%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO621+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 05:27:43 EDT 2022
% Result : Theorem 97.78s 97.97s
% Output : CNFRefutation 97.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 28
% Syntax : Number of formulae : 356 ( 142 unt; 0 def)
% Number of atoms : 686 ( 0 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 583 ( 253 ~; 248 |; 52 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 844 ( 109 sgn 391 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ) ).
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,C)
& coll(A,B,D) )
=> coll(C,D,A) ) ).
fof(ruleD7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ) ).
fof(ruleD8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ) ).
fof(ruleD11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ) ).
fof(ruleD12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,B)
& cong(O,A,O,C) )
=> circle(O,A,B,C) ) ).
fof(ruleD13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,B)
& cong(O,A,O,C)
& cong(O,A,O,D) )
=> cyclic(A,B,C,D) ) ).
fof(ruleD14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ) ).
fof(ruleD15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ) ).
fof(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ) ).
fof(ruleD17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,D)
& cyclic(A,B,C,E) )
=> cyclic(B,C,D,E) ) ).
fof(ruleD19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ) ).
fof(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ) ).
fof(ruleD24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ) ).
fof(ruleD39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ) ).
fof(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ) ).
fof(ruleD41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ) ).
fof(ruleD52,axiom,
! [A,B,C,M] :
( ( perp(A,B,B,C)
& midp(M,A,C) )
=> cong(A,M,B,M) ) ).
fof(ruleD53,axiom,
! [A,B,C,O] :
( ( circle(O,A,B,C)
& coll(O,A,C) )
=> perp(A,B,B,C) ) ).
fof(ruleD57,axiom,
! [A,B,P,Q] :
( ( cong(A,P,B,P)
& cong(A,Q,B,Q)
& cyclic(A,B,P,Q) )
=> perp(P,A,A,Q) ) ).
fof(ruleD64,axiom,
! [A,B,C,D,M] :
( ( midp(M,A,B)
& para(A,C,B,D)
& para(A,D,B,C) )
=> midp(M,C,D) ) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ) ).
fof(ruleD67,axiom,
! [A,B,C] :
( ( cong(A,B,A,C)
& coll(A,B,C) )
=> midp(A,B,C) ) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ) ).
fof(ruleD69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ) ).
fof(ruleX7,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( midp(M,A,B)
& midp(N,C,D)
& coll(C,A,B)
& coll(D,A,B) )
=> midp(P,A,Q) ) ).
fof(exemplo6GDDFULL8110984,conjecture,
! [A,B,C,D,E,F,G,H,I] :
( ( midp(D,B,A)
& midp(E,C,B)
& midp(F,A,C)
& circle(G,D,E,F)
& perp(E,G,E,H)
& coll(H,A,B)
& coll(I,E,H)
& coll(I,A,C) )
=> cyclic(B,H,C,I) ) ).
fof(subgoal_0,plain,
! [A,B,C,D,E,F,G,H,I] :
( ( midp(D,B,A)
& midp(E,C,B)
& midp(F,A,C)
& circle(G,D,E,F)
& perp(E,G,E,H)
& coll(H,A,B)
& coll(I,E,H)
& coll(I,A,C) )
=> cyclic(B,H,C,I) ),
inference(strip,[],[exemplo6GDDFULL8110984]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D,E,F,G,H,I] :
( ( midp(D,B,A)
& midp(E,C,B)
& midp(F,A,C)
& circle(G,D,E,F)
& perp(E,G,E,H)
& coll(H,A,B)
& coll(I,E,H)
& coll(I,A,C) )
=> cyclic(B,H,C,I) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D,E,F,G,H,I] :
( ~ cyclic(B,H,C,I)
& circle(G,D,E,F)
& coll(H,A,B)
& coll(I,A,C)
& coll(I,E,H)
& midp(D,B,A)
& midp(E,C,B)
& midp(F,A,C)
& perp(E,G,E,H) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_I)
& circle(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_F)
& coll(skolemFOFtoCNF_H,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& coll(skolemFOFtoCNF_I,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_I,skolemFOFtoCNF_E,skolemFOFtoCNF_H)
& midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
& midp(skolemFOFtoCNF_E,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
& midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& perp(skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_H) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_I),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[ruleD15]) ).
fof(normalize_0_4,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[ruleD16]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,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_8,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_7]) ).
fof(normalize_0_9,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[ruleD23]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[ruleD24]) ).
fof(normalize_0_12,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,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_14,plain,
! [A,B,C,M] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,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_16,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_15]) ).
fof(normalize_0_17,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_18,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_17]) ).
fof(normalize_0_19,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[ruleD14]) ).
fof(normalize_0_20,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[ruleD68]) ).
fof(normalize_0_22,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,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_24,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_23]) ).
fof(normalize_0_25,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_24]) ).
fof(normalize_0_26,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[ruleD1]) ).
fof(normalize_0_27,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[ruleD2]) ).
fof(normalize_0_29,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD66]) ).
fof(normalize_0_31,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,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_33,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_32]) ).
fof(normalize_0_34,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_33]) ).
fof(normalize_0_35,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_36,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(specialize,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_38,plain,
! [A,B,C,D] :
( ~ para(A,B,C,D)
| ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[ruleD40]) ).
fof(normalize_0_39,plain,
! [A,B,C,D] :
( ~ para(A,B,C,D)
| ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q) ),
inference(specialize,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [A,B,C,D,P,Q] :
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(clausify,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [A,B,C,D,P,Q,U,V] :
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[ruleD19]) ).
fof(normalize_0_42,plain,
! [A,B,C,D,P,Q,U,V] :
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(specialize,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [A,B,C,D,M] :
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[ruleD64]) ).
fof(normalize_0_44,plain,
! [A,B,C,D,M] :
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[ruleD67]) ).
fof(normalize_0_46,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(specialize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_48,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[ruleD11]) ).
fof(normalize_0_49,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(specialize,[],[normalize_0_48]) ).
fof(normalize_0_50,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_51,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_50]) ).
fof(normalize_0_52,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_53,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_52]) ).
fof(normalize_0_54,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_55,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(specialize,[],[normalize_0_54]) ).
fof(normalize_0_56,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_57,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(specialize,[],[normalize_0_56]) ).
