TSTP Solution File: GEO634+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO634+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:27:47 EDT 2022
% Result : Theorem 38.84s 39.06s
% Output : CNFRefutation 38.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 32
% Syntax : Number of formulae : 454 ( 185 unt; 0 def)
% Number of atoms : 919 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 806 ( 341 ~; 336 |; 95 &)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-6 aty)
% Number of variables : 1033 ( 168 sgn 482 !; 29 ?)
% 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(ruleX6,axiom,
! [A,B,C,D,M,N] :
? [P] :
( ( midp(M,A,B)
& midp(N,C,D) )
=> ( midp(P,A,D)
& para(P,M,B,D)
& para(P,N,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(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ) ).
fof(exemplo6GDDFULL8110997,conjecture,
! [A,B,C,O,A1,P,Q,S,D,G,NWPNT1,NWPNT2] :
( ( circle(O,A,B,C)
& midp(A1,C,B)
& circle(O,A,P,NWPNT1)
& coll(P,A,A1)
& eqangle(Q,A,A,B,C,A,A,A1)
& circle(O,A,Q,NWPNT2)
& coll(S,B,C)
& coll(S,A,Q)
& perp(D,Q,B,C)
& coll(D,B,C)
& perp(G,Q,A,B)
& coll(G,A,B) )
=> perp(D,G,P,A) ) ).
fof(subgoal_0,plain,
! [A,B,C,O,A1,P,Q,S,D,G,NWPNT1,NWPNT2] :
( ( circle(O,A,B,C)
& midp(A1,C,B)
& circle(O,A,P,NWPNT1)
& coll(P,A,A1)
& eqangle(Q,A,A,B,C,A,A,A1)
& circle(O,A,Q,NWPNT2)
& coll(S,B,C)
& coll(S,A,Q)
& perp(D,Q,B,C)
& coll(D,B,C)
& perp(G,Q,A,B)
& coll(G,A,B) )
=> perp(D,G,P,A) ),
inference(strip,[],[exemplo6GDDFULL8110997]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,O,A1,P,Q,S,D,G,NWPNT1,NWPNT2] :
( ( circle(O,A,B,C)
& midp(A1,C,B)
& circle(O,A,P,NWPNT1)
& coll(P,A,A1)
& eqangle(Q,A,A,B,C,A,A,A1)
& circle(O,A,Q,NWPNT2)
& coll(S,B,C)
& coll(S,A,Q)
& perp(D,Q,B,C)
& coll(D,B,C)
& perp(G,Q,A,B)
& coll(G,A,B) )
=> perp(D,G,P,A) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,A1,B,C,D,G,O,P,Q,S] :
( ~ perp(D,G,P,A)
& circle(O,A,B,C)
& coll(D,B,C)
& coll(G,A,B)
& coll(P,A,A1)
& coll(S,A,Q)
& coll(S,B,C)
& eqangle(Q,A,A,B,C,A,A,A1)
& midp(A1,C,B)
& perp(D,Q,B,C)
& perp(G,Q,A,B)
& ? [NWPNT1] : circle(O,A,P,NWPNT1)
& ? [NWPNT2] : circle(O,A,Q,NWPNT2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_P_8,skolemFOFtoCNF_A)
& circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_A,skolemFOFtoCNF_A1)
& coll(skolemFOFtoCNF_S,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3)
& coll(skolemFOFtoCNF_S,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& eqangle(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A1)
& midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
& perp(skolemFOFtoCNF_D,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& perp(skolemFOFtoCNF_G,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& ? [NWPNT1] : circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_P_8,NWPNT1)
& ? [NWPNT2] : circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,NWPNT2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_P_8,skolemFOFtoCNF_A),
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,
midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_34,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_35,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(specialize,[],[normalize_0_34]) ).
fof(normalize_0_36,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_37,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_36]) ).
fof(normalize_0_38,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_37]) ).
fof(normalize_0_39,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_40,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_39]) ).
fof(normalize_0_41,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_42,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_41]) ).
fof(normalize_0_43,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[ruleD67]) ).
fof(normalize_0_44,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[ruleD11]) ).
fof(normalize_0_46,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(specialize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
! [A,B,C,D,M,N] :
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| ? [P] :
( midp(P,A,D)
& para(P,M,B,D)
& para(P,N,A,C) ) ),
inference(canonicalize,[],[ruleX6]) ).
fof(normalize_0_48,plain,
! [A,B,C,D,M,N] :
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| ? [P] :
( midp(P,A,D)
& para(P,M,B,D)
& para(P,N,A,C) ) ),
inference(specialize,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
! [A,B,C,D,M,N] :
( ( ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P(A,B,C,D,M,N),A,D) )
& ( ~ midp(M,A,B)
| ~ midp(N,C,D)
| para(skolemFOFtoCNF_P(A,B,C,D,M,N),M,B,D) )
& ( ~ midp(M,A,B)
| ~ midp(N,C,D)
| para(skolemFOFtoCNF_P(A,B,C,D,M,N),N,A,C) ) ),
inference(clausify,[],[normalize_0_48]) ).
fof(normalize_0_50,plain,
! [A,B,C,D,M,N] :
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P(A,B,C,D,M,N),A,D) ),
inference(conjunct,[],[normalize_0_49]) ).
fof(normalize_0_51,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_52,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_51]) ).
fof(normalize_0_53,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_54,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_53]) ).
fof(normalize_0_55,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_56,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(specialize,[],[normalize_0_55]) ).
fof(normalize_0_57,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_58,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(specialize,[],[normalize_0_57]) ).
fof(normalize_0_59,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_60,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_59]) ).
fof(normalize_0_61,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD69]) ).
fof(normalize_0_62,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_61]) ).
fof(normalize_0_63,plain,
coll(skolemFOFtoCNF_S,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_64,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_65,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_66,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_65]) ).
fof(normalize_0_67,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_66]) ).
fof(normalize_0_68,plain,
! [A,B,C,H] :
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| perp(A,skolemFOFtoCNF_P_3(A,B,C),C,B) ),
inference(conjunct,[],[normalize_0_67]) ).
fof(normalize_0_69,plain,
circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_70,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ? [P] : perp(P,A,A,O) ),
inference(canonicalize,[],[ruleX11]) ).
fof(normalize_0_71,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ? [P] : perp(P,A,A,O) ),
inference(specialize,[],[normalize_0_70]) ).
fof(normalize_0_72,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| perp(skolemFOFtoCNF_P_4(A,O),A,A,O) ),
inference(clausify,[],[normalize_0_71]) ).
fof(normalize_0_73,plain,
! [A,B,C,H] :
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_Q_1(A,B,C),C,A) ),
inference(conjunct,[],[normalize_0_67]) ).
fof(normalize_0_74,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_75,plain,
coll(skolemFOFtoCNF_S,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_76,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[ruleD23]) ).
fof(normalize_0_77,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(specialize,[],[normalize_0_76]) ).
fof(normalize_0_78,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[ruleD24]) ).
fof(normalize_0_79,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(specialize,[],[normalize_0_78]) ).
cnf(refute_0_0,plain,
~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_P_8,skolemFOFtoCNF_A),
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_3671,X_3671)
| ~ perp(X_3671,X_3670,X_3670,X_3671)
| cong(X_3671,M,X_3670,M) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_3671)),bind(B,$fot(X_3670)),bind(C,$fot(X_3671))]]) ).
cnf(refute_0_4,plain,
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ cong(X_3668,X_3669,X_3668,X_3669)
| ~ cyclic(X_3668,X_3668,X_3669,X_3669)
| perp(X_3669,X_3668,X_3668,X_3669) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_3668)),bind(B,$fot(X_3668)),bind(P,$fot(X_3669)),bind(Q,$fot(X_3669))]]) ).
cnf(refute_0_6,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ cyclic(X_3666,X_3666,X_3666,X_3667)
| cyclic(X_3666,X_3666,X_3667,X_3667) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_3666)),bind(B,$fot(X_3666)),bind(C,$fot(X_3666)),bind(D,$fot(X_3667)),bind(E,$fot(X_3667))]]) ).
