%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO552+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 05:27:09 EDT 2022
% Result : Theorem 36.31s 36.50s
% Output : CNFRefutation 36.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 86
% Number of leaves : 29
% Syntax : Number of formulae : 339 ( 130 unt; 0 def)
% Number of atoms : 659 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 571 ( 251 ~; 246 |; 43 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 825 ( 102 sgn 400 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ) ).
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,C)
& coll(A,B,D) )
=> coll(C,D,A) ) ).
fof(ruleD7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ) ).
fof(ruleD8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ) ).
fof(ruleD11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ) ).
fof(ruleD12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,B)
& cong(O,A,O,C) )
=> circle(O,A,B,C) ) ).
fof(ruleD13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,B)
& cong(O,A,O,C)
& cong(O,A,O,D) )
=> cyclic(A,B,C,D) ) ).
fof(ruleD14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ) ).
fof(ruleD15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ) ).
fof(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ) ).
fof(ruleD17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,D)
& cyclic(A,B,C,E) )
=> cyclic(B,C,D,E) ) ).
fof(ruleD19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ) ).
fof(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ) ).
fof(ruleD24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ) ).
fof(ruleD39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ) ).
fof(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ) ).
fof(ruleD41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ) ).
fof(ruleD52,axiom,
! [A,B,C,M] :
( ( perp(A,B,B,C)
& midp(M,A,C) )
=> cong(A,M,B,M) ) ).
fof(ruleD53,axiom,
! [A,B,C,O] :
( ( circle(O,A,B,C)
& coll(O,A,C) )
=> perp(A,B,B,C) ) ).
fof(ruleD56,axiom,
! [A,B,P,Q] :
( ( cong(A,P,B,P)
& cong(A,Q,B,Q) )
=> perp(A,B,P,Q) ) ).
fof(ruleD57,axiom,
! [A,B,P,Q] :
( ( cong(A,P,B,P)
& cong(A,Q,B,Q)
& cyclic(A,B,P,Q) )
=> perp(P,A,A,Q) ) ).
fof(ruleD64,axiom,
! [A,B,C,D,M] :
( ( midp(M,A,B)
& para(A,C,B,D)
& para(A,D,B,C) )
=> midp(M,C,D) ) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ) ).
fof(ruleD67,axiom,
! [A,B,C] :
( ( cong(A,B,A,C)
& coll(A,B,C) )
=> midp(A,B,C) ) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ) ).
fof(ruleD69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ) ).
fof(ruleX7,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( midp(M,A,B)
& midp(N,C,D)
& coll(C,A,B)
& coll(D,A,B) )
=> midp(P,A,Q) ) ).
fof(exemplo6GDDFULL012012,conjecture,
! [A,B,C,O,D,E,F,NWPNT1] :
( ( circle(O,A,B,C)
& perp(A,C,B,D)
& circle(O,A,D,NWPNT1)
& coll(E,A,C)
& coll(E,B,D)
& midp(F,B,A) )
=> perp(F,E,C,D) ) ).
fof(subgoal_0,plain,
! [A,B,C,O,D,E,F,NWPNT1] :
( ( circle(O,A,B,C)
& perp(A,C,B,D)
& circle(O,A,D,NWPNT1)
& coll(E,A,C)
& coll(E,B,D)
& midp(F,B,A) )
=> perp(F,E,C,D) ),
inference(strip,[],[exemplo6GDDFULL012012]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,O,D,E,F,NWPNT1] :
( ( circle(O,A,B,C)
& perp(A,C,B,D)
& circle(O,A,D,NWPNT1)
& coll(E,A,C)
& coll(E,B,D)
& midp(F,B,A) )
=> perp(F,E,C,D) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D,E,F,O] :
( ~ perp(F,E,C,D)
& circle(O,A,B,C)
& coll(E,A,C)
& coll(E,B,D)
& midp(F,B,A)
& perp(A,C,B,D)
& ? [NWPNT1] : circle(O,A,D,NWPNT1) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ perp(skolemFOFtoCNF_F,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D)
& circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D)
& midp(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
& perp(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D)
& ? [NWPNT1] : circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_D,NWPNT1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ perp(skolemFOFtoCNF_F,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,P,Q] :
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| perp(A,B,P,Q) ),
inference(canonicalize,[],[ruleD56]) ).
fof(normalize_0_4,plain,
! [A,B,P,Q] :
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| perp(A,B,P,Q) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,M] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(canonicalize,[],[ruleD52]) ).
fof(normalize_0_6,plain,
! [A,B,C,M] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,P,Q] :
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(canonicalize,[],[ruleD57]) ).
fof(normalize_0_8,plain,
! [A,B,P,Q] :
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C,D,E] :
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[ruleD17]) ).
