2782)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_2782))]]) ).
cnf(refute_0_248,plain,
( ~ cong(skolemFOFtoCNF_C_1,X_2777,X_2777,skolemFOFtoCNF_C_1)
| cong(X_2777,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2777) ),
inference(subst,[],[refute_0_173:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(X_2777)),bind(C,$fot(X_2777)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_249,plain,
( ~ cong(skolemFOFtoCNF_C_1,X_2772,skolemFOFtoCNF_C_1,X_2772)
| cong(skolemFOFtoCNF_C_1,X_2772,X_2772,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_171:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(X_2772)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_2772))]]) ).
cnf(refute_0_250,plain,
( ~ midp(skolemFOFtoCNF_C_1,X_2769,X_2769)
| cong(skolemFOFtoCNF_C_1,X_2769,skolemFOFtoCNF_C_1,X_2769) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(X_2769)),bind(C,$fot(X_2769))]]) ).
cnf(refute_0_251,plain,
( ~ midp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| midp(skolemFOFtoCNF_C_1,X_2724,X_2724) ),
inference(subst,[],[refute_0_197:[bind(X_2723,$fot(skolemFOFtoCNF_F)),bind(X_2725,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_252,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| ~ cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F)
| midp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_199:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_253,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| midp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F) )],[refute_0_220,refute_0_252]) ).
cnf(refute_0_254,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_166:[bind(C,$fot(skolemFOFtoCNF_C_1)),bind(X_2693,$fot(skolemFOFtoCNF_F)),bind(X_2694,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_255,plain,
midp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F) )],[refute_0_254,refute_0_253]) ).
cnf(refute_0_256,plain,
midp(skolemFOFtoCNF_C_1,X_2724,X_2724),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_F) )],[refute_0_255,refute_0_251]) ).
cnf(refute_0_257,plain,
midp(skolemFOFtoCNF_C_1,X_2769,X_2769),
inference(subst,[],[refute_0_256:[bind(X_2724,$fot(X_2769))]]) ).
cnf(refute_0_258,plain,
cong(skolemFOFtoCNF_C_1,X_2769,skolemFOFtoCNF_C_1,X_2769),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_C_1,X_2769,X_2769) )],[refute_0_257,refute_0_250]) ).
cnf(refute_0_259,plain,
cong(skolemFOFtoCNF_C_1,X_2772,skolemFOFtoCNF_C_1,X_2772),
inference(subst,[],[refute_0_258:[bind(X_2769,$fot(X_2772))]]) ).
cnf(refute_0_260,plain,
cong(skolemFOFtoCNF_C_1,X_2772,X_2772,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_C_1,X_2772,skolemFOFtoCNF_C_1,X_2772) )],[refute_0_259,refute_0_249]) ).
cnf(refute_0_261,plain,
cong(skolemFOFtoCNF_C_1,X_2777,X_2777,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_260:[bind(X_2772,$fot(X_2777))]]) ).
cnf(refute_0_262,plain,
cong(X_2777,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2777),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_C_1,X_2777,X_2777,skolemFOFtoCNF_C_1) )],[refute_0_261,refute_0_248]) ).
cnf(refute_0_263,plain,
cong(X_2782,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2782),
inference(subst,[],[refute_0_262:[bind(X_2777,$fot(X_2782))]]) ).
cnf(refute_0_264,plain,
cong(X_2782,skolemFOFtoCNF_C_1,X_2782,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cong(X_2782,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2782) )],[refute_0_263,refute_0_247]) ).
cnf(refute_0_265,plain,
cong(X_2784,skolemFOFtoCNF_C_1,X_2784,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_264:[bind(X_2782,$fot(X_2784))]]) ).
cnf(refute_0_266,plain,
( ~ coll(X_2784,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| midp(X_2784,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( cong(X_2784,skolemFOFtoCNF_C_1,X_2784,skolemFOFtoCNF_C_1) )],[refute_0_265,refute_0_246]) ).
cnf(refute_0_267,plain,
coll(X_2784,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_166:[bind(C,$fot(X_2784)),bind(X_2693,$fot(skolemFOFtoCNF_C_1)),bind(X_2694,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_268,plain,
midp(X_2784,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(X_2784,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) )],[refute_0_267,refute_0_266]) ).
cnf(refute_0_269,plain,
midp(X_2785,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_268:[bind(X_2784,$fot(X_2785))]]) ).
cnf(refute_0_270,plain,
midp(X_2785,X_2724,X_2724),
inference(resolve,[$cnf( midp(X_2785,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) )],[refute_0_269,refute_0_245]) ).
cnf(refute_0_271,plain,
midp(X_2804,X_2803,X_2803),
inference(subst,[],[refute_0_270:[bind(X_2724,$fot(X_2803)),bind(X_2785,$fot(X_2804))]]) ).
cnf(refute_0_272,plain,
cong(X_2804,X_2803,X_2804,X_2803),
inference(resolve,[$cnf( midp(X_2804,X_2803,X_2803) )],[refute_0_271,refute_0_244]) ).