fof(normalize_0_58,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_59,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_58]) ).
fof(normalize_0_60,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD69]) ).
fof(normalize_0_61,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_60]) ).
cnf(refute_0_0,plain,
~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_I),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ cyclic(X_18669,X_18668,X_18669,X_18670)
| cyclic(X_18669,X_18669,X_18668,X_18670) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_18669)),bind(B,$fot(X_18668)),bind(C,$fot(X_18669)),bind(D,$fot(X_18670))]]) ).
cnf(refute_0_3,plain,
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( ~ cyclic(X_18665,X_18666,X_18666,X_18667)
| cyclic(X_18666,X_18665,X_18666,X_18667) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_18665)),bind(B,$fot(X_18666)),bind(C,$fot(X_18666)),bind(D,$fot(X_18667))]]) ).
cnf(refute_0_5,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_8]) ).
cnf(refute_0_6,plain,
( ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,C,C,D) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(C))]]) ).
cnf(refute_0_7,plain,
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ cong(X_8724,X_8725,X_8726,X_8724)
| cong(X_8724,X_8725,X_8724,X_8726) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_8724)),bind(B,$fot(X_8725)),bind(C,$fot(X_8726)),bind(D,$fot(X_8724))]]) ).
cnf(refute_0_9,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ cong(X_8701,X_8699,X_8699,X_8700)
| cong(X_8699,X_8700,X_8701,X_8699) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_8701)),bind(B,$fot(X_8699)),bind(C,$fot(X_8699)),bind(D,$fot(X_8700))]]) ).
cnf(refute_0_11,plain,
( ~ cong(X_8698,X_8696,X_8697,X_8696)
| cong(X_8698,X_8696,X_8696,X_8697) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_8698)),bind(B,$fot(X_8696)),bind(C,$fot(X_8697)),bind(D,$fot(X_8696))]]) ).
cnf(refute_0_12,plain,
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
( ~ midp(M,X_8679,X_8679)
| ~ perp(X_8679,X_8678,X_8678,X_8679)
| cong(X_8679,M,X_8678,M) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_8679)),bind(B,$fot(X_8678)),bind(C,$fot(X_8679))]]) ).
cnf(refute_0_14,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_16]) ).
cnf(refute_0_15,plain,
( ~ cong(X_8676,X_8677,X_8676,X_8677)
| ~ cyclic(X_8676,X_8676,X_8677,X_8677)
| perp(X_8677,X_8676,X_8676,X_8677) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_8676)),bind(B,$fot(X_8676)),bind(P,$fot(X_8677)),bind(Q,$fot(X_8677))]]) ).
cnf(refute_0_16,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_17,plain,
( ~ cyclic(X_8674,X_8674,X_8674,X_8675)
| cyclic(X_8674,X_8674,X_8675,X_8675) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_8674)),bind(B,$fot(X_8674)),bind(C,$fot(X_8674)),bind(D,$fot(X_8675)),bind(E,$fot(X_8675))]]) ).
cnf(refute_0_18,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_19,plain,
( ~ cyclic(X_8672,X_8672,X_8673,X_8672)
| cyclic(X_8672,X_8672,X_8672,X_8673) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(X_8672)),bind(B,$fot(X_8672)),bind(C,$fot(X_8673)),bind(D,$fot(X_8672))]]) ).
cnf(refute_0_20,plain,
( ~ cyclic(X_8670,X_8671,X_8670,X_8670)
| cyclic(X_8670,X_8670,X_8671,X_8670) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_8670)),bind(B,$fot(X_8671)),bind(C,$fot(X_8670)),bind(D,$fot(X_8670))]]) ).
cnf(refute_0_21,plain,
( ~ cyclic(X_8669,X_8668,X_8668,X_8668)
| cyclic(X_8668,X_8669,X_8668,X_8668) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_8669)),bind(B,$fot(X_8668)),bind(C,$fot(X_8668)),bind(D,$fot(X_8668))]]) ).
cnf(refute_0_22,plain,
( ~ cong(skolemFOFtoCNF_P_1(X_8667,X_8666),X_8667,skolemFOFtoCNF_P_1(X_8667,X_8666),X_8666)
| cyclic(X_8667,X_8666,X_8666,X_8666) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_8667)),bind(B,$fot(X_8666)),bind(C,$fot(X_8666)),bind(D,$fot(X_8666)),bind(O,$fot(skolemFOFtoCNF_P_1(X_8667,X_8666)))]]) ).
cnf(refute_0_23,plain,
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_24,plain,
( ~ midp(skolemFOFtoCNF_P_1(X_5375,X_5374),X_5375,X_5374)
| cong(skolemFOFtoCNF_P_1(X_5375,X_5374),X_5375,skolemFOFtoCNF_P_1(X_5375,X_5374),X_5374) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_P_1(X_5375,X_5374))),bind(B,$fot(X_5375)),bind(C,$fot(X_5374))]]) ).
cnf(refute_0_25,plain,
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P_1(A,Q),A,Q) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_26,plain,
( ~ coll(D,D,D)
| ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(D)),bind(B,$fot(D)),bind(C,$fot(D)),bind(M,$fot(N))]]) ).
cnf(refute_0_27,plain,
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_28,plain,
( ~ coll(X_598,X_597,X_598)
| coll(X_598,X_598,X_597) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_598)),bind(B,$fot(X_597)),bind(C,$fot(X_598))]]) ).
cnf(refute_0_29,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_30,plain,
( ~ coll(X_595,X_596,X_596)
| coll(X_596,X_595,X_596) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_595)),bind(B,$fot(X_596)),bind(C,$fot(X_596))]]) ).
cnf(refute_0_31,plain,
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_32,plain,
( ~ para(X_593,X_594,X_593,X_594)
| coll(X_593,X_594,X_594) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(X_593)),bind(B,$fot(X_594)),bind(C,$fot(X_594))]]) ).
cnf(refute_0_33,plain,
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_34,plain,
( ~ eqangle(X_591,X_592,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_591,X_592,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(X_591,X_592,X_591,X_592) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(X_591)),bind(B,$fot(X_592)),bind(C,$fot(X_591)),bind(D,$fot(X_592)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_35,plain,
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_36,plain,
( ~ cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_35:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_37,plain,
( ~ cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(E,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_38,plain,
( ~ cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_39,plain,
( ~ cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_F)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_40,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_41,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_42,plain,
cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1) )],[refute_0_42,refute_0_39]) ).