fof(normalize_0_10,plain,
! [A,B,C,D,E] :
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[ruleD14]) ).
fof(normalize_0_12,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[ruleD15]) ).
fof(normalize_0_14,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[ruleD16]) ).
fof(normalize_0_16,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B,C,D,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,B,C,D) ),
inference(canonicalize,[],[ruleD13]) ).
fof(normalize_0_18,plain,
! [A,B,C,D,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,B,C,D) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[ruleD68]) ).
fof(normalize_0_20,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B,C,D] :
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ! [M] : ~ midp(M,A,B)
| ! [N] : ~ midp(N,C,D)
| ! [Q] :
? [P] : midp(P,A,Q) ),
inference(canonicalize,[],[ruleX7]) ).
fof(normalize_0_22,plain,
! [A,B,C,D] :
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ! [M] : ~ midp(M,A,B)
| ! [N] : ~ midp(N,C,D)
| ! [Q] :
? [P] : midp(P,A,Q) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B,C,D,M,N,Q] :
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P_1(A,Q),A,Q) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[ruleD1]) ).
fof(normalize_0_25,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[ruleD2]) ).
fof(normalize_0_27,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD66]) ).
fof(normalize_0_29,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q] : ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[ruleD39]) ).
fof(normalize_0_31,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q] : ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [A,B,C,D,P,Q] :
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(clausify,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[ruleD41]) ).
fof(normalize_0_34,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(specialize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_1]) ).
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,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[ruleD23]) ).
fof(normalize_0_46,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(specialize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[ruleD24]) ).
fof(normalize_0_48,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(specialize,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[ruleD11]) ).
fof(normalize_0_50,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(specialize,[],[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_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
~ perp(skolemFOFtoCNF_F,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D),
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_4087,X_4087)
| ~ perp(X_4087,X_4086,X_4086,X_4087)
| cong(X_4087,M,X_4086,M) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_4087)),bind(B,$fot(X_4086)),bind(C,$fot(X_4087))]]) ).
cnf(refute_0_4,plain,
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ cong(X_4084,X_4085,X_4084,X_4085)
| ~ cyclic(X_4084,X_4084,X_4085,X_4085)
| perp(X_4085,X_4084,X_4084,X_4085) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_4084)),bind(B,$fot(X_4084)),bind(P,$fot(X_4085)),bind(Q,$fot(X_4085))]]) ).
cnf(refute_0_6,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ cyclic(X_4082,X_4082,X_4082,X_4083)
| cyclic(X_4082,X_4082,X_4083,X_4083) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_4082)),bind(B,$fot(X_4082)),bind(C,$fot(X_4082)),bind(D,$fot(X_4083)),bind(E,$fot(X_4083))]]) ).
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_4080,X_4080,X_4081,X_4080)
| cyclic(X_4080,X_4080,X_4080,X_4081) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_4080)),bind(B,$fot(X_4080)),bind(C,$fot(X_4081)),bind(D,$fot(X_4080))]]) ).
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_4078,X_4079,X_4078,X_4078)
| cyclic(X_4078,X_4078,X_4079,X_4078) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_4078)),bind(B,$fot(X_4079)),bind(C,$fot(X_4078)),bind(D,$fot(X_4078))]]) ).
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_4077,X_4076,X_4076,X_4076)
| cyclic(X_4076,X_4077,X_4076,X_4076) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_4077)),bind(B,$fot(X_4076)),bind(C,$fot(X_4076)),bind(D,$fot(X_4076))]]) ).
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_4075,X_4074),X_4075,skolemFOFtoCNF_P_1(X_4075,X_4074),X_4074)
| cyclic(X_4075,X_4074,X_4074,X_4074) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_4075)),bind(B,$fot(X_4074)),bind(C,$fot(X_4074)),bind(D,$fot(X_4074)),bind(O,$fot(skolemFOFtoCNF_P_1(X_4075,X_4074)))]]) ).
cnf(refute_0_16,plain,
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_17,plain,
( ~ midp(skolemFOFtoCNF_P_1(X_1546,X_1545),X_1546,X_1545)
| cong(skolemFOFtoCNF_P_1(X_1546,X_1545),X_1546,skolemFOFtoCNF_P_1(X_1546,X_1545),X_1545) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_P_1(X_1546,X_1545))),bind(B,$fot(X_1546)),bind(C,$fot(X_1545))]]) ).
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_354,X_353,X_354)
| coll(X_354,X_354,X_353) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(X_354)),bind(B,$fot(X_353)),bind(C,$fot(X_354))]]) ).
cnf(refute_0_22,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_23,plain,
( ~ coll(X_351,X_352,X_352)
| coll(X_352,X_351,X_352) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_351)),bind(B,$fot(X_352)),bind(C,$fot(X_352))]]) ).