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_3664,X_3664,X_3665,X_3664)
| cyclic(X_3664,X_3664,X_3664,X_3665) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_3664)),bind(B,$fot(X_3664)),bind(C,$fot(X_3665)),bind(D,$fot(X_3664))]]) ).
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_3662,X_3663,X_3662,X_3662)
| cyclic(X_3662,X_3662,X_3663,X_3662) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_3662)),bind(B,$fot(X_3663)),bind(C,$fot(X_3662)),bind(D,$fot(X_3662))]]) ).
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_3661,X_3660,X_3660,X_3660)
| cyclic(X_3660,X_3661,X_3660,X_3660) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_3661)),bind(B,$fot(X_3660)),bind(C,$fot(X_3660)),bind(D,$fot(X_3660))]]) ).
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_3659,X_3658),X_3659,skolemFOFtoCNF_P_1(X_3659,X_3658),X_3658)
| cyclic(X_3659,X_3658,X_3658,X_3658) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_3659)),bind(B,$fot(X_3658)),bind(C,$fot(X_3658)),bind(D,$fot(X_3658)),bind(O,$fot(skolemFOFtoCNF_P_1(X_3659,X_3658)))]]) ).
cnf(refute_0_16,plain,
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_17,plain,
( ~ midp(skolemFOFtoCNF_P_1(X_1692,X_1691),X_1692,X_1691)
| cong(skolemFOFtoCNF_P_1(X_1692,X_1691),X_1692,skolemFOFtoCNF_P_1(X_1692,X_1691),X_1691) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_P_1(X_1692,X_1691))),bind(B,$fot(X_1692)),bind(C,$fot(X_1691))]]) ).
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_363,X_362,X_363)
| coll(X_363,X_363,X_362) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(X_363)),bind(B,$fot(X_362)),bind(C,$fot(X_363))]]) ).
cnf(refute_0_22,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_23,plain,
( ~ coll(X_360,X_361,X_361)
| coll(X_361,X_360,X_361) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_360)),bind(B,$fot(X_361)),bind(C,$fot(X_361))]]) ).
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_355,X_356,X_355,X_356)
| coll(X_355,X_356,X_356) ),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_355)),bind(B,$fot(X_356)),bind(C,$fot(X_356))]]) ).
cnf(refute_0_26,plain,
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_27,plain,
( ~ eqangle(X_353,X_354,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_353,X_354,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| para(X_353,X_354,X_353,X_354) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_353)),bind(B,$fot(X_354)),bind(C,$fot(X_353)),bind(D,$fot(X_354)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_28,plain,
( ~ cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1)),bind(E,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_29,plain,
( ~ cong(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1)),bind(O,$fot(skolemFOFtoCNF_A1))]]) ).
cnf(refute_0_30,plain,
midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_31,plain,
( ~ midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_A1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_32,plain,
cong(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1) )],[refute_0_32,refute_0_29]) ).
cnf(refute_0_34,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_33,refute_0_28]) ).
cnf(refute_0_35,plain,
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_36,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_35:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_37,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_39,plain,
para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_41,plain,
( ~ para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154) ),
inference(subst,[],[refute_0_40:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1)),bind(P,$fot(X_153)),bind(Q,$fot(X_154))]]) ).
cnf(refute_0_42,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346),
inference(subst,[],[refute_0_42:[bind(X_153,$fot(X_345)),bind(X_154,$fot(X_346))]]) ).
cnf(refute_0_44,plain,
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_45,plain,
( ~ eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346)
| eqangle(X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_44:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_345)),bind(D,$fot(X_346)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1)),bind(U,$fot(X_345)),bind(V,$fot(X_346))]]) ).
cnf(refute_0_46,plain,
eqangle(X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346) )],[refute_0_43,refute_0_45]) ).
cnf(refute_0_47,plain,
eqangle(X_353,X_354,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_353,X_354,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_46:[bind(X_345,$fot(X_353)),bind(X_346,$fot(X_354))]]) ).
cnf(refute_0_48,plain,
para(X_353,X_354,X_353,X_354),
inference(resolve,[$cnf( eqangle(X_353,X_354,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_353,X_354,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_47,refute_0_27]) ).
cnf(refute_0_49,plain,
para(X_355,X_356,X_355,X_356),
inference(subst,[],[refute_0_48:[bind(X_353,$fot(X_355)),bind(X_354,$fot(X_356))]]) ).
cnf(refute_0_50,plain,
coll(X_355,X_356,X_356),
inference(resolve,[$cnf( para(X_355,X_356,X_355,X_356) )],[refute_0_49,refute_0_25]) ).
cnf(refute_0_51,plain,
coll(X_360,X_361,X_361),
inference(subst,[],[refute_0_50:[bind(X_355,$fot(X_360)),bind(X_356,$fot(X_361))]]) ).
cnf(refute_0_52,plain,
coll(X_361,X_360,X_361),
inference(resolve,[$cnf( coll(X_360,X_361,X_361) )],[refute_0_51,refute_0_23]) ).
cnf(refute_0_53,plain,
coll(X_363,X_362,X_363),
inference(subst,[],[refute_0_52:[bind(X_360,$fot(X_362)),bind(X_361,$fot(X_363))]]) ).
cnf(refute_0_54,plain,
coll(X_363,X_363,X_362),
inference(resolve,[$cnf( coll(X_363,X_362,X_363) )],[refute_0_53,refute_0_21]) ).
cnf(refute_0_55,plain,
coll(D,D,D),
inference(subst,[],[refute_0_54:[bind(X_362,$fot(D)),bind(X_363,$fot(D))]]) ).
cnf(refute_0_56,plain,
( ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(resolve,[$cnf( coll(D,D,D) )],[refute_0_55,refute_0_19]) ).
cnf(refute_0_57,plain,
( ~ midp(skolemFOFtoCNF_B_1,X_1672,X_1672)
| midp(skolemFOFtoCNF_P_1(X_1672,Q),X_1672,Q) ),
inference(subst,[],[refute_0_56:[bind(D,$fot(X_1672)),bind(N,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_58,plain,
para(X_1581,X_1582,X_1581,X_1582),
inference(subst,[],[refute_0_48:[bind(X_353,$fot(X_1581)),bind(X_354,$fot(X_1582))]]) ).
cnf(refute_0_59,plain,
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_60,plain,
( ~ midp(X_1583,X_1581,X_1581)
| ~ para(X_1581,X_1582,X_1581,X_1582)
| midp(X_1583,X_1582,X_1582) ),
inference(subst,[],[refute_0_59:[bind(A,$fot(X_1581)),bind(B,$fot(X_1581)),bind(C,$fot(X_1582)),bind(D,$fot(X_1582)),bind(M,$fot(X_1583))]]) ).
cnf(refute_0_61,plain,
( ~ midp(X_1583,X_1581,X_1581)
| midp(X_1583,X_1582,X_1582) ),
inference(resolve,[$cnf( para(X_1581,X_1582,X_1581,X_1582) )],[refute_0_58,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1))
| midp(skolemFOFtoCNF_B_1,X_1582,X_1582) ),
inference(subst,[],[refute_0_61:[bind(X_1581,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1))),bind(X_1583,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_63,plain,
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_64,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1))
| ~ cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1))
| midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1))),bind(C,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)))]]) ).
cnf(refute_0_65,plain,
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_66,plain,
( ~ midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_65:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(M,$fot(skolemFOFtoCNF_A1))]]) ).