cnf(refute_0_44,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A) )],[refute_0_43,refute_0_38]) ).
cnf(refute_0_45,plain,
cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_44,refute_0_37]) ).
cnf(refute_0_46,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_45,refute_0_36]) ).
cnf(refute_0_47,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_48,plain,
para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_50,plain,
( ~ para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154) ),
inference(subst,[],[refute_0_49:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(P,$fot(X_153)),bind(Q,$fot(X_154))]]) ).
cnf(refute_0_51,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_48,refute_0_50]) ).
cnf(refute_0_52,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_589,X_590,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_589,X_590),
inference(subst,[],[refute_0_51:[bind(X_153,$fot(X_589)),bind(X_154,$fot(X_590))]]) ).
cnf(refute_0_53,plain,
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_54,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_589,X_590,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_589,X_590)
| eqangle(X_589,X_590,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_589,X_590,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_53:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(X_589)),bind(D,$fot(X_590)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A)),bind(U,$fot(X_589)),bind(V,$fot(X_590))]]) ).
cnf(refute_0_55,plain,
eqangle(X_589,X_590,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_589,X_590,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_589,X_590,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_589,X_590) )],[refute_0_52,refute_0_54]) ).
cnf(refute_0_56,plain,
eqangle(X_591,X_592,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_591,X_592,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_55:[bind(X_589,$fot(X_591)),bind(X_590,$fot(X_592))]]) ).
cnf(refute_0_57,plain,
para(X_591,X_592,X_591,X_592),
inference(resolve,[$cnf( eqangle(X_591,X_592,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_591,X_592,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_56,refute_0_34]) ).
cnf(refute_0_58,plain,
para(X_593,X_594,X_593,X_594),
inference(subst,[],[refute_0_57:[bind(X_591,$fot(X_593)),bind(X_592,$fot(X_594))]]) ).
cnf(refute_0_59,plain,
coll(X_593,X_594,X_594),
inference(resolve,[$cnf( para(X_593,X_594,X_593,X_594) )],[refute_0_58,refute_0_32]) ).
cnf(refute_0_60,plain,
coll(X_595,X_596,X_596),
inference(subst,[],[refute_0_59:[bind(X_593,$fot(X_595)),bind(X_594,$fot(X_596))]]) ).
cnf(refute_0_61,plain,
coll(X_596,X_595,X_596),
inference(resolve,[$cnf( coll(X_595,X_596,X_596) )],[refute_0_60,refute_0_30]) ).
cnf(refute_0_62,plain,
coll(X_598,X_597,X_598),
inference(subst,[],[refute_0_61:[bind(X_595,$fot(X_597)),bind(X_596,$fot(X_598))]]) ).
cnf(refute_0_63,plain,
coll(X_598,X_598,X_597),
inference(resolve,[$cnf( coll(X_598,X_597,X_598) )],[refute_0_62,refute_0_28]) ).
cnf(refute_0_64,plain,
coll(D,D,D),
inference(subst,[],[refute_0_63:[bind(X_597,$fot(D)),bind(X_598,$fot(D))]]) ).
cnf(refute_0_65,plain,
( ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(resolve,[$cnf( coll(D,D,D) )],[refute_0_64,refute_0_26]) ).
cnf(refute_0_66,plain,
( ~ midp(skolemFOFtoCNF_A,X_5292,X_5292)
| midp(skolemFOFtoCNF_P_1(X_5292,Q),X_5292,Q) ),
inference(subst,[],[refute_0_65:[bind(D,$fot(X_5292)),bind(N,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_67,plain,
para(X_5231,X_5232,X_5231,X_5232),
inference(subst,[],[refute_0_57:[bind(X_591,$fot(X_5231)),bind(X_592,$fot(X_5232))]]) ).
cnf(refute_0_68,plain,
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_69,plain,
( ~ midp(X_5233,X_5231,X_5231)
| ~ para(X_5231,X_5232,X_5231,X_5232)
| midp(X_5233,X_5232,X_5232) ),
inference(subst,[],[refute_0_68:[bind(A,$fot(X_5231)),bind(B,$fot(X_5231)),bind(C,$fot(X_5232)),bind(D,$fot(X_5232)),bind(M,$fot(X_5233))]]) ).
cnf(refute_0_70,plain,
( ~ midp(X_5233,X_5231,X_5231)
| midp(X_5233,X_5232,X_5232) ),
inference(resolve,[$cnf( para(X_5231,X_5232,X_5231,X_5232) )],[refute_0_67,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ midp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| midp(skolemFOFtoCNF_A,X_5232,X_5232) ),
inference(subst,[],[refute_0_70:[bind(X_5231,$fot(skolemFOFtoCNF_D)),bind(X_5233,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_72,plain,
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_73,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| ~ cong(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| midp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_72:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_74,plain,
midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_75,plain,
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[normalize_0_49]) ).
cnf(refute_0_76,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_75:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(M,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_77,plain,
midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_74,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_79,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_78:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_80,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_53]) ).
cnf(refute_0_81,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_80:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_82,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_83,plain,
( ~ cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| circle(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_84,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_85,plain,
cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_74,refute_0_84]) ).
cnf(refute_0_86,plain,
circle(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_85,refute_0_83]) ).
cnf(refute_0_87,plain,
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_88,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_59]) ).
cnf(refute_0_89,plain,
( ~ coll(X_3735,skolemFOFtoCNF_C_1,C)
| ~ coll(X_3735,skolemFOFtoCNF_C_1,X_3736)
| coll(C,X_3736,X_3735) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(X_3735)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_3736))]]) ).
cnf(refute_0_90,plain,
( ~ coll(X_3700,skolemFOFtoCNF_A,C)
| ~ coll(X_3700,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
| coll(C,skolemFOFtoCNF_C_1,X_3700) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(X_3700)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_91,plain,
( ~ coll(skolemFOFtoCNF_A,X_3646,skolemFOFtoCNF_C_1)
| coll(X_3646,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_3646)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_92,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_93,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_F)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_94,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_95,plain,
( ~ coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_96,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
| midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_75:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(M,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_97,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) )],[refute_0_40,refute_0_96]) ).