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_349,X_350,X_349,X_350)
| coll(X_349,X_350,X_350) ),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_349)),bind(B,$fot(X_350)),bind(C,$fot(X_350))]]) ).
cnf(refute_0_26,plain,
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_27,plain,
( ~ eqangle(X_347,X_348,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_347,X_348,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(X_347,X_348,X_347,X_348) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_347)),bind(B,$fot(X_348)),bind(C,$fot(X_347)),bind(D,$fot(X_348)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_28,plain,
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_29,plain,
( ~ cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_28:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_30,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(E,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_31,plain,
( ~ cong(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_32,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_33,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_34,plain,
cong(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A) )],[refute_0_34,refute_0_31]) ).
cnf(refute_0_36,plain,
cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_35,refute_0_30]) ).
cnf(refute_0_37,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_36,refute_0_29]) ).
cnf(refute_0_38,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_39,plain,
para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_41,plain,
( ~ para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154) ),
inference(subst,[],[refute_0_40:[bind(A,$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,$fot(X_154))]]) ).
cnf(refute_0_42,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_345,X_346,skolemFOFtoCNF_A,skolemFOFtoCNF_A,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_A,skolemFOFtoCNF_A,X_345,X_346,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_345,X_346)
| eqangle(X_345,X_346,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_345,X_346,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_44:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(X_345)),bind(D,$fot(X_346)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A)),bind(U,$fot(X_345)),bind(V,$fot(X_346))]]) ).
cnf(refute_0_46,plain,
eqangle(X_345,X_346,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_345,X_346,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_345,X_346,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_345,X_346) )],[refute_0_43,refute_0_45]) ).
cnf(refute_0_47,plain,
eqangle(X_347,X_348,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_347,X_348,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_46:[bind(X_345,$fot(X_347)),bind(X_346,$fot(X_348))]]) ).
cnf(refute_0_48,plain,
para(X_347,X_348,X_347,X_348),
inference(resolve,[$cnf( eqangle(X_347,X_348,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_347,X_348,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_47,refute_0_27]) ).
cnf(refute_0_49,plain,
para(X_349,X_350,X_349,X_350),
inference(subst,[],[refute_0_48:[bind(X_347,$fot(X_349)),bind(X_348,$fot(X_350))]]) ).
cnf(refute_0_50,plain,
coll(X_349,X_350,X_350),
inference(resolve,[$cnf( para(X_349,X_350,X_349,X_350) )],[refute_0_49,refute_0_25]) ).
cnf(refute_0_51,plain,
coll(X_351,X_352,X_352),
inference(subst,[],[refute_0_50:[bind(X_349,$fot(X_351)),bind(X_350,$fot(X_352))]]) ).
cnf(refute_0_52,plain,
coll(X_352,X_351,X_352),
inference(resolve,[$cnf( coll(X_351,X_352,X_352) )],[refute_0_51,refute_0_23]) ).
cnf(refute_0_53,plain,
coll(X_354,X_353,X_354),
inference(subst,[],[refute_0_52:[bind(X_351,$fot(X_353)),bind(X_352,$fot(X_354))]]) ).
cnf(refute_0_54,plain,
coll(X_354,X_354,X_353),
inference(resolve,[$cnf( coll(X_354,X_353,X_354) )],[refute_0_53,refute_0_21]) ).
cnf(refute_0_55,plain,
coll(D,D,D),
inference(subst,[],[refute_0_54:[bind(X_353,$fot(D)),bind(X_354,$fot(D))]]) ).
cnf(refute_0_56,plain,
( ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(resolve,[$cnf( coll(D,D,D) )],[refute_0_55,refute_0_19]) ).
cnf(refute_0_57,plain,
( ~ midp(X_1541,X_1540,X_1540)
| midp(skolemFOFtoCNF_P_1(X_1540,Q),X_1540,Q) ),
inference(subst,[],[refute_0_56:[bind(D,$fot(X_1540)),bind(N,$fot(X_1541))]]) ).
cnf(refute_0_58,plain,
para(X_1480,X_1481,X_1480,X_1481),
inference(subst,[],[refute_0_48:[bind(X_347,$fot(X_1480)),bind(X_348,$fot(X_1481))]]) ).