cnf(refute_0_67,plain,
midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_30,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P(A,B,C,D,M,N),A,D) ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_69,plain,
( ~ midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_68:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_C_1)),bind(M,$fot(skolemFOFtoCNF_A1)),bind(N,$fot(skolemFOFtoCNF_A1))]]) ).
cnf(refute_0_70,plain,
midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_67,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| ~ perp(skolemFOFtoCNF_B_1,X_1613,X_1613,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),X_1613,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_1613)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(M,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)))]]) ).
cnf(refute_0_72,plain,
( ~ perp(skolemFOFtoCNF_B_1,X_1613,X_1613,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),X_1613,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)) ),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)) ),
inference(subst,[],[refute_0_72:[bind(X_1613,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_74,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_75,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_74:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_76,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_77,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_78,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[normalize_0_56]) ).
cnf(refute_0_79,plain,
( ~ cong(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1)
| circle(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_78:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(O,$fot(skolemFOFtoCNF_A1))]]) ).
cnf(refute_0_80,plain,
circle(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1) )],[refute_0_32,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_82,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_60]) ).
cnf(refute_0_83,plain,
( ~ coll(X_1531,skolemFOFtoCNF_A1,C)
| ~ coll(X_1531,skolemFOFtoCNF_A1,X_1532)
| coll(C,X_1532,X_1531) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1531)),bind(B,$fot(skolemFOFtoCNF_A1)),bind(D,$fot(X_1532))]]) ).
cnf(refute_0_84,plain,
( ~ coll(X_1471,skolemFOFtoCNF_B_1,C)
| ~ coll(X_1471,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A1)
| coll(C,skolemFOFtoCNF_A1,X_1471) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1471)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_A1))]]) ).
cnf(refute_0_85,plain,
( ~ coll(skolemFOFtoCNF_A1,X_1470,C)
| ~ coll(skolemFOFtoCNF_A1,X_1470,skolemFOFtoCNF_B_1)
| coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A1) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_A1)),bind(B,$fot(X_1470)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_86,plain,
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_62]) ).
cnf(refute_0_87,plain,
( ~ midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_86:[bind(A,$fot(skolemFOFtoCNF_A1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_88,plain,
coll(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_30,refute_0_87]) ).
cnf(refute_0_89,plain,
( ~ coll(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A1) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_A1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_90,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1396)
| ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A1)
| coll(skolemFOFtoCNF_A1,X_1396,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A1)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_92,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1396)
| coll(skolemFOFtoCNF_A1,X_1396,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A1) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1396),
inference(subst,[],[refute_0_54:[bind(X_362,$fot(X_1396)),bind(X_363,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_94,plain,
coll(skolemFOFtoCNF_A1,X_1396,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1396) )],[refute_0_93,refute_0_92]) ).
cnf(refute_0_95,plain,
coll(skolemFOFtoCNF_A1,X_1470,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_94:[bind(X_1396,$fot(X_1470))]]) ).
cnf(refute_0_96,plain,
( ~ coll(skolemFOFtoCNF_A1,X_1470,C)
| coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A1,X_1470,skolemFOFtoCNF_B_1) )],[refute_0_95,refute_0_85]) ).
cnf(refute_0_97,plain,
( ~ coll(X_1463,skolemFOFtoCNF_Q_3,C)
| ~ coll(X_1463,skolemFOFtoCNF_Q_3,X_1464)
| coll(C,X_1464,X_1463) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1463)),bind(B,$fot(skolemFOFtoCNF_Q_3)),bind(D,$fot(X_1464))]]) ).
cnf(refute_0_98,plain,
( ~ coll(X_1440,skolemFOFtoCNF_A,C)
| ~ coll(X_1440,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3)
| coll(C,skolemFOFtoCNF_Q_3,X_1440) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1440)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_99,plain,
( ~ coll(skolemFOFtoCNF_A,X_1438,skolemFOFtoCNF_Q_3)
| coll(X_1438,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_1438)),bind(C,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_100,plain,
coll(skolemFOFtoCNF_S,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3),
inference(canonicalize,[],[normalize_0_63]) ).
cnf(refute_0_101,plain,
( ~ coll(skolemFOFtoCNF_S,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_S,skolemFOFtoCNF_Q_3) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_S)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_102,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_S,skolemFOFtoCNF_Q_3),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_S,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_S,skolemFOFtoCNF_Q_3)
| coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_S)),bind(C,$fot(skolemFOFtoCNF_Q_3)),bind(D,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_104,plain,
coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_S,skolemFOFtoCNF_Q_3) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( ~ coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,X_1396)
| ~ coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,X_1396,skolemFOFtoCNF_Q_3) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_Q_3)),bind(B,$fot(skolemFOFtoCNF_Q_3)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_106,plain,
( ~ coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,X_1396)
| coll(skolemFOFtoCNF_A,X_1396,skolemFOFtoCNF_Q_3) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,X_1396),
inference(subst,[],[refute_0_54:[bind(X_362,$fot(X_1396)),bind(X_363,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_108,plain,
coll(skolemFOFtoCNF_A,X_1396,skolemFOFtoCNF_Q_3),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,X_1396) )],[refute_0_107,refute_0_106]) ).
cnf(refute_0_109,plain,
coll(skolemFOFtoCNF_A,X_1438,skolemFOFtoCNF_Q_3),
inference(subst,[],[refute_0_108:[bind(X_1396,$fot(X_1438))]]) ).
cnf(refute_0_110,plain,
coll(X_1438,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_1438,skolemFOFtoCNF_Q_3) )],[refute_0_109,refute_0_99]) ).
cnf(refute_0_111,plain,
coll(X_1440,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3),
inference(subst,[],[refute_0_110:[bind(X_1438,$fot(X_1440))]]) ).
cnf(refute_0_112,plain,
( ~ coll(X_1440,skolemFOFtoCNF_A,C)
| coll(C,skolemFOFtoCNF_Q_3,X_1440) ),
inference(resolve,[$cnf( coll(X_1440,skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3) )],[refute_0_111,refute_0_98]) ).
cnf(refute_0_113,plain,
coll(X_1394,X_1394,X_1395),
inference(subst,[],[refute_0_54:[bind(X_362,$fot(X_1395)),bind(X_363,$fot(X_1394))]]) ).
cnf(refute_0_114,plain,
( ~ coll(X_1394,X_1394,X_1395)
| ~ coll(X_1394,X_1394,X_1396)
| coll(X_1395,X_1396,X_1394) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1394)),bind(B,$fot(X_1394)),bind(C,$fot(X_1395)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_115,plain,
( ~ coll(X_1394,X_1394,X_1396)
| coll(X_1395,X_1396,X_1394) ),
inference(resolve,[$cnf( coll(X_1394,X_1394,X_1395) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
coll(X_1394,X_1394,X_1396),
inference(subst,[],[refute_0_54:[bind(X_362,$fot(X_1396)),bind(X_363,$fot(X_1394))]]) ).
cnf(refute_0_117,plain,
coll(X_1395,X_1396,X_1394),
inference(resolve,[$cnf( coll(X_1394,X_1394,X_1396) )],[refute_0_116,refute_0_115]) ).
cnf(refute_0_118,plain,
coll(X_1440,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_117:[bind(X_1394,$fot(C)),bind(X_1395,$fot(X_1440)),bind(X_1396,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_119,plain,
coll(C,skolemFOFtoCNF_Q_3,X_1440),
inference(resolve,[$cnf( coll(X_1440,skolemFOFtoCNF_A,C) )],[refute_0_118,refute_0_112]) ).