cnf(refute_0_273,plain,
cong(X_6168,X_6169,X_6168,X_6169),
inference(subst,[],[refute_0_272:[bind(X_2803,$fot(X_6169)),bind(X_2804,$fot(X_6168))]]) ).
cnf(refute_0_274,plain,
perp(X_6169,X_6168,X_6168,X_6169),
inference(resolve,[$cnf( cong(X_6168,X_6169,X_6168,X_6169) )],[refute_0_273,refute_0_243]) ).
cnf(refute_0_275,plain,
perp(X_6171,X_6170,X_6170,X_6171),
inference(subst,[],[refute_0_274:[bind(X_6168,$fot(X_6170)),bind(X_6169,$fot(X_6171))]]) ).
cnf(refute_0_276,plain,
( ~ midp(M,X_6171,X_6171)
| cong(X_6171,M,X_6170,M) ),
inference(resolve,[$cnf( perp(X_6171,X_6170,X_6170,X_6171) )],[refute_0_275,refute_0_177]) ).
cnf(refute_0_277,plain,
( ~ midp(X_2793,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| midp(X_2793,X_2724,X_2724) ),
inference(subst,[],[refute_0_197:[bind(X_2723,$fot(skolemFOFtoCNF_F)),bind(X_2725,$fot(X_2793))]]) ).
cnf(refute_0_278,plain,
( ~ coll(X_2792,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| ~ cong(X_2792,skolemFOFtoCNF_F,X_2792,skolemFOFtoCNF_F)
| midp(X_2792,skolemFOFtoCNF_F,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_199:[bind(A,$fot(X_2792)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_279,plain,
( ~ cong(X_2790,skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_2790)
| cong(X_2790,skolemFOFtoCNF_F,X_2790,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_171:[bind(A,$fot(X_2790)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_F)),bind(D,$fot(X_2790))]]) ).
cnf(refute_0_280,plain,
( ~ cong(skolemFOFtoCNF_F,X_2786,X_2786,skolemFOFtoCNF_F)
| cong(X_2786,skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_2786) ),
inference(subst,[],[refute_0_173:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(X_2786)),bind(C,$fot(X_2786)),bind(D,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_281,plain,
( ~ cong(skolemFOFtoCNF_F,X_2775,skolemFOFtoCNF_F,X_2775)
| cong(skolemFOFtoCNF_F,X_2775,X_2775,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_171:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(X_2775)),bind(C,$fot(skolemFOFtoCNF_F)),bind(D,$fot(X_2775))]]) ).
cnf(refute_0_282,plain,
( ~ midp(skolemFOFtoCNF_F,X_2770,X_2770)
| cong(skolemFOFtoCNF_F,X_2770,skolemFOFtoCNF_F,X_2770) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(X_2770)),bind(C,$fot(X_2770))]]) ).
cnf(refute_0_283,plain,
cong(skolemFOFtoCNF_F,X_2770,skolemFOFtoCNF_F,X_2770),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,X_2770,X_2770) )],[refute_0_228,refute_0_282]) ).
cnf(refute_0_284,plain,
cong(skolemFOFtoCNF_F,X_2775,skolemFOFtoCNF_F,X_2775),
inference(subst,[],[refute_0_283:[bind(X_2770,$fot(X_2775))]]) ).
cnf(refute_0_285,plain,
cong(skolemFOFtoCNF_F,X_2775,X_2775,skolemFOFtoCNF_F),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,X_2775,skolemFOFtoCNF_F,X_2775) )],[refute_0_284,refute_0_281]) ).
cnf(refute_0_286,plain,
cong(skolemFOFtoCNF_F,X_2786,X_2786,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_285:[bind(X_2775,$fot(X_2786))]]) ).
cnf(refute_0_287,plain,
cong(X_2786,skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_2786),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,X_2786,X_2786,skolemFOFtoCNF_F) )],[refute_0_286,refute_0_280]) ).
cnf(refute_0_288,plain,
cong(X_2790,skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_2790),
inference(subst,[],[refute_0_287:[bind(X_2786,$fot(X_2790))]]) ).
cnf(refute_0_289,plain,
cong(X_2790,skolemFOFtoCNF_F,X_2790,skolemFOFtoCNF_F),
inference(resolve,[$cnf( cong(X_2790,skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_2790) )],[refute_0_288,refute_0_279]) ).
cnf(refute_0_290,plain,
cong(X_2792,skolemFOFtoCNF_F,X_2792,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_289:[bind(X_2790,$fot(X_2792))]]) ).
cnf(refute_0_291,plain,
( ~ coll(X_2792,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| midp(X_2792,skolemFOFtoCNF_F,skolemFOFtoCNF_F) ),
inference(resolve,[$cnf( cong(X_2792,skolemFOFtoCNF_F,X_2792,skolemFOFtoCNF_F) )],[refute_0_290,refute_0_278]) ).
cnf(refute_0_292,plain,
coll(X_2792,skolemFOFtoCNF_F,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_166:[bind(C,$fot(X_2792)),bind(X_2693,$fot(skolemFOFtoCNF_F)),bind(X_2694,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_293,plain,
midp(X_2792,skolemFOFtoCNF_F,skolemFOFtoCNF_F),
inference(resolve,[$cnf( coll(X_2792,skolemFOFtoCNF_F,skolemFOFtoCNF_F) )],[refute_0_292,refute_0_291]) ).