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_1482,X_1480,X_1480)
| ~ para(X_1480,X_1481,X_1480,X_1481)
| midp(X_1482,X_1481,X_1481) ),
inference(subst,[],[refute_0_59:[bind(A,$fot(X_1480)),bind(B,$fot(X_1480)),bind(C,$fot(X_1481)),bind(D,$fot(X_1481)),bind(M,$fot(X_1482))]]) ).
cnf(refute_0_61,plain,
( ~ midp(X_1482,X_1480,X_1480)
| midp(X_1482,X_1481,X_1481) ),
inference(resolve,[$cnf( para(X_1480,X_1481,X_1480,X_1481) )],[refute_0_58,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ midp(X_1521,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(X_1521,X_1481,X_1481) ),
inference(subst,[],[refute_0_61:[bind(X_1480,$fot(skolemFOFtoCNF_A)),bind(X_1482,$fot(X_1521))]]) ).
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(X_1520,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| ~ cong(X_1520,skolemFOFtoCNF_A,X_1520,skolemFOFtoCNF_A)
| midp(X_1520,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_1520)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_65,plain,
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_66,plain,
( ~ cong(X_1517,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_1517)
| cong(X_1517,skolemFOFtoCNF_A,X_1517,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_65:[bind(A,$fot(X_1517)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_1517))]]) ).
cnf(refute_0_67,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_68,plain,
( ~ cong(skolemFOFtoCNF_A,X_1512,X_1512,skolemFOFtoCNF_A)
| cong(X_1512,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_1512) ),
inference(subst,[],[refute_0_67:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_1512)),bind(C,$fot(X_1512)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_69,plain,
( ~ cong(skolemFOFtoCNF_A,X_1507,skolemFOFtoCNF_A,X_1507)
| cong(skolemFOFtoCNF_A,X_1507,X_1507,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_65:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_1507)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_1507))]]) ).
cnf(refute_0_70,plain,
( ~ midp(skolemFOFtoCNF_A,X_1505,X_1505)
| cong(skolemFOFtoCNF_A,X_1505,skolemFOFtoCNF_A,X_1505) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_1505)),bind(C,$fot(X_1505))]]) ).
cnf(refute_0_71,plain,
( ~ midp(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| midp(skolemFOFtoCNF_A,X_1481,X_1481) ),
inference(subst,[],[refute_0_61:[bind(X_1480,$fot(skolemFOFtoCNF_F)),bind(X_1482,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_72,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| ~ cong(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F)
| midp(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_73,plain,
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_74,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_73:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(M,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_75,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_32,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_77,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_78,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_79,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_78:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_80,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[normalize_0_56]) ).
cnf(refute_0_81,plain,
( ~ cong(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A)
| circle(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_80:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_82,plain,
circle(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F,skolemFOFtoCNF_A) )],[refute_0_34,refute_0_81]) ).
cnf(refute_0_83,plain,
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_84,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_60]) ).
cnf(refute_0_85,plain,
( ~ coll(X_1444,skolemFOFtoCNF_A,C)
| ~ coll(X_1444,skolemFOFtoCNF_A,X_1445)
| coll(C,X_1445,X_1444) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(X_1444)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_1445))]]) ).
cnf(refute_0_86,plain,
( ~ coll(X_1402,skolemFOFtoCNF_B_1,C)
| ~ coll(X_1402,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| coll(C,skolemFOFtoCNF_A,X_1402) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(X_1402)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_87,plain,
( ~ coll(skolemFOFtoCNF_A,X_1401,C)
| ~ coll(skolemFOFtoCNF_A,X_1401,skolemFOFtoCNF_B_1)
| coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_1401)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_88,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_89,plain,
( ~ coll(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_90,plain,
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_62]) ).
cnf(refute_0_91,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_90:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_92,plain,
coll(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_75,refute_0_91]) ).
cnf(refute_0_93,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_92,refute_0_89]) ).
cnf(refute_0_94,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1) )],[refute_0_93,refute_0_88]) ).
cnf(refute_0_95,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1395)
| ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,X_1395,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_1395))]]) ).
cnf(refute_0_96,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1395)
| coll(skolemFOFtoCNF_A,X_1395,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1395),
inference(subst,[],[refute_0_54:[bind(X_353,$fot(X_1395)),bind(X_354,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_98,plain,
coll(skolemFOFtoCNF_A,X_1395,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1395) )],[refute_0_97,refute_0_96]) ).
cnf(refute_0_99,plain,
coll(skolemFOFtoCNF_A,X_1401,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_98:[bind(X_1395,$fot(X_1401))]]) ).
cnf(refute_0_100,plain,
( ~ coll(skolemFOFtoCNF_A,X_1401,C)
| coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_1401,skolemFOFtoCNF_B_1) )],[refute_0_99,refute_0_87]) ).
cnf(refute_0_101,plain,
( ~ coll(X_351,X_352,X_352)
| coll(X_352,X_352,X_351) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(X_351)),bind(B,$fot(X_352)),bind(C,$fot(X_352)),bind(D,$fot(X_352))]]) ).