cnf(refute_0_120,plain,
coll(X_1463,skolemFOFtoCNF_Q_3,X_1464),
inference(subst,[],[refute_0_119:[bind(C,$fot(X_1463)),bind(X_1440,$fot(X_1464))]]) ).
cnf(refute_0_121,plain,
( ~ coll(X_1463,skolemFOFtoCNF_Q_3,C)
| coll(C,X_1464,X_1463) ),
inference(resolve,[$cnf( coll(X_1463,skolemFOFtoCNF_Q_3,X_1464) )],[refute_0_120,refute_0_97]) ).
cnf(refute_0_122,plain,
( ~ coll(X_1456,skolemFOFtoCNF_G,C)
| ~ coll(X_1456,skolemFOFtoCNF_G,X_1457)
| coll(C,X_1457,X_1456) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1456)),bind(B,$fot(skolemFOFtoCNF_G)),bind(D,$fot(X_1457))]]) ).
cnf(refute_0_123,plain,
( ~ coll(X_1455,skolemFOFtoCNF_B_1,C)
| ~ coll(X_1455,skolemFOFtoCNF_B_1,skolemFOFtoCNF_G)
| coll(C,skolemFOFtoCNF_G,X_1455) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1455)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_124,plain,
( ~ coll(skolemFOFtoCNF_B_1,X_1437,skolemFOFtoCNF_G)
| coll(X_1437,skolemFOFtoCNF_B_1,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_1437)),bind(C,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_125,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_126,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_64]) ).
cnf(refute_0_127,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_128,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_130,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_G) )],[refute_0_130,refute_0_125]) ).
cnf(refute_0_132,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_133,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_1396)
| ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,X_1396,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_135,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_1396)
| coll(skolemFOFtoCNF_B_1,X_1396,skolemFOFtoCNF_G) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_1396),
inference(subst,[],[refute_0_54:[bind(X_362,$fot(X_1396)),bind(X_363,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_137,plain,
coll(skolemFOFtoCNF_B_1,X_1396,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_1396) )],[refute_0_136,refute_0_135]) ).
cnf(refute_0_138,plain,
coll(skolemFOFtoCNF_B_1,X_1437,skolemFOFtoCNF_G),
inference(subst,[],[refute_0_137:[bind(X_1396,$fot(X_1437))]]) ).
cnf(refute_0_139,plain,
coll(X_1437,skolemFOFtoCNF_B_1,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,X_1437,skolemFOFtoCNF_G) )],[refute_0_138,refute_0_124]) ).
cnf(refute_0_140,plain,
coll(X_1455,skolemFOFtoCNF_B_1,skolemFOFtoCNF_G),
inference(subst,[],[refute_0_139:[bind(X_1437,$fot(X_1455))]]) ).
cnf(refute_0_141,plain,
( ~ coll(X_1455,skolemFOFtoCNF_B_1,C)
| coll(C,skolemFOFtoCNF_G,X_1455) ),
inference(resolve,[$cnf( coll(X_1455,skolemFOFtoCNF_B_1,skolemFOFtoCNF_G) )],[refute_0_140,refute_0_123]) ).
cnf(refute_0_142,plain,
coll(X_1455,skolemFOFtoCNF_B_1,C),
inference(subst,[],[refute_0_117:[bind(X_1394,$fot(C)),bind(X_1395,$fot(X_1455)),bind(X_1396,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_143,plain,
coll(C,skolemFOFtoCNF_G,X_1455),
inference(resolve,[$cnf( coll(X_1455,skolemFOFtoCNF_B_1,C) )],[refute_0_142,refute_0_141]) ).
cnf(refute_0_144,plain,
coll(X_1456,skolemFOFtoCNF_G,X_1457),
inference(subst,[],[refute_0_143:[bind(C,$fot(X_1456)),bind(X_1455,$fot(X_1457))]]) ).
cnf(refute_0_145,plain,
( ~ coll(X_1456,skolemFOFtoCNF_G,C)
| coll(C,X_1457,X_1456) ),
inference(resolve,[$cnf( coll(X_1456,skolemFOFtoCNF_G,X_1457) )],[refute_0_144,refute_0_122]) ).
cnf(refute_0_146,plain,
coll(X_1456,skolemFOFtoCNF_G,C),
inference(subst,[],[refute_0_117:[bind(X_1394,$fot(C)),bind(X_1395,$fot(X_1456)),bind(X_1396,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_147,plain,
coll(C,X_1457,X_1456),
inference(resolve,[$cnf( coll(X_1456,skolemFOFtoCNF_G,C) )],[refute_0_146,refute_0_145]) ).
cnf(refute_0_148,plain,
coll(X_1463,skolemFOFtoCNF_Q_3,C),
inference(subst,[],[refute_0_147:[bind(C,$fot(X_1463)),bind(X_1456,$fot(C)),bind(X_1457,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_149,plain,
coll(C,X_1464,X_1463),
inference(resolve,[$cnf( coll(X_1463,skolemFOFtoCNF_Q_3,C) )],[refute_0_148,refute_0_121]) ).
cnf(refute_0_150,plain,
coll(skolemFOFtoCNF_A1,X_1470,C),
inference(subst,[],[refute_0_149:[bind(C,$fot(skolemFOFtoCNF_A1)),bind(X_1463,$fot(C)),bind(X_1464,$fot(X_1470))]]) ).
cnf(refute_0_151,plain,
coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A1,X_1470,C) )],[refute_0_150,refute_0_96]) ).
cnf(refute_0_152,plain,
coll(X_1471,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A1),
inference(subst,[],[refute_0_151:[bind(C,$fot(X_1471))]]) ).
cnf(refute_0_153,plain,
( ~ coll(X_1471,skolemFOFtoCNF_B_1,C)
| coll(C,skolemFOFtoCNF_A1,X_1471) ),
inference(resolve,[$cnf( coll(X_1471,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A1) )],[refute_0_152,refute_0_84]) ).
cnf(refute_0_154,plain,
coll(X_1471,skolemFOFtoCNF_B_1,C),
inference(subst,[],[refute_0_149:[bind(C,$fot(X_1471)),bind(X_1463,$fot(C)),bind(X_1464,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_155,plain,
coll(C,skolemFOFtoCNF_A1,X_1471),
inference(resolve,[$cnf( coll(X_1471,skolemFOFtoCNF_B_1,C) )],[refute_0_154,refute_0_153]) ).
cnf(refute_0_156,plain,
coll(X_1531,skolemFOFtoCNF_A1,X_1532),
inference(subst,[],[refute_0_155:[bind(C,$fot(X_1531)),bind(X_1471,$fot(X_1532))]]) ).
cnf(refute_0_157,plain,
( ~ coll(X_1531,skolemFOFtoCNF_A1,C)
| coll(C,X_1532,X_1531) ),
inference(resolve,[$cnf( coll(X_1531,skolemFOFtoCNF_A1,X_1532) )],[refute_0_156,refute_0_83]) ).
cnf(refute_0_158,plain,
( ~ coll(X_1501,skolemFOFtoCNF_B_1,C)
| ~ coll(X_1501,skolemFOFtoCNF_B_1,X_1502)
| coll(C,X_1502,X_1501) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1501)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_1502))]]) ).
cnf(refute_0_159,plain,
( ~ coll(X_1474,skolemFOFtoCNF_C_1,C)
| ~ coll(X_1474,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| coll(C,skolemFOFtoCNF_B_1,X_1474) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1474)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_160,plain,
( ~ coll(skolemFOFtoCNF_C_1,X_1472,skolemFOFtoCNF_B_1)
| coll(X_1472,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(X_1472)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_161,plain,
( ~ coll(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_A1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_162,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_88,refute_0_161]) ).
cnf(refute_0_163,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_A1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_164,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_B_1) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1396)
| ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_166,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1396)
| coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1396) )],[refute_0_93,refute_0_166]) ).