cnf(refute_0_98,plain,
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_61]) ).
cnf(refute_0_99,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_98:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_100,plain,
coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) )],[refute_0_97,refute_0_99]) ).
cnf(refute_0_101,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) )],[refute_0_100,refute_0_95]) ).
cnf(refute_0_102,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_F),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A) )],[refute_0_101,refute_0_94]) ).
cnf(refute_0_103,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_F) )],[refute_0_102,refute_0_93]) ).
cnf(refute_0_104,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F) )],[refute_0_103,refute_0_92]) ).
cnf(refute_0_105,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_106,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_C_1) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_3629)
| ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,X_3629,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_3629))]]) ).
cnf(refute_0_108,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_3629)
| coll(skolemFOFtoCNF_A,X_3629,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_3629),
inference(subst,[],[refute_0_63:[bind(X_597,$fot(X_3629)),bind(X_598,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_110,plain,
coll(skolemFOFtoCNF_A,X_3629,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_3629) )],[refute_0_109,refute_0_108]) ).
cnf(refute_0_111,plain,
coll(skolemFOFtoCNF_A,X_3646,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_110:[bind(X_3629,$fot(X_3646))]]) ).
cnf(refute_0_112,plain,
coll(X_3646,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_3646,skolemFOFtoCNF_C_1) )],[refute_0_111,refute_0_91]) ).
cnf(refute_0_113,plain,
coll(X_3700,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_112:[bind(X_3646,$fot(X_3700))]]) ).
cnf(refute_0_114,plain,
( ~ coll(X_3700,skolemFOFtoCNF_A,C)
| coll(C,skolemFOFtoCNF_C_1,X_3700) ),
inference(resolve,[$cnf( coll(X_3700,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) )],[refute_0_113,refute_0_90]) ).
cnf(refute_0_115,plain,
coll(X_3627,X_3627,X_3628),
inference(subst,[],[refute_0_63:[bind(X_597,$fot(X_3628)),bind(X_598,$fot(X_3627))]]) ).
cnf(refute_0_116,plain,
( ~ coll(X_3627,X_3627,X_3628)
| ~ coll(X_3627,X_3627,X_3629)
| coll(X_3628,X_3629,X_3627) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(X_3627)),bind(B,$fot(X_3627)),bind(C,$fot(X_3628)),bind(D,$fot(X_3629))]]) ).
cnf(refute_0_117,plain,
( ~ coll(X_3627,X_3627,X_3629)
| coll(X_3628,X_3629,X_3627) ),
inference(resolve,[$cnf( coll(X_3627,X_3627,X_3628) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
coll(X_3627,X_3627,X_3629),
inference(subst,[],[refute_0_63:[bind(X_597,$fot(X_3629)),bind(X_598,$fot(X_3627))]]) ).
cnf(refute_0_119,plain,
coll(X_3628,X_3629,X_3627),
inference(resolve,[$cnf( coll(X_3627,X_3627,X_3629) )],[refute_0_118,refute_0_117]) ).
cnf(refute_0_120,plain,
coll(X_3700,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_119:[bind(X_3627,$fot(C)),bind(X_3628,$fot(X_3700)),bind(X_3629,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_121,plain,
coll(C,skolemFOFtoCNF_C_1,X_3700),
inference(resolve,[$cnf( coll(X_3700,skolemFOFtoCNF_A,C) )],[refute_0_120,refute_0_114]) ).
cnf(refute_0_122,plain,
coll(X_3735,skolemFOFtoCNF_C_1,X_3736),
inference(subst,[],[refute_0_121:[bind(C,$fot(X_3735)),bind(X_3700,$fot(X_3736))]]) ).
cnf(refute_0_123,plain,
( ~ coll(X_3735,skolemFOFtoCNF_C_1,C)
| coll(C,X_3736,X_3735) ),
inference(resolve,[$cnf( coll(X_3735,skolemFOFtoCNF_C_1,X_3736) )],[refute_0_122,refute_0_89]) ).
cnf(refute_0_124,plain,
( ~ coll(X_3709,skolemFOFtoCNF_D,C)
| ~ coll(X_3709,skolemFOFtoCNF_D,X_3710)
| coll(C,X_3710,X_3709) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(X_3709)),bind(B,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_3710))]]) ).
cnf(refute_0_125,plain,
( ~ coll(X_3659,skolemFOFtoCNF_A,C)
| ~ coll(X_3659,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| coll(C,skolemFOFtoCNF_D,X_3659) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(X_3659)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_126,plain,
( ~ coll(skolemFOFtoCNF_A,X_3648,skolemFOFtoCNF_D)
| coll(X_3648,skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_3648)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_127,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_128,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_129,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_130,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_98:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_131,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_74,refute_0_130]) ).
cnf(refute_0_132,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_131,refute_0_129]) ).
cnf(refute_0_133,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_132,refute_0_128]) ).
cnf(refute_0_134,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_133,refute_0_127]) ).
cnf(refute_0_135,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_136,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_3629)
| ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,X_3629,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_3629))]]) ).
cnf(refute_0_138,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_3629)
| coll(skolemFOFtoCNF_A,X_3629,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_3629),
inference(subst,[],[refute_0_63:[bind(X_597,$fot(X_3629)),bind(X_598,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_140,plain,
coll(skolemFOFtoCNF_A,X_3629,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_3629) )],[refute_0_139,refute_0_138]) ).
cnf(refute_0_141,plain,
coll(skolemFOFtoCNF_A,X_3648,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_140:[bind(X_3629,$fot(X_3648))]]) ).
cnf(refute_0_142,plain,
coll(X_3648,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_3648,skolemFOFtoCNF_D) )],[refute_0_141,refute_0_126]) ).
cnf(refute_0_143,plain,
coll(X_3659,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_142:[bind(X_3648,$fot(X_3659))]]) ).