cnf(refute_0_294,plain,
midp(X_2793,skolemFOFtoCNF_F,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_293:[bind(X_2792,$fot(X_2793))]]) ).
cnf(refute_0_295,plain,
midp(X_2793,X_2724,X_2724),
inference(resolve,[$cnf( midp(X_2793,skolemFOFtoCNF_F,skolemFOFtoCNF_F) )],[refute_0_294,refute_0_277]) ).
cnf(refute_0_296,plain,
midp(M,X_6171,X_6171),
inference(subst,[],[refute_0_295:[bind(X_2724,$fot(X_6171)),bind(X_2793,$fot(M))]]) ).
cnf(refute_0_297,plain,
cong(X_6171,M,X_6170,M),
inference(resolve,[$cnf( midp(M,X_6171,X_6171) )],[refute_0_296,refute_0_276]) ).
cnf(refute_0_298,plain,
cong(X_6190,X_6188,X_6189,X_6188),
inference(subst,[],[refute_0_297:[bind(M,$fot(X_6188)),bind(X_6170,$fot(X_6189)),bind(X_6171,$fot(X_6190))]]) ).
cnf(refute_0_299,plain,
cong(X_6190,X_6188,X_6188,X_6189),
inference(resolve,[$cnf( cong(X_6190,X_6188,X_6189,X_6188) )],[refute_0_298,refute_0_175]) ).
cnf(refute_0_300,plain,
cong(X_6193,X_6191,X_6191,X_6192),
inference(subst,[],[refute_0_299:[bind(X_6188,$fot(X_6191)),bind(X_6189,$fot(X_6192)),bind(X_6190,$fot(X_6193))]]) ).
cnf(refute_0_301,plain,
cong(X_6191,X_6192,X_6193,X_6191),
inference(resolve,[$cnf( cong(X_6193,X_6191,X_6191,X_6192) )],[refute_0_300,refute_0_174]) ).
cnf(refute_0_302,plain,
cong(X_6214,X_6215,X_6216,X_6214),
inference(subst,[],[refute_0_301:[bind(X_6191,$fot(X_6214)),bind(X_6192,$fot(X_6215)),bind(X_6193,$fot(X_6216))]]) ).
cnf(refute_0_303,plain,
cong(X_6214,X_6215,X_6214,X_6216),
inference(resolve,[$cnf( cong(X_6214,X_6215,X_6216,X_6214) )],[refute_0_302,refute_0_172]) ).
cnf(refute_0_304,plain,
cong(O,A,O,B),
inference(subst,[],[refute_0_303:[bind(X_6214,$fot(O)),bind(X_6215,$fot(A)),bind(X_6216,$fot(B))]]) ).
cnf(refute_0_305,plain,
( ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(resolve,[$cnf( cong(O,A,O,B) )],[refute_0_304,refute_0_170]) ).
cnf(refute_0_306,plain,
cong(O,A,O,C),
inference(subst,[],[refute_0_303:[bind(X_6214,$fot(O)),bind(X_6215,$fot(A)),bind(X_6216,$fot(C))]]) ).
cnf(refute_0_307,plain,
circle(O,A,B,C),
inference(resolve,[$cnf( cong(O,A,O,C) )],[refute_0_306,refute_0_305]) ).
cnf(refute_0_308,plain,
circle(X_20072,X_20069,X_20070,X_20071),
inference(subst,[],[refute_0_307:[bind(A,$fot(X_20069)),bind(B,$fot(X_20070)),bind(C,$fot(X_20071)),bind(O,$fot(X_20072))]]) ).
cnf(refute_0_309,plain,
perp(X_20069,X_20070,X_20070,X_20071),
inference(resolve,[$cnf( circle(X_20072,X_20069,X_20070,X_20071) )],[refute_0_308,refute_0_169]) ).
cnf(refute_0_310,plain,
perp(X_20073,X_20074,X_20074,X_20075),
inference(subst,[],[refute_0_309:[bind(X_20069,$fot(X_20073)),bind(X_20070,$fot(X_20074)),bind(X_20071,$fot(X_20075))]]) ).
cnf(refute_0_311,plain,
perp(X_20073,X_20074,X_20075,X_20074),
inference(resolve,[$cnf( perp(X_20073,X_20074,X_20074,X_20075) )],[refute_0_310,refute_0_2]) ).
cnf(refute_0_312,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_D,skolemFOFtoCNF_H),
inference(subst,[],[refute_0_311:[bind(X_20073,$fot(skolemFOFtoCNF_C_1)),bind(X_20074,$fot(skolemFOFtoCNF_H)),bind(X_20075,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_313,plain,
$false,
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_D,skolemFOFtoCNF_H) )],[refute_0_312,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GEO638+1 : TPTP v8.1.0. Released v7.5.0.
% 0.09/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.37 % Computer : n029.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sat Jun 18 03:18:13 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 76.19/76.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 76.19/76.38
% 76.19/76.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 76.25/76.42
%------------------------------------------------------------------------------