cnf(refute_0_102,plain,
coll(X_352,X_352,X_351),
inference(resolve,[$cnf( coll(X_351,X_352,X_352) )],[refute_0_51,refute_0_101]) ).
cnf(refute_0_103,plain,
coll(X_1393,X_1393,X_1394),
inference(subst,[],[refute_0_102:[bind(X_351,$fot(X_1394)),bind(X_352,$fot(X_1393))]]) ).
cnf(refute_0_104,plain,
( ~ coll(X_1393,X_1393,X_1394)
| ~ coll(X_1393,X_1393,X_1395)
| coll(X_1394,X_1395,X_1393) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(X_1393)),bind(B,$fot(X_1393)),bind(C,$fot(X_1394)),bind(D,$fot(X_1395))]]) ).
cnf(refute_0_105,plain,
( ~ coll(X_1393,X_1393,X_1395)
| coll(X_1394,X_1395,X_1393) ),
inference(resolve,[$cnf( coll(X_1393,X_1393,X_1394) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
coll(X_1393,X_1393,X_1395),
inference(subst,[],[refute_0_54:[bind(X_353,$fot(X_1395)),bind(X_354,$fot(X_1393))]]) ).
cnf(refute_0_107,plain,
coll(X_1394,X_1395,X_1393),
inference(resolve,[$cnf( coll(X_1393,X_1393,X_1395) )],[refute_0_106,refute_0_105]) ).
cnf(refute_0_108,plain,
coll(skolemFOFtoCNF_A,X_1401,C),
inference(subst,[],[refute_0_107:[bind(X_1393,$fot(C)),bind(X_1394,$fot(skolemFOFtoCNF_A)),bind(X_1395,$fot(X_1401))]]) ).
cnf(refute_0_109,plain,
coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_1401,C) )],[refute_0_108,refute_0_100]) ).
cnf(refute_0_110,plain,
coll(X_1402,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_109:[bind(C,$fot(X_1402))]]) ).
cnf(refute_0_111,plain,
( ~ coll(X_1402,skolemFOFtoCNF_B_1,C)
| coll(C,skolemFOFtoCNF_A,X_1402) ),
inference(resolve,[$cnf( coll(X_1402,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_110,refute_0_86]) ).
cnf(refute_0_112,plain,
coll(X_1402,skolemFOFtoCNF_B_1,C),
inference(subst,[],[refute_0_107:[bind(X_1393,$fot(C)),bind(X_1394,$fot(X_1402)),bind(X_1395,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_113,plain,
coll(C,skolemFOFtoCNF_A,X_1402),
inference(resolve,[$cnf( coll(X_1402,skolemFOFtoCNF_B_1,C) )],[refute_0_112,refute_0_111]) ).
cnf(refute_0_114,plain,
coll(X_1444,skolemFOFtoCNF_A,X_1445),
inference(subst,[],[refute_0_113:[bind(C,$fot(X_1444)),bind(X_1402,$fot(X_1445))]]) ).
cnf(refute_0_115,plain,
( ~ coll(X_1444,skolemFOFtoCNF_A,C)
| coll(C,X_1445,X_1444) ),
inference(resolve,[$cnf( coll(X_1444,skolemFOFtoCNF_A,X_1445) )],[refute_0_114,refute_0_85]) ).
cnf(refute_0_116,plain,
( ~ coll(X_1442,skolemFOFtoCNF_E,C)
| ~ coll(X_1442,skolemFOFtoCNF_E,X_1443)
| coll(C,X_1443,X_1442) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(X_1442)),bind(B,$fot(skolemFOFtoCNF_E)),bind(D,$fot(X_1443))]]) ).
cnf(refute_0_117,plain,
( ~ coll(X_1422,skolemFOFtoCNF_B_1,C)
| ~ coll(X_1422,skolemFOFtoCNF_B_1,skolemFOFtoCNF_E)
| coll(C,skolemFOFtoCNF_E,X_1422) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(X_1422)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_118,plain,
( ~ coll(skolemFOFtoCNF_B_1,X_1411,skolemFOFtoCNF_E)
| coll(X_1411,skolemFOFtoCNF_B_1,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_1411)),bind(C,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_119,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_E,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_120,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D),
inference(canonicalize,[],[normalize_0_63]) ).
cnf(refute_0_121,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_E,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_122,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_E,skolemFOFtoCNF_D) )],[refute_0_122,refute_0_119]) ).
cnf(refute_0_124,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
| coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_125,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_1395)
| ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,X_1395,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_1395))]]) ).