cnf(refute_0_168,plain,
coll(skolemFOFtoCNF_C_1,X_1472,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_167:[bind(X_1396,$fot(X_1472))]]) ).
cnf(refute_0_169,plain,
coll(X_1472,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,X_1472,skolemFOFtoCNF_B_1) )],[refute_0_168,refute_0_160]) ).
cnf(refute_0_170,plain,
coll(X_1474,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_169:[bind(X_1472,$fot(X_1474))]]) ).
cnf(refute_0_171,plain,
( ~ coll(X_1474,skolemFOFtoCNF_C_1,C)
| coll(C,skolemFOFtoCNF_B_1,X_1474) ),
inference(resolve,[$cnf( coll(X_1474,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_170,refute_0_159]) ).
cnf(refute_0_172,plain,
coll(X_1474,skolemFOFtoCNF_C_1,C),
inference(subst,[],[refute_0_149:[bind(C,$fot(X_1474)),bind(X_1463,$fot(C)),bind(X_1464,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_173,plain,
coll(C,skolemFOFtoCNF_B_1,X_1474),
inference(resolve,[$cnf( coll(X_1474,skolemFOFtoCNF_C_1,C) )],[refute_0_172,refute_0_171]) ).
cnf(refute_0_174,plain,
coll(X_1501,skolemFOFtoCNF_B_1,X_1502),
inference(subst,[],[refute_0_173:[bind(C,$fot(X_1501)),bind(X_1474,$fot(X_1502))]]) ).
cnf(refute_0_175,plain,
( ~ coll(X_1501,skolemFOFtoCNF_B_1,C)
| coll(C,X_1502,X_1501) ),
inference(resolve,[$cnf( coll(X_1501,skolemFOFtoCNF_B_1,X_1502) )],[refute_0_174,refute_0_158]) ).
cnf(refute_0_176,plain,
( ~ coll(X_1498,skolemFOFtoCNF_O_2,C)
| ~ coll(X_1498,skolemFOFtoCNF_O_2,X_1499)
| coll(C,X_1499,X_1498) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1498)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(X_1499))]]) ).
cnf(refute_0_177,plain,
( ~ coll(X_1497,skolemFOFtoCNF_A,C)
| ~ coll(X_1497,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)
| coll(C,skolemFOFtoCNF_O_2,X_1497) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1497)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_178,plain,
( ~ coll(skolemFOFtoCNF_A,X_1478,skolemFOFtoCNF_O_2)
| coll(X_1478,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_1478)),bind(C,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_179,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)
| coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_180,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_Q_1(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(skolemFOFtoCNF_Q_1(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2))),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_181,plain,
( ~ coll(skolemFOFtoCNF_Q_1(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_Q_1(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_Q_1(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2))),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_182,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_74:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2))),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_183,plain,
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| perp(A,skolemFOFtoCNF_P_3(A,B,C),C,B) ),
inference(canonicalize,[],[normalize_0_68]) ).
cnf(refute_0_184,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_183:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(H,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)))]]) ).
cnf(refute_0_185,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_74:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2))),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_186,plain,
( ~ perp(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2))
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)))]]) ).
cnf(refute_0_187,plain,
( ~ perp(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)) ),
inference(subst,[],[refute_0_74:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2))),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_188,plain,
( ~ perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2))),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_189,plain,
( ~ perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)
| perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_74:[bind(A,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2))),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_190,plain,
circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_69]) ).
cnf(refute_0_191,plain,
( ~ circle(O,A,B,C)
| perp(skolemFOFtoCNF_P_4(A,O),A,A,O) ),
inference(canonicalize,[],[normalize_0_72]) ).
cnf(refute_0_192,plain,
( ~ circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_191:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(O,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_193,plain,
perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_190,refute_0_192]) ).
cnf(refute_0_194,plain,
perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) )],[refute_0_193,refute_0_189]) ).
cnf(refute_0_195,plain,
perp(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) )],[refute_0_194,refute_0_188]) ).
cnf(refute_0_196,plain,
perp(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A) )],[refute_0_195,refute_0_187]) ).
cnf(refute_0_197,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)) )],[refute_0_196,refute_0_186]) ).
cnf(refute_0_198,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) )],[refute_0_197,refute_0_185]) ).
cnf(refute_0_199,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) )],[refute_0_198,refute_0_184]) ).
cnf(refute_0_200,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) )],[refute_0_199,refute_0_182]) ).
cnf(refute_0_201,plain,
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_Q_1(A,B,C),C,A) ),
inference(canonicalize,[],[normalize_0_73]) ).
cnf(refute_0_202,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)
| coll(skolemFOFtoCNF_Q_1(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_201:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(H,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)))]]) ).
cnf(refute_0_203,plain,
coll(skolemFOFtoCNF_Q_1(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) )],[refute_0_200,refute_0_202]) ).
cnf(refute_0_204,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_Q_1(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_Q_1(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) )],[refute_0_203,refute_0_181]) ).
cnf(refute_0_205,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_Q_1(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A) )],[refute_0_204,refute_0_180]) ).
cnf(refute_0_206,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) )],[refute_0_205,refute_0_179]) ).
cnf(refute_0_207,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_1396)
| ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,X_1396,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_208,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_1396)
| coll(skolemFOFtoCNF_A,X_1396,skolemFOFtoCNF_O_2) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_1396),
inference(subst,[],[refute_0_54:[bind(X_362,$fot(X_1396)),bind(X_363,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_210,plain,
coll(skolemFOFtoCNF_A,X_1396,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_1396) )],[refute_0_209,refute_0_208]) ).
cnf(refute_0_211,plain,
coll(skolemFOFtoCNF_A,X_1478,skolemFOFtoCNF_O_2),
inference(subst,[],[refute_0_210:[bind(X_1396,$fot(X_1478))]]) ).
cnf(refute_0_212,plain,
coll(X_1478,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_1478,skolemFOFtoCNF_O_2) )],[refute_0_211,refute_0_178]) ).
cnf(refute_0_213,plain,
coll(X_1497,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),
inference(subst,[],[refute_0_212:[bind(X_1478,$fot(X_1497))]]) ).
cnf(refute_0_214,plain,
( ~ coll(X_1497,skolemFOFtoCNF_A,C)
| coll(C,skolemFOFtoCNF_O_2,X_1497) ),
inference(resolve,[$cnf( coll(X_1497,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) )],[refute_0_213,refute_0_177]) ).
cnf(refute_0_215,plain,
( ~ coll(X_1495,skolemFOFtoCNF_D,C)
| ~ coll(X_1495,skolemFOFtoCNF_D,X_1496)
| coll(C,X_1496,X_1495) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1495)),bind(B,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_1496))]]) ).
cnf(refute_0_216,plain,
( ~ coll(X_1494,skolemFOFtoCNF_C_1,C)
| ~ coll(X_1494,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D)
| coll(C,skolemFOFtoCNF_D,X_1494) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1494)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_217,plain,
( ~ coll(skolemFOFtoCNF_C_1,X_1475,skolemFOFtoCNF_D)
| coll(X_1475,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(X_1475)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_218,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_219,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_74]) ).
cnf(refute_0_220,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_221,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_223,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) )],[refute_0_223,refute_0_218]) ).
cnf(refute_0_225,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_226,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_1396)
| ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_228,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_1396)
| coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_1396),
inference(subst,[],[refute_0_54:[bind(X_362,$fot(X_1396)),bind(X_363,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_230,plain,
coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_1396) )],[refute_0_229,refute_0_228]) ).
cnf(refute_0_231,plain,
coll(skolemFOFtoCNF_C_1,X_1475,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_230:[bind(X_1396,$fot(X_1475))]]) ).