cnf(refute_0_144,plain,
( ~ coll(X_3659,skolemFOFtoCNF_A,C)
| coll(C,skolemFOFtoCNF_D,X_3659) ),
inference(resolve,[$cnf( coll(X_3659,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_143,refute_0_125]) ).
cnf(refute_0_145,plain,
coll(X_3659,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_119:[bind(X_3627,$fot(C)),bind(X_3628,$fot(X_3659)),bind(X_3629,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_146,plain,
coll(C,skolemFOFtoCNF_D,X_3659),
inference(resolve,[$cnf( coll(X_3659,skolemFOFtoCNF_A,C) )],[refute_0_145,refute_0_144]) ).
cnf(refute_0_147,plain,
coll(X_3709,skolemFOFtoCNF_D,X_3710),
inference(subst,[],[refute_0_146:[bind(C,$fot(X_3709)),bind(X_3659,$fot(X_3710))]]) ).
cnf(refute_0_148,plain,
( ~ coll(X_3709,skolemFOFtoCNF_D,C)
| coll(C,X_3710,X_3709) ),
inference(resolve,[$cnf( coll(X_3709,skolemFOFtoCNF_D,X_3710) )],[refute_0_147,refute_0_124]) ).
cnf(refute_0_149,plain,
coll(X_3709,skolemFOFtoCNF_D,C),
inference(subst,[],[refute_0_119:[bind(X_3627,$fot(C)),bind(X_3628,$fot(X_3709)),bind(X_3629,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_150,plain,
coll(C,X_3710,X_3709),
inference(resolve,[$cnf( coll(X_3709,skolemFOFtoCNF_D,C) )],[refute_0_149,refute_0_148]) ).
cnf(refute_0_151,plain,
coll(X_3735,skolemFOFtoCNF_C_1,C),
inference(subst,[],[refute_0_150:[bind(C,$fot(X_3735)),bind(X_3709,$fot(C)),bind(X_3710,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_152,plain,
coll(C,X_3736,X_3735),
inference(resolve,[$cnf( coll(X_3735,skolemFOFtoCNF_C_1,C) )],[refute_0_151,refute_0_123]) ).
cnf(refute_0_153,plain,
coll(O,A,C),
inference(subst,[],[refute_0_152:[bind(C,$fot(O)),bind(X_3735,$fot(C)),bind(X_3736,$fot(A))]]) ).
cnf(refute_0_154,plain,
( ~ circle(O,A,B,C)
| perp(A,B,B,C) ),
inference(resolve,[$cnf( coll(O,A,C) )],[refute_0_153,refute_0_87]) ).
cnf(refute_0_155,plain,
( ~ circle(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_154:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_156,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_86,refute_0_155]) ).
cnf(refute_0_157,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_156,refute_0_81]) ).
cnf(refute_0_158,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_157,refute_0_79]) ).
cnf(refute_0_159,plain,
( ~ midp(X_5285,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_A,X_5285,skolemFOFtoCNF_A,X_5285) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(M,$fot(X_5285))]]) ).
cnf(refute_0_160,plain,
( ~ midp(X_5285,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_A,X_5285,skolemFOFtoCNF_A,X_5285) ),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_160:[bind(X_5285,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_162,plain,
cong(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_77,refute_0_161]) ).
cnf(refute_0_163,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| midp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_162,refute_0_73]) ).
cnf(refute_0_164,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_152:[bind(C,$fot(skolemFOFtoCNF_A)),bind(X_3735,$fot(skolemFOFtoCNF_D)),bind(X_3736,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_165,plain,
midp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_164,refute_0_163]) ).
cnf(refute_0_166,plain,
midp(skolemFOFtoCNF_A,X_5232,X_5232),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_165,refute_0_71]) ).
cnf(refute_0_167,plain,
midp(skolemFOFtoCNF_A,X_5292,X_5292),
inference(subst,[],[refute_0_166:[bind(X_5232,$fot(X_5292))]]) ).
cnf(refute_0_168,plain,
midp(skolemFOFtoCNF_P_1(X_5292,Q),X_5292,Q),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A,X_5292,X_5292) )],[refute_0_167,refute_0_66]) ).
cnf(refute_0_169,plain,
midp(skolemFOFtoCNF_P_1(X_5375,X_5374),X_5375,X_5374),
inference(subst,[],[refute_0_168:[bind(Q,$fot(X_5374)),bind(X_5292,$fot(X_5375))]]) ).
cnf(refute_0_170,plain,
cong(skolemFOFtoCNF_P_1(X_5375,X_5374),X_5375,skolemFOFtoCNF_P_1(X_5375,X_5374),X_5374),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(X_5375,X_5374),X_5375,X_5374) )],[refute_0_169,refute_0_24]) ).
cnf(refute_0_171,plain,
cong(skolemFOFtoCNF_P_1(X_8667,X_8666),X_8667,skolemFOFtoCNF_P_1(X_8667,X_8666),X_8666),
inference(subst,[],[refute_0_170:[bind(X_5374,$fot(X_8666)),bind(X_5375,$fot(X_8667))]]) ).
cnf(refute_0_172,plain,
cyclic(X_8667,X_8666,X_8666,X_8666),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_P_1(X_8667,X_8666),X_8667,skolemFOFtoCNF_P_1(X_8667,X_8666),X_8666) )],[refute_0_171,refute_0_22]) ).
cnf(refute_0_173,plain,
cyclic(X_8669,X_8668,X_8668,X_8668),
inference(subst,[],[refute_0_172:[bind(X_8666,$fot(X_8668)),bind(X_8667,$fot(X_8669))]]) ).
cnf(refute_0_174,plain,
cyclic(X_8668,X_8669,X_8668,X_8668),
inference(resolve,[$cnf( cyclic(X_8669,X_8668,X_8668,X_8668) )],[refute_0_173,refute_0_21]) ).
cnf(refute_0_175,plain,
cyclic(X_8670,X_8671,X_8670,X_8670),
inference(subst,[],[refute_0_174:[bind(X_8668,$fot(X_8670)),bind(X_8669,$fot(X_8671))]]) ).
cnf(refute_0_176,plain,
cyclic(X_8670,X_8670,X_8671,X_8670),
inference(resolve,[$cnf( cyclic(X_8670,X_8671,X_8670,X_8670) )],[refute_0_175,refute_0_20]) ).