cnf(refute_0_127,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_1395)
| coll(skolemFOFtoCNF_B_1,X_1395,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_B_1) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_1395),
inference(subst,[],[refute_0_54:[bind(X_353,$fot(X_1395)),bind(X_354,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_129,plain,
coll(skolemFOFtoCNF_B_1,X_1395,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_1395) )],[refute_0_128,refute_0_127]) ).
cnf(refute_0_130,plain,
coll(skolemFOFtoCNF_B_1,X_1411,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_129:[bind(X_1395,$fot(X_1411))]]) ).
cnf(refute_0_131,plain,
coll(X_1411,skolemFOFtoCNF_B_1,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,X_1411,skolemFOFtoCNF_E) )],[refute_0_130,refute_0_118]) ).
cnf(refute_0_132,plain,
coll(X_1422,skolemFOFtoCNF_B_1,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_131:[bind(X_1411,$fot(X_1422))]]) ).
cnf(refute_0_133,plain,
( ~ coll(X_1422,skolemFOFtoCNF_B_1,C)
| coll(C,skolemFOFtoCNF_E,X_1422) ),
inference(resolve,[$cnf( coll(X_1422,skolemFOFtoCNF_B_1,skolemFOFtoCNF_E) )],[refute_0_132,refute_0_117]) ).
cnf(refute_0_134,plain,
coll(X_1422,skolemFOFtoCNF_B_1,C),
inference(subst,[],[refute_0_107:[bind(X_1393,$fot(C)),bind(X_1394,$fot(X_1422)),bind(X_1395,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_135,plain,
coll(C,skolemFOFtoCNF_E,X_1422),
inference(resolve,[$cnf( coll(X_1422,skolemFOFtoCNF_B_1,C) )],[refute_0_134,refute_0_133]) ).
cnf(refute_0_136,plain,
coll(X_1442,skolemFOFtoCNF_E,X_1443),
inference(subst,[],[refute_0_135:[bind(C,$fot(X_1442)),bind(X_1422,$fot(X_1443))]]) ).
cnf(refute_0_137,plain,
( ~ coll(X_1442,skolemFOFtoCNF_E,C)
| coll(C,X_1443,X_1442) ),
inference(resolve,[$cnf( coll(X_1442,skolemFOFtoCNF_E,X_1443) )],[refute_0_136,refute_0_116]) ).
cnf(refute_0_138,plain,
( ~ coll(X_1438,skolemFOFtoCNF_B_1,C)
| ~ coll(X_1438,skolemFOFtoCNF_B_1,X_1439)
| coll(C,X_1439,X_1438) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(X_1438)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_1439))]]) ).
cnf(refute_0_139,plain,
( ~ coll(X_1419,skolemFOFtoCNF_A,C)
| ~ coll(X_1419,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(C,skolemFOFtoCNF_B_1,X_1419) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(X_1419)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_140,plain,
( ~ coll(skolemFOFtoCNF_A,X_1401,skolemFOFtoCNF_B_1)
| coll(X_1401,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_1401)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_141,plain,
coll(X_1401,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_1401,skolemFOFtoCNF_B_1) )],[refute_0_99,refute_0_140]) ).
cnf(refute_0_142,plain,
coll(X_1419,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_141:[bind(X_1401,$fot(X_1419))]]) ).
cnf(refute_0_143,plain,
( ~ coll(X_1419,skolemFOFtoCNF_A,C)
| coll(C,skolemFOFtoCNF_B_1,X_1419) ),
inference(resolve,[$cnf( coll(X_1419,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_142,refute_0_139]) ).
cnf(refute_0_144,plain,
coll(X_1419,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_107:[bind(X_1393,$fot(C)),bind(X_1394,$fot(X_1419)),bind(X_1395,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_145,plain,
coll(C,skolemFOFtoCNF_B_1,X_1419),
inference(resolve,[$cnf( coll(X_1419,skolemFOFtoCNF_A,C) )],[refute_0_144,refute_0_143]) ).
cnf(refute_0_146,plain,
coll(X_1438,skolemFOFtoCNF_B_1,X_1439),
inference(subst,[],[refute_0_145:[bind(C,$fot(X_1438)),bind(X_1419,$fot(X_1439))]]) ).
cnf(refute_0_147,plain,
( ~ coll(X_1438,skolemFOFtoCNF_B_1,C)
| coll(C,X_1439,X_1438) ),
inference(resolve,[$cnf( coll(X_1438,skolemFOFtoCNF_B_1,X_1439) )],[refute_0_146,refute_0_138]) ).