cnf(refute_0_232,plain,
coll(X_1475,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,X_1475,skolemFOFtoCNF_D) )],[refute_0_231,refute_0_217]) ).
cnf(refute_0_233,plain,
coll(X_1494,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_232:[bind(X_1475,$fot(X_1494))]]) ).
cnf(refute_0_234,plain,
( ~ coll(X_1494,skolemFOFtoCNF_C_1,C)
| coll(C,skolemFOFtoCNF_D,X_1494) ),
inference(resolve,[$cnf( coll(X_1494,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) )],[refute_0_233,refute_0_216]) ).
cnf(refute_0_235,plain,
( ~ coll(X_1483,skolemFOFtoCNF_S,C)
| ~ coll(X_1483,skolemFOFtoCNF_S,X_1484)
| coll(C,X_1484,X_1483) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1483)),bind(B,$fot(skolemFOFtoCNF_S)),bind(D,$fot(X_1484))]]) ).
cnf(refute_0_236,plain,
( ~ coll(X_1421,skolemFOFtoCNF_C_1,C)
| ~ coll(X_1421,skolemFOFtoCNF_C_1,skolemFOFtoCNF_S)
| coll(C,skolemFOFtoCNF_S,X_1421) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_1421)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_S))]]) ).
cnf(refute_0_237,plain,
( ~ coll(skolemFOFtoCNF_C_1,X_1403,skolemFOFtoCNF_S)
| coll(X_1403,skolemFOFtoCNF_C_1,skolemFOFtoCNF_S) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(X_1403)),bind(C,$fot(skolemFOFtoCNF_S))]]) ).
cnf(refute_0_238,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_S)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_S) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_S))]]) ).
cnf(refute_0_239,plain,
coll(skolemFOFtoCNF_S,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_75]) ).
cnf(refute_0_240,plain,
( ~ coll(skolemFOFtoCNF_S,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_S,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_S)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_241,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_S,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_S,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_S,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_S) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_S)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_243,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_S),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_S,skolemFOFtoCNF_C_1) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_S),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_S) )],[refute_0_243,refute_0_238]) ).
cnf(refute_0_245,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_S)
| coll(skolemFOFtoCNF_S,skolemFOFtoCNF_S,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_S)),bind(D,$fot(skolemFOFtoCNF_S))]]) ).
cnf(refute_0_246,plain,
coll(skolemFOFtoCNF_S,skolemFOFtoCNF_S,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_S) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
( ~ coll(skolemFOFtoCNF_S,skolemFOFtoCNF_S,X_1396)
| ~ coll(skolemFOFtoCNF_S,skolemFOFtoCNF_S,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_S) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_S)),bind(B,$fot(skolemFOFtoCNF_S)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_248,plain,
( ~ coll(skolemFOFtoCNF_S,skolemFOFtoCNF_S,X_1396)
| coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_S) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_S,skolemFOFtoCNF_S,skolemFOFtoCNF_C_1) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
coll(skolemFOFtoCNF_S,skolemFOFtoCNF_S,X_1396),
inference(subst,[],[refute_0_54:[bind(X_362,$fot(X_1396)),bind(X_363,$fot(skolemFOFtoCNF_S))]]) ).
cnf(refute_0_250,plain,
coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_S),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_S,skolemFOFtoCNF_S,X_1396) )],[refute_0_249,refute_0_248]) ).
cnf(refute_0_251,plain,
coll(skolemFOFtoCNF_C_1,X_1403,skolemFOFtoCNF_S),
inference(subst,[],[refute_0_250:[bind(X_1396,$fot(X_1403))]]) ).
cnf(refute_0_252,plain,
coll(X_1403,skolemFOFtoCNF_C_1,skolemFOFtoCNF_S),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,X_1403,skolemFOFtoCNF_S) )],[refute_0_251,refute_0_237]) ).
cnf(refute_0_253,plain,
coll(X_1421,skolemFOFtoCNF_C_1,skolemFOFtoCNF_S),
inference(subst,[],[refute_0_252:[bind(X_1403,$fot(X_1421))]]) ).
cnf(refute_0_254,plain,
( ~ coll(X_1421,skolemFOFtoCNF_C_1,C)
| coll(C,skolemFOFtoCNF_S,X_1421) ),
inference(resolve,[$cnf( coll(X_1421,skolemFOFtoCNF_C_1,skolemFOFtoCNF_S) )],[refute_0_253,refute_0_236]) ).
cnf(refute_0_255,plain,
coll(X_1421,skolemFOFtoCNF_C_1,C),
inference(subst,[],[refute_0_117:[bind(X_1394,$fot(C)),bind(X_1395,$fot(X_1421)),bind(X_1396,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_256,plain,
coll(C,skolemFOFtoCNF_S,X_1421),
inference(resolve,[$cnf( coll(X_1421,skolemFOFtoCNF_C_1,C) )],[refute_0_255,refute_0_254]) ).
cnf(refute_0_257,plain,
coll(X_1483,skolemFOFtoCNF_S,X_1484),
inference(subst,[],[refute_0_256:[bind(C,$fot(X_1483)),bind(X_1421,$fot(X_1484))]]) ).
cnf(refute_0_258,plain,
( ~ coll(X_1483,skolemFOFtoCNF_S,C)
| coll(C,X_1484,X_1483) ),
inference(resolve,[$cnf( coll(X_1483,skolemFOFtoCNF_S,X_1484) )],[refute_0_257,refute_0_235]) ).
cnf(refute_0_259,plain,
coll(X_1483,skolemFOFtoCNF_S,C),
inference(subst,[],[refute_0_149:[bind(C,$fot(X_1483)),bind(X_1463,$fot(C)),bind(X_1464,$fot(skolemFOFtoCNF_S))]]) ).
cnf(refute_0_260,plain,
coll(C,X_1484,X_1483),
inference(resolve,[$cnf( coll(X_1483,skolemFOFtoCNF_S,C) )],[refute_0_259,refute_0_258]) ).
cnf(refute_0_261,plain,
coll(X_1494,skolemFOFtoCNF_C_1,C),
inference(subst,[],[refute_0_260:[bind(C,$fot(X_1494)),bind(X_1483,$fot(C)),bind(X_1484,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_262,plain,
coll(C,skolemFOFtoCNF_D,X_1494),
inference(resolve,[$cnf( coll(X_1494,skolemFOFtoCNF_C_1,C) )],[refute_0_261,refute_0_234]) ).
cnf(refute_0_263,plain,
coll(X_1495,skolemFOFtoCNF_D,X_1496),
inference(subst,[],[refute_0_262:[bind(C,$fot(X_1495)),bind(X_1494,$fot(X_1496))]]) ).
cnf(refute_0_264,plain,
( ~ coll(X_1495,skolemFOFtoCNF_D,C)
| coll(C,X_1496,X_1495) ),
inference(resolve,[$cnf( coll(X_1495,skolemFOFtoCNF_D,X_1496) )],[refute_0_263,refute_0_215]) ).
cnf(refute_0_265,plain,
coll(X_1495,skolemFOFtoCNF_D,C),
inference(subst,[],[refute_0_260:[bind(C,$fot(X_1495)),bind(X_1483,$fot(C)),bind(X_1484,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_266,plain,
coll(C,X_1496,X_1495),
inference(resolve,[$cnf( coll(X_1495,skolemFOFtoCNF_D,C) )],[refute_0_265,refute_0_264]) ).
cnf(refute_0_267,plain,
coll(X_1497,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_266:[bind(C,$fot(X_1497)),bind(X_1495,$fot(C)),bind(X_1496,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_268,plain,
coll(C,skolemFOFtoCNF_O_2,X_1497),
inference(resolve,[$cnf( coll(X_1497,skolemFOFtoCNF_A,C) )],[refute_0_267,refute_0_214]) ).