cnf(refute_0_177,plain,
cyclic(X_8672,X_8672,X_8673,X_8672),
inference(subst,[],[refute_0_176:[bind(X_8670,$fot(X_8672)),bind(X_8671,$fot(X_8673))]]) ).
cnf(refute_0_178,plain,
cyclic(X_8672,X_8672,X_8672,X_8673),
inference(resolve,[$cnf( cyclic(X_8672,X_8672,X_8673,X_8672) )],[refute_0_177,refute_0_19]) ).
cnf(refute_0_179,plain,
cyclic(X_8674,X_8674,X_8674,X_8675),
inference(subst,[],[refute_0_178:[bind(X_8672,$fot(X_8674)),bind(X_8673,$fot(X_8675))]]) ).
cnf(refute_0_180,plain,
cyclic(X_8674,X_8674,X_8675,X_8675),
inference(resolve,[$cnf( cyclic(X_8674,X_8674,X_8674,X_8675) )],[refute_0_179,refute_0_17]) ).
cnf(refute_0_181,plain,
cyclic(X_8676,X_8676,X_8677,X_8677),
inference(subst,[],[refute_0_180:[bind(X_8674,$fot(X_8676)),bind(X_8675,$fot(X_8677))]]) ).
cnf(refute_0_182,plain,
( ~ cong(X_8676,X_8677,X_8676,X_8677)
| perp(X_8677,X_8676,X_8676,X_8677) ),
inference(resolve,[$cnf( cyclic(X_8676,X_8676,X_8677,X_8677) )],[refute_0_181,refute_0_15]) ).
cnf(refute_0_183,plain,
( ~ midp(X_5344,X_5343,X_5343)
| cong(X_5344,X_5343,X_5344,X_5343) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_5344)),bind(B,$fot(X_5343)),bind(C,$fot(X_5343))]]) ).
cnf(refute_0_184,plain,
( ~ midp(X_5304,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(X_5304,X_5232,X_5232) ),
inference(subst,[],[refute_0_70:[bind(X_5231,$fot(skolemFOFtoCNF_A)),bind(X_5233,$fot(X_5304))]]) ).
cnf(refute_0_185,plain,
( ~ coll(X_5303,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| ~ cong(X_5303,skolemFOFtoCNF_A,X_5303,skolemFOFtoCNF_A)
| midp(X_5303,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_72:[bind(A,$fot(X_5303)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_186,plain,
( ~ cong(X_5301,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_5301)
| cong(X_5301,skolemFOFtoCNF_A,X_5301,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_5301)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_5301))]]) ).
cnf(refute_0_187,plain,
( ~ cong(skolemFOFtoCNF_A,X_5297,X_5297,skolemFOFtoCNF_A)
| cong(X_5297,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_5297) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_5297)),bind(C,$fot(X_5297)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_188,plain,
( ~ cong(skolemFOFtoCNF_A,X_5294,skolemFOFtoCNF_A,X_5294)
| cong(skolemFOFtoCNF_A,X_5294,X_5294,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_5294)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_5294))]]) ).
cnf(refute_0_189,plain,
( ~ midp(skolemFOFtoCNF_A,X_5292,X_5292)
| cong(skolemFOFtoCNF_A,X_5292,skolemFOFtoCNF_A,X_5292) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_5292)),bind(C,$fot(X_5292))]]) ).
cnf(refute_0_190,plain,
cong(skolemFOFtoCNF_A,X_5292,skolemFOFtoCNF_A,X_5292),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A,X_5292,X_5292) )],[refute_0_167,refute_0_189]) ).
cnf(refute_0_191,plain,
cong(skolemFOFtoCNF_A,X_5294,skolemFOFtoCNF_A,X_5294),
inference(subst,[],[refute_0_190:[bind(X_5292,$fot(X_5294))]]) ).
cnf(refute_0_192,plain,
cong(skolemFOFtoCNF_A,X_5294,X_5294,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,X_5294,skolemFOFtoCNF_A,X_5294) )],[refute_0_191,refute_0_188]) ).
cnf(refute_0_193,plain,
cong(skolemFOFtoCNF_A,X_5297,X_5297,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_192:[bind(X_5294,$fot(X_5297))]]) ).
cnf(refute_0_194,plain,
cong(X_5297,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_5297),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,X_5297,X_5297,skolemFOFtoCNF_A) )],[refute_0_193,refute_0_187]) ).
cnf(refute_0_195,plain,
cong(X_5301,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_5301),
inference(subst,[],[refute_0_194:[bind(X_5297,$fot(X_5301))]]) ).
cnf(refute_0_196,plain,
cong(X_5301,skolemFOFtoCNF_A,X_5301,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(X_5301,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_5301) )],[refute_0_195,refute_0_186]) ).
cnf(refute_0_197,plain,
cong(X_5303,skolemFOFtoCNF_A,X_5303,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_196:[bind(X_5301,$fot(X_5303))]]) ).
cnf(refute_0_198,plain,
( ~ coll(X_5303,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(X_5303,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( cong(X_5303,skolemFOFtoCNF_A,X_5303,skolemFOFtoCNF_A) )],[refute_0_197,refute_0_185]) ).
cnf(refute_0_199,plain,
coll(X_5303,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_152:[bind(C,$fot(X_5303)),bind(X_3735,$fot(skolemFOFtoCNF_A)),bind(X_3736,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_200,plain,
midp(X_5303,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(X_5303,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_199,refute_0_198]) ).
cnf(refute_0_201,plain,
midp(X_5304,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_200:[bind(X_5303,$fot(X_5304))]]) ).
cnf(refute_0_202,plain,
midp(X_5304,X_5232,X_5232),
inference(resolve,[$cnf( midp(X_5304,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_201,refute_0_184]) ).
cnf(refute_0_203,plain,
midp(X_5344,X_5343,X_5343),
inference(subst,[],[refute_0_202:[bind(X_5232,$fot(X_5343)),bind(X_5304,$fot(X_5344))]]) ).
cnf(refute_0_204,plain,
cong(X_5344,X_5343,X_5344,X_5343),
inference(resolve,[$cnf( midp(X_5344,X_5343,X_5343) )],[refute_0_203,refute_0_183]) ).