cnf(refute_0_148,plain,
coll(X_1438,skolemFOFtoCNF_B_1,C),
inference(subst,[],[refute_0_107:[bind(X_1393,$fot(C)),bind(X_1394,$fot(X_1438)),bind(X_1395,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_149,plain,
coll(C,X_1439,X_1438),
inference(resolve,[$cnf( coll(X_1438,skolemFOFtoCNF_B_1,C) )],[refute_0_148,refute_0_147]) ).
cnf(refute_0_150,plain,
coll(X_1442,skolemFOFtoCNF_E,C),
inference(subst,[],[refute_0_149:[bind(C,$fot(X_1442)),bind(X_1438,$fot(C)),bind(X_1439,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_151,plain,
coll(C,X_1443,X_1442),
inference(resolve,[$cnf( coll(X_1442,skolemFOFtoCNF_E,C) )],[refute_0_150,refute_0_137]) ).
cnf(refute_0_152,plain,
coll(X_1444,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_151:[bind(C,$fot(X_1444)),bind(X_1442,$fot(C)),bind(X_1443,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_153,plain,
coll(C,X_1445,X_1444),
inference(resolve,[$cnf( coll(X_1444,skolemFOFtoCNF_A,C) )],[refute_0_152,refute_0_115]) ).
cnf(refute_0_154,plain,
coll(O,A,C),
inference(subst,[],[refute_0_153:[bind(C,$fot(O)),bind(X_1444,$fot(C)),bind(X_1445,$fot(A))]]) ).
cnf(refute_0_155,plain,
( ~ circle(O,A,B,C)
| perp(A,B,B,C) ),
inference(resolve,[$cnf( coll(O,A,C) )],[refute_0_154,refute_0_83]) ).
cnf(refute_0_156,plain,
( ~ circle(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_155:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_157,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_F,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_82,refute_0_156]) ).
cnf(refute_0_158,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_157,refute_0_79]) ).
cnf(refute_0_159,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_158,refute_0_77]) ).
cnf(refute_0_160,plain,
( ~ midp(X_1503,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_A,X_1503,skolemFOFtoCNF_A,X_1503) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(M,$fot(X_1503))]]) ).
cnf(refute_0_161,plain,
( ~ midp(X_1503,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_A,X_1503,skolemFOFtoCNF_A,X_1503) ),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_161:[bind(X_1503,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_163,plain,
cong(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_75,refute_0_162]) ).
cnf(refute_0_164,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| midp(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F) )],[refute_0_163,refute_0_72]) ).
cnf(refute_0_165,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_153:[bind(C,$fot(skolemFOFtoCNF_A)),bind(X_1444,$fot(skolemFOFtoCNF_F)),bind(X_1445,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_166,plain,
midp(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F) )],[refute_0_165,refute_0_164]) ).
cnf(refute_0_167,plain,
midp(skolemFOFtoCNF_A,X_1481,X_1481),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F) )],[refute_0_166,refute_0_71]) ).
cnf(refute_0_168,plain,
midp(skolemFOFtoCNF_A,X_1505,X_1505),
inference(subst,[],[refute_0_167:[bind(X_1481,$fot(X_1505))]]) ).
cnf(refute_0_169,plain,
cong(skolemFOFtoCNF_A,X_1505,skolemFOFtoCNF_A,X_1505),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_A,X_1505,X_1505) )],[refute_0_168,refute_0_70]) ).
cnf(refute_0_170,plain,
cong(skolemFOFtoCNF_A,X_1507,skolemFOFtoCNF_A,X_1507),
inference(subst,[],[refute_0_169:[bind(X_1505,$fot(X_1507))]]) ).
cnf(refute_0_171,plain,
cong(skolemFOFtoCNF_A,X_1507,X_1507,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,X_1507,skolemFOFtoCNF_A,X_1507) )],[refute_0_170,refute_0_69]) ).
cnf(refute_0_172,plain,
cong(skolemFOFtoCNF_A,X_1512,X_1512,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_171:[bind(X_1507,$fot(X_1512))]]) ).
cnf(refute_0_173,plain,
cong(X_1512,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_1512),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,X_1512,X_1512,skolemFOFtoCNF_A) )],[refute_0_172,refute_0_68]) ).
cnf(refute_0_174,plain,
cong(X_1517,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_1517),
inference(subst,[],[refute_0_173:[bind(X_1512,$fot(X_1517))]]) ).
cnf(refute_0_175,plain,
cong(X_1517,skolemFOFtoCNF_A,X_1517,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(X_1517,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_1517) )],[refute_0_174,refute_0_66]) ).
cnf(refute_0_176,plain,
cong(X_1520,skolemFOFtoCNF_A,X_1520,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_175:[bind(X_1517,$fot(X_1520))]]) ).