cnf(refute_0_269,plain,
coll(X_1498,skolemFOFtoCNF_O_2,X_1499),
inference(subst,[],[refute_0_268:[bind(C,$fot(X_1498)),bind(X_1497,$fot(X_1499))]]) ).
cnf(refute_0_270,plain,
( ~ coll(X_1498,skolemFOFtoCNF_O_2,C)
| coll(C,X_1499,X_1498) ),
inference(resolve,[$cnf( coll(X_1498,skolemFOFtoCNF_O_2,X_1499) )],[refute_0_269,refute_0_176]) ).
cnf(refute_0_271,plain,
coll(X_1498,skolemFOFtoCNF_O_2,C),
inference(subst,[],[refute_0_266:[bind(C,$fot(X_1498)),bind(X_1495,$fot(C)),bind(X_1496,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_272,plain,
coll(C,X_1499,X_1498),
inference(resolve,[$cnf( coll(X_1498,skolemFOFtoCNF_O_2,C) )],[refute_0_271,refute_0_270]) ).
cnf(refute_0_273,plain,
coll(X_1501,skolemFOFtoCNF_B_1,C),
inference(subst,[],[refute_0_272:[bind(C,$fot(X_1501)),bind(X_1498,$fot(C)),bind(X_1499,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_274,plain,
coll(C,X_1502,X_1501),
inference(resolve,[$cnf( coll(X_1501,skolemFOFtoCNF_B_1,C) )],[refute_0_273,refute_0_175]) ).
cnf(refute_0_275,plain,
coll(X_1531,skolemFOFtoCNF_A1,C),
inference(subst,[],[refute_0_274:[bind(C,$fot(X_1531)),bind(X_1501,$fot(C)),bind(X_1502,$fot(skolemFOFtoCNF_A1))]]) ).
cnf(refute_0_276,plain,
coll(C,X_1532,X_1531),
inference(resolve,[$cnf( coll(X_1531,skolemFOFtoCNF_A1,C) )],[refute_0_275,refute_0_157]) ).
cnf(refute_0_277,plain,
coll(O,A,C),
inference(subst,[],[refute_0_276:[bind(C,$fot(O)),bind(X_1531,$fot(C)),bind(X_1532,$fot(A))]]) ).
cnf(refute_0_278,plain,
( ~ circle(O,A,B,C)
| perp(A,B,B,C) ),
inference(resolve,[$cnf( coll(O,A,C) )],[refute_0_277,refute_0_81]) ).
cnf(refute_0_279,plain,
( ~ circle(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_278:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(O,$fot(skolemFOFtoCNF_A1))]]) ).
cnf(refute_0_280,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_A1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_80,refute_0_279]) ).
cnf(refute_0_281,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_280,refute_0_77]) ).
cnf(refute_0_282,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_281,refute_0_75]) ).
cnf(refute_0_283,plain,
cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_282,refute_0_73]) ).
cnf(refute_0_284,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1))
| midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)) )],[refute_0_283,refute_0_64]) ).
cnf(refute_0_285,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)),
inference(subst,[],[refute_0_276:[bind(C,$fot(skolemFOFtoCNF_B_1)),bind(X_1531,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1))),bind(X_1532,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)))]]) ).
cnf(refute_0_286,plain,
midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)) )],[refute_0_285,refute_0_284]) ).
cnf(refute_0_287,plain,
midp(skolemFOFtoCNF_B_1,X_1582,X_1582),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A1,skolemFOFtoCNF_A1)) )],[refute_0_286,refute_0_62]) ).
cnf(refute_0_288,plain,
midp(skolemFOFtoCNF_B_1,X_1672,X_1672),
inference(subst,[],[refute_0_287:[bind(X_1582,$fot(X_1672))]]) ).
cnf(refute_0_289,plain,
midp(skolemFOFtoCNF_P_1(X_1672,Q),X_1672,Q),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,X_1672,X_1672) )],[refute_0_288,refute_0_57]) ).
cnf(refute_0_290,plain,
midp(skolemFOFtoCNF_P_1(X_1692,X_1691),X_1692,X_1691),
inference(subst,[],[refute_0_289:[bind(Q,$fot(X_1691)),bind(X_1672,$fot(X_1692))]]) ).
cnf(refute_0_291,plain,
cong(skolemFOFtoCNF_P_1(X_1692,X_1691),X_1692,skolemFOFtoCNF_P_1(X_1692,X_1691),X_1691),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(X_1692,X_1691),X_1692,X_1691) )],[refute_0_290,refute_0_17]) ).
cnf(refute_0_292,plain,
cong(skolemFOFtoCNF_P_1(X_3659,X_3658),X_3659,skolemFOFtoCNF_P_1(X_3659,X_3658),X_3658),
inference(subst,[],[refute_0_291:[bind(X_1691,$fot(X_3658)),bind(X_1692,$fot(X_3659))]]) ).
cnf(refute_0_293,plain,
cyclic(X_3659,X_3658,X_3658,X_3658),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_P_1(X_3659,X_3658),X_3659,skolemFOFtoCNF_P_1(X_3659,X_3658),X_3658) )],[refute_0_292,refute_0_15]) ).
cnf(refute_0_294,plain,
cyclic(X_3661,X_3660,X_3660,X_3660),
inference(subst,[],[refute_0_293:[bind(X_3658,$fot(X_3660)),bind(X_3659,$fot(X_3661))]]) ).
cnf(refute_0_295,plain,
cyclic(X_3660,X_3661,X_3660,X_3660),
inference(resolve,[$cnf( cyclic(X_3661,X_3660,X_3660,X_3660) )],[refute_0_294,refute_0_13]) ).
cnf(refute_0_296,plain,
cyclic(X_3662,X_3663,X_3662,X_3662),
inference(subst,[],[refute_0_295:[bind(X_3660,$fot(X_3662)),bind(X_3661,$fot(X_3663))]]) ).
cnf(refute_0_297,plain,
cyclic(X_3662,X_3662,X_3663,X_3662),
inference(resolve,[$cnf( cyclic(X_3662,X_3663,X_3662,X_3662) )],[refute_0_296,refute_0_11]) ).
cnf(refute_0_298,plain,
cyclic(X_3664,X_3664,X_3665,X_3664),
inference(subst,[],[refute_0_297:[bind(X_3662,$fot(X_3664)),bind(X_3663,$fot(X_3665))]]) ).
cnf(refute_0_299,plain,
cyclic(X_3664,X_3664,X_3664,X_3665),
inference(resolve,[$cnf( cyclic(X_3664,X_3664,X_3665,X_3664) )],[refute_0_298,refute_0_9]) ).
cnf(refute_0_300,plain,
cyclic(X_3666,X_3666,X_3666,X_3667),
inference(subst,[],[refute_0_299:[bind(X_3664,$fot(X_3666)),bind(X_3665,$fot(X_3667))]]) ).
cnf(refute_0_301,plain,
cyclic(X_3666,X_3666,X_3667,X_3667),
inference(resolve,[$cnf( cyclic(X_3666,X_3666,X_3666,X_3667) )],[refute_0_300,refute_0_7]) ).
cnf(refute_0_302,plain,
cyclic(X_3668,X_3668,X_3669,X_3669),
inference(subst,[],[refute_0_301:[bind(X_3666,$fot(X_3668)),bind(X_3667,$fot(X_3669))]]) ).
cnf(refute_0_303,plain,
( ~ cong(X_3668,X_3669,X_3668,X_3669)
| perp(X_3669,X_3668,X_3668,X_3669) ),
inference(resolve,[$cnf( cyclic(X_3668,X_3668,X_3669,X_3669) )],[refute_0_302,refute_0_5]) ).