cnf(refute_0_205,plain,
cong(X_8676,X_8677,X_8676,X_8677),
inference(subst,[],[refute_0_204:[bind(X_5343,$fot(X_8677)),bind(X_5344,$fot(X_8676))]]) ).
cnf(refute_0_206,plain,
perp(X_8677,X_8676,X_8676,X_8677),
inference(resolve,[$cnf( cong(X_8676,X_8677,X_8676,X_8677) )],[refute_0_205,refute_0_182]) ).
cnf(refute_0_207,plain,
perp(X_8679,X_8678,X_8678,X_8679),
inference(subst,[],[refute_0_206:[bind(X_8676,$fot(X_8678)),bind(X_8677,$fot(X_8679))]]) ).
cnf(refute_0_208,plain,
( ~ midp(M,X_8679,X_8679)
| cong(X_8679,M,X_8678,M) ),
inference(resolve,[$cnf( perp(X_8679,X_8678,X_8678,X_8679) )],[refute_0_207,refute_0_13]) ).
cnf(refute_0_209,plain,
( ~ midp(X_5313,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| midp(X_5313,X_5232,X_5232) ),
inference(subst,[],[refute_0_70:[bind(X_5231,$fot(skolemFOFtoCNF_D)),bind(X_5233,$fot(X_5313))]]) ).
cnf(refute_0_210,plain,
( ~ coll(X_5312,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| ~ cong(X_5312,skolemFOFtoCNF_D,X_5312,skolemFOFtoCNF_D)
| midp(X_5312,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_72:[bind(A,$fot(X_5312)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_211,plain,
( ~ cong(X_5310,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_5310)
| cong(X_5310,skolemFOFtoCNF_D,X_5310,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_5310)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_5310))]]) ).
cnf(refute_0_212,plain,
( ~ cong(skolemFOFtoCNF_D,X_5306,X_5306,skolemFOFtoCNF_D)
| cong(X_5306,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_5306) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_5306)),bind(C,$fot(X_5306)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_213,plain,
( ~ cong(skolemFOFtoCNF_D,X_5296,skolemFOFtoCNF_D,X_5296)
| cong(skolemFOFtoCNF_D,X_5296,X_5296,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_5296)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_5296))]]) ).
cnf(refute_0_214,plain,
( ~ midp(skolemFOFtoCNF_D,X_5291,X_5291)
| cong(skolemFOFtoCNF_D,X_5291,skolemFOFtoCNF_D,X_5291) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_5291)),bind(C,$fot(X_5291))]]) ).
cnf(refute_0_215,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_D,X_5232,X_5232) ),
inference(subst,[],[refute_0_70:[bind(X_5231,$fot(skolemFOFtoCNF_A)),bind(X_5233,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_216,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| ~ cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_72:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_217,plain,
( ~ cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_218,plain,
( ~ cong(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_219,plain,
( ~ cong(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_220,plain,
cong(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_162,refute_0_219]) ).
cnf(refute_0_221,plain,
cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_220,refute_0_218]) ).
cnf(refute_0_222,plain,
cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_221,refute_0_217]) ).
cnf(refute_0_223,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_222,refute_0_216]) ).
cnf(refute_0_224,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_152:[bind(C,$fot(skolemFOFtoCNF_D)),bind(X_3735,$fot(skolemFOFtoCNF_A)),bind(X_3736,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_225,plain,
midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_224,refute_0_223]) ).
cnf(refute_0_226,plain,
midp(skolemFOFtoCNF_D,X_5232,X_5232),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_225,refute_0_215]) ).
cnf(refute_0_227,plain,
midp(skolemFOFtoCNF_D,X_5291,X_5291),
inference(subst,[],[refute_0_226:[bind(X_5232,$fot(X_5291))]]) ).
cnf(refute_0_228,plain,
cong(skolemFOFtoCNF_D,X_5291,skolemFOFtoCNF_D,X_5291),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,X_5291,X_5291) )],[refute_0_227,refute_0_214]) ).
cnf(refute_0_229,plain,
cong(skolemFOFtoCNF_D,X_5296,skolemFOFtoCNF_D,X_5296),
inference(subst,[],[refute_0_228:[bind(X_5291,$fot(X_5296))]]) ).
cnf(refute_0_230,plain,
cong(skolemFOFtoCNF_D,X_5296,X_5296,skolemFOFtoCNF_D),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,X_5296,skolemFOFtoCNF_D,X_5296) )],[refute_0_229,refute_0_213]) ).
cnf(refute_0_231,plain,
cong(skolemFOFtoCNF_D,X_5306,X_5306,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_230:[bind(X_5296,$fot(X_5306))]]) ).
cnf(refute_0_232,plain,
cong(X_5306,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_5306),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,X_5306,X_5306,skolemFOFtoCNF_D) )],[refute_0_231,refute_0_212]) ).
cnf(refute_0_233,plain,
cong(X_5310,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_5310),
inference(subst,[],[refute_0_232:[bind(X_5306,$fot(X_5310))]]) ).
cnf(refute_0_234,plain,
cong(X_5310,skolemFOFtoCNF_D,X_5310,skolemFOFtoCNF_D),
inference(resolve,[$cnf( cong(X_5310,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_5310) )],[refute_0_233,refute_0_211]) ).
cnf(refute_0_235,plain,
cong(X_5312,skolemFOFtoCNF_D,X_5312,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_234:[bind(X_5310,$fot(X_5312))]]) ).
cnf(refute_0_236,plain,
( ~ coll(X_5312,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| midp(X_5312,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( cong(X_5312,skolemFOFtoCNF_D,X_5312,skolemFOFtoCNF_D) )],[refute_0_235,refute_0_210]) ).
cnf(refute_0_237,plain,
coll(X_5312,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_152:[bind(C,$fot(X_5312)),bind(X_3735,$fot(skolemFOFtoCNF_D)),bind(X_3736,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_238,plain,
midp(X_5312,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(X_5312,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_237,refute_0_236]) ).
cnf(refute_0_239,plain,
midp(X_5313,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_238:[bind(X_5312,$fot(X_5313))]]) ).