cnf(refute_0_304,plain,
( ~ midp(X_1686,X_1685,X_1685)
| cong(X_1686,X_1685,X_1686,X_1685) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_1686)),bind(B,$fot(X_1685)),bind(C,$fot(X_1685))]]) ).
cnf(refute_0_305,plain,
( ~ midp(X_1684,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| midp(X_1684,X_1582,X_1582) ),
inference(subst,[],[refute_0_61:[bind(X_1581,$fot(skolemFOFtoCNF_B_1)),bind(X_1583,$fot(X_1684))]]) ).
cnf(refute_0_306,plain,
( ~ coll(X_1683,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| ~ cong(X_1683,skolemFOFtoCNF_B_1,X_1683,skolemFOFtoCNF_B_1)
| midp(X_1683,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_1683)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_307,plain,
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_77]) ).
cnf(refute_0_308,plain,
( ~ cong(X_1682,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1682)
| cong(X_1682,skolemFOFtoCNF_B_1,X_1682,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_307:[bind(A,$fot(X_1682)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_1682))]]) ).
cnf(refute_0_309,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_79]) ).
cnf(refute_0_310,plain,
( ~ cong(skolemFOFtoCNF_B_1,X_1676,X_1676,skolemFOFtoCNF_B_1)
| cong(X_1676,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1676) ),
inference(subst,[],[refute_0_309:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_1676)),bind(C,$fot(X_1676)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_311,plain,
( ~ cong(skolemFOFtoCNF_B_1,X_1674,skolemFOFtoCNF_B_1,X_1674)
| cong(skolemFOFtoCNF_B_1,X_1674,X_1674,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_307:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_1674)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_1674))]]) ).
cnf(refute_0_312,plain,
( ~ midp(skolemFOFtoCNF_B_1,X_1672,X_1672)
| cong(skolemFOFtoCNF_B_1,X_1672,skolemFOFtoCNF_B_1,X_1672) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_1672)),bind(C,$fot(X_1672))]]) ).
cnf(refute_0_313,plain,
cong(skolemFOFtoCNF_B_1,X_1672,skolemFOFtoCNF_B_1,X_1672),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,X_1672,X_1672) )],[refute_0_288,refute_0_312]) ).
cnf(refute_0_314,plain,
cong(skolemFOFtoCNF_B_1,X_1674,skolemFOFtoCNF_B_1,X_1674),
inference(subst,[],[refute_0_313:[bind(X_1672,$fot(X_1674))]]) ).
cnf(refute_0_315,plain,
cong(skolemFOFtoCNF_B_1,X_1674,X_1674,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,X_1674,skolemFOFtoCNF_B_1,X_1674) )],[refute_0_314,refute_0_311]) ).
cnf(refute_0_316,plain,
cong(skolemFOFtoCNF_B_1,X_1676,X_1676,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_315:[bind(X_1674,$fot(X_1676))]]) ).
cnf(refute_0_317,plain,
cong(X_1676,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1676),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,X_1676,X_1676,skolemFOFtoCNF_B_1) )],[refute_0_316,refute_0_310]) ).
cnf(refute_0_318,plain,
cong(X_1682,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1682),
inference(subst,[],[refute_0_317:[bind(X_1676,$fot(X_1682))]]) ).
cnf(refute_0_319,plain,
cong(X_1682,skolemFOFtoCNF_B_1,X_1682,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(X_1682,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1682) )],[refute_0_318,refute_0_308]) ).
cnf(refute_0_320,plain,
cong(X_1683,skolemFOFtoCNF_B_1,X_1683,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_319:[bind(X_1682,$fot(X_1683))]]) ).
cnf(refute_0_321,plain,
( ~ coll(X_1683,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| midp(X_1683,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( cong(X_1683,skolemFOFtoCNF_B_1,X_1683,skolemFOFtoCNF_B_1) )],[refute_0_320,refute_0_306]) ).
cnf(refute_0_322,plain,
coll(X_1683,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_276:[bind(C,$fot(X_1683)),bind(X_1531,$fot(skolemFOFtoCNF_B_1)),bind(X_1532,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_323,plain,
midp(X_1683,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(X_1683,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_322,refute_0_321]) ).
cnf(refute_0_324,plain,
midp(X_1684,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_323:[bind(X_1683,$fot(X_1684))]]) ).
cnf(refute_0_325,plain,
midp(X_1684,X_1582,X_1582),
inference(resolve,[$cnf( midp(X_1684,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_324,refute_0_305]) ).
cnf(refute_0_326,plain,
midp(X_1686,X_1685,X_1685),
inference(subst,[],[refute_0_325:[bind(X_1582,$fot(X_1685)),bind(X_1684,$fot(X_1686))]]) ).
cnf(refute_0_327,plain,
cong(X_1686,X_1685,X_1686,X_1685),
inference(resolve,[$cnf( midp(X_1686,X_1685,X_1685) )],[refute_0_326,refute_0_304]) ).
cnf(refute_0_328,plain,
cong(X_3668,X_3669,X_3668,X_3669),
inference(subst,[],[refute_0_327:[bind(X_1685,$fot(X_3669)),bind(X_1686,$fot(X_3668))]]) ).
cnf(refute_0_329,plain,
perp(X_3669,X_3668,X_3668,X_3669),
inference(resolve,[$cnf( cong(X_3668,X_3669,X_3668,X_3669) )],[refute_0_328,refute_0_303]) ).
cnf(refute_0_330,plain,
perp(X_3671,X_3670,X_3670,X_3671),
inference(subst,[],[refute_0_329:[bind(X_3668,$fot(X_3670)),bind(X_3669,$fot(X_3671))]]) ).
cnf(refute_0_331,plain,
( ~ midp(M,X_3671,X_3671)
| cong(X_3671,M,X_3670,M) ),
inference(resolve,[$cnf( perp(X_3671,X_3670,X_3670,X_3671) )],[refute_0_330,refute_0_3]) ).
cnf(refute_0_332,plain,
midp(M,X_3671,X_3671),
inference(subst,[],[refute_0_325:[bind(X_1582,$fot(X_3671)),bind(X_1684,$fot(M))]]) ).
cnf(refute_0_333,plain,
cong(X_3671,M,X_3670,M),
inference(resolve,[$cnf( midp(M,X_3671,X_3671) )],[refute_0_332,refute_0_331]) ).
cnf(refute_0_334,plain,
cong(A,P,B,P),
inference(subst,[],[refute_0_333:[bind(M,$fot(P)),bind(X_3670,$fot(B)),bind(X_3671,$fot(A))]]) ).
cnf(refute_0_335,plain,
( ~ cong(A,Q,B,Q)
| perp(A,B,P,Q) ),
inference(resolve,[$cnf( cong(A,P,B,P) )],[refute_0_334,refute_0_1]) ).
cnf(refute_0_336,plain,
cong(A,Q,B,Q),
inference(subst,[],[refute_0_333:[bind(M,$fot(Q)),bind(X_3670,$fot(B)),bind(X_3671,$fot(A))]]) ).
cnf(refute_0_337,plain,
perp(A,B,P,Q),
inference(resolve,[$cnf( cong(A,Q,B,Q) )],[refute_0_336,refute_0_335]) ).
cnf(refute_0_338,plain,
perp(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_P_8,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_337:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_G)),bind(P,$fot(skolemFOFtoCNF_P_8)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_339,plain,
$false,
inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_P_8,skolemFOFtoCNF_A) )],[refute_0_338,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GEO634+1 : TPTP v8.1.0. Released v7.5.0.
% 0.02/0.11 % Command : metis --show proof --show saturation %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Sat Jun 18 05:47:46 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 38.84/39.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.84/39.06
% 38.84/39.06 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 38.92/39.09
%------------------------------------------------------------------------------