cnf(refute_0_240,plain,
midp(X_5313,X_5232,X_5232),
inference(resolve,[$cnf( midp(X_5313,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_239,refute_0_209]) ).
cnf(refute_0_241,plain,
midp(M,X_8679,X_8679),
inference(subst,[],[refute_0_240:[bind(X_5232,$fot(X_8679)),bind(X_5313,$fot(M))]]) ).
cnf(refute_0_242,plain,
cong(X_8679,M,X_8678,M),
inference(resolve,[$cnf( midp(M,X_8679,X_8679) )],[refute_0_241,refute_0_208]) ).
cnf(refute_0_243,plain,
cong(X_8698,X_8696,X_8697,X_8696),
inference(subst,[],[refute_0_242:[bind(M,$fot(X_8696)),bind(X_8678,$fot(X_8697)),bind(X_8679,$fot(X_8698))]]) ).
cnf(refute_0_244,plain,
cong(X_8698,X_8696,X_8696,X_8697),
inference(resolve,[$cnf( cong(X_8698,X_8696,X_8697,X_8696) )],[refute_0_243,refute_0_11]) ).
cnf(refute_0_245,plain,
cong(X_8701,X_8699,X_8699,X_8700),
inference(subst,[],[refute_0_244:[bind(X_8696,$fot(X_8699)),bind(X_8697,$fot(X_8700)),bind(X_8698,$fot(X_8701))]]) ).
cnf(refute_0_246,plain,
cong(X_8699,X_8700,X_8701,X_8699),
inference(resolve,[$cnf( cong(X_8701,X_8699,X_8699,X_8700) )],[refute_0_245,refute_0_10]) ).
cnf(refute_0_247,plain,
cong(X_8724,X_8725,X_8726,X_8724),
inference(subst,[],[refute_0_246:[bind(X_8699,$fot(X_8724)),bind(X_8700,$fot(X_8725)),bind(X_8701,$fot(X_8726))]]) ).
cnf(refute_0_248,plain,
cong(X_8724,X_8725,X_8724,X_8726),
inference(resolve,[$cnf( cong(X_8724,X_8725,X_8726,X_8724) )],[refute_0_247,refute_0_8]) ).
cnf(refute_0_249,plain,
cong(O,A,O,C),
inference(subst,[],[refute_0_248:[bind(X_8724,$fot(O)),bind(X_8725,$fot(A)),bind(X_8726,$fot(C))]]) ).
cnf(refute_0_250,plain,
( ~ cong(O,A,O,D)
| cyclic(A,C,C,D) ),
inference(resolve,[$cnf( cong(O,A,O,C) )],[refute_0_249,refute_0_6]) ).
cnf(refute_0_251,plain,
cong(O,A,O,D),
inference(subst,[],[refute_0_248:[bind(X_8724,$fot(O)),bind(X_8725,$fot(A)),bind(X_8726,$fot(D))]]) ).
cnf(refute_0_252,plain,
cyclic(A,C,C,D),
inference(resolve,[$cnf( cong(O,A,O,D) )],[refute_0_251,refute_0_250]) ).
cnf(refute_0_253,plain,
cyclic(X_18665,X_18666,X_18666,X_18667),
inference(subst,[],[refute_0_252:[bind(A,$fot(X_18665)),bind(C,$fot(X_18666)),bind(D,$fot(X_18667))]]) ).
cnf(refute_0_254,plain,
cyclic(X_18666,X_18665,X_18666,X_18667),
inference(resolve,[$cnf( cyclic(X_18665,X_18666,X_18666,X_18667) )],[refute_0_253,refute_0_4]) ).
cnf(refute_0_255,plain,
cyclic(X_18669,X_18668,X_18669,X_18670),
inference(subst,[],[refute_0_254:[bind(X_18665,$fot(X_18668)),bind(X_18666,$fot(X_18669)),bind(X_18667,$fot(X_18670))]]) ).
cnf(refute_0_256,plain,
cyclic(X_18669,X_18669,X_18668,X_18670),
inference(resolve,[$cnf( cyclic(X_18669,X_18668,X_18669,X_18670) )],[refute_0_255,refute_0_2]) ).
cnf(refute_0_257,plain,
cyclic(X_19439,X_19439,X_19440,X_19441),
inference(subst,[],[refute_0_256:[bind(X_18668,$fot(X_19440)),bind(X_18669,$fot(X_19439)),bind(X_18670,$fot(X_19441))]]) ).
cnf(refute_0_258,plain,
( ~ cyclic(X_19439,X_19439,X_19440,X_19441)
| ~ cyclic(X_19439,X_19439,X_19440,X_19442)
| cyclic(X_19439,X_19440,X_19441,X_19442) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_19439)),bind(B,$fot(X_19439)),bind(C,$fot(X_19440)),bind(D,$fot(X_19441)),bind(E,$fot(X_19442))]]) ).
cnf(refute_0_259,plain,
( ~ cyclic(X_19439,X_19439,X_19440,X_19442)
| cyclic(X_19439,X_19440,X_19441,X_19442) ),
inference(resolve,[$cnf( cyclic(X_19439,X_19439,X_19440,X_19441) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
cyclic(X_19439,X_19439,X_19440,X_19442),
inference(subst,[],[refute_0_256:[bind(X_18668,$fot(X_19440)),bind(X_18669,$fot(X_19439)),bind(X_18670,$fot(X_19442))]]) ).
cnf(refute_0_261,plain,
cyclic(X_19439,X_19440,X_19441,X_19442),
inference(resolve,[$cnf( cyclic(X_19439,X_19439,X_19440,X_19442) )],[refute_0_260,refute_0_259]) ).
cnf(refute_0_262,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_I),
inference(subst,[],[refute_0_261:[bind(X_19439,$fot(skolemFOFtoCNF_B_1)),bind(X_19440,$fot(skolemFOFtoCNF_H)),bind(X_19441,$fot(skolemFOFtoCNF_C_1)),bind(X_19442,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_263,plain,
$false,
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_I) )],[refute_0_262,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO621+1 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 08:58:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 97.78/97.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 97.78/97.97
% 97.78/97.97 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 97.78/97.99
%------------------------------------------------------------------------------