cnf(refute_0_177,plain,
( ~ coll(X_1520,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(X_1520,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( cong(X_1520,skolemFOFtoCNF_A,X_1520,skolemFOFtoCNF_A) )],[refute_0_176,refute_0_64]) ).
cnf(refute_0_178,plain,
coll(X_1520,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_153:[bind(C,$fot(X_1520)),bind(X_1444,$fot(skolemFOFtoCNF_A)),bind(X_1445,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_179,plain,
midp(X_1520,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(X_1520,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_178,refute_0_177]) ).
cnf(refute_0_180,plain,
midp(X_1521,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_179:[bind(X_1520,$fot(X_1521))]]) ).
cnf(refute_0_181,plain,
midp(X_1521,X_1481,X_1481),
inference(resolve,[$cnf( midp(X_1521,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_180,refute_0_62]) ).
cnf(refute_0_182,plain,
midp(X_1541,X_1540,X_1540),
inference(subst,[],[refute_0_181:[bind(X_1481,$fot(X_1540)),bind(X_1521,$fot(X_1541))]]) ).
cnf(refute_0_183,plain,
midp(skolemFOFtoCNF_P_1(X_1540,Q),X_1540,Q),
inference(resolve,[$cnf( midp(X_1541,X_1540,X_1540) )],[refute_0_182,refute_0_57]) ).
cnf(refute_0_184,plain,
midp(skolemFOFtoCNF_P_1(X_1546,X_1545),X_1546,X_1545),
inference(subst,[],[refute_0_183:[bind(Q,$fot(X_1545)),bind(X_1540,$fot(X_1546))]]) ).
cnf(refute_0_185,plain,
cong(skolemFOFtoCNF_P_1(X_1546,X_1545),X_1546,skolemFOFtoCNF_P_1(X_1546,X_1545),X_1545),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(X_1546,X_1545),X_1546,X_1545) )],[refute_0_184,refute_0_17]) ).
cnf(refute_0_186,plain,
cong(skolemFOFtoCNF_P_1(X_4075,X_4074),X_4075,skolemFOFtoCNF_P_1(X_4075,X_4074),X_4074),
inference(subst,[],[refute_0_185:[bind(X_1545,$fot(X_4074)),bind(X_1546,$fot(X_4075))]]) ).
cnf(refute_0_187,plain,
cyclic(X_4075,X_4074,X_4074,X_4074),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_P_1(X_4075,X_4074),X_4075,skolemFOFtoCNF_P_1(X_4075,X_4074),X_4074) )],[refute_0_186,refute_0_15]) ).
cnf(refute_0_188,plain,
cyclic(X_4077,X_4076,X_4076,X_4076),
inference(subst,[],[refute_0_187:[bind(X_4074,$fot(X_4076)),bind(X_4075,$fot(X_4077))]]) ).
cnf(refute_0_189,plain,
cyclic(X_4076,X_4077,X_4076,X_4076),
inference(resolve,[$cnf( cyclic(X_4077,X_4076,X_4076,X_4076) )],[refute_0_188,refute_0_13]) ).
cnf(refute_0_190,plain,
cyclic(X_4078,X_4079,X_4078,X_4078),
inference(subst,[],[refute_0_189:[bind(X_4076,$fot(X_4078)),bind(X_4077,$fot(X_4079))]]) ).
cnf(refute_0_191,plain,
cyclic(X_4078,X_4078,X_4079,X_4078),
inference(resolve,[$cnf( cyclic(X_4078,X_4079,X_4078,X_4078) )],[refute_0_190,refute_0_11]) ).
cnf(refute_0_192,plain,
cyclic(X_4080,X_4080,X_4081,X_4080),
inference(subst,[],[refute_0_191:[bind(X_4078,$fot(X_4080)),bind(X_4079,$fot(X_4081))]]) ).
cnf(refute_0_193,plain,
cyclic(X_4080,X_4080,X_4080,X_4081),
inference(resolve,[$cnf( cyclic(X_4080,X_4080,X_4081,X_4080) )],[refute_0_192,refute_0_9]) ).
cnf(refute_0_194,plain,
cyclic(X_4082,X_4082,X_4082,X_4083),
inference(subst,[],[refute_0_193:[bind(X_4080,$fot(X_4082)),bind(X_4081,$fot(X_4083))]]) ).
cnf(refute_0_195,plain,
cyclic(X_4082,X_4082,X_4083,X_4083),
inference(resolve,[$cnf( cyclic(X_4082,X_4082,X_4082,X_4083) )],[refute_0_194,refute_0_7]) ).
cnf(refute_0_196,plain,
cyclic(X_4084,X_4084,X_4085,X_4085),
inference(subst,[],[refute_0_195:[bind(X_4082,$fot(X_4084)),bind(X_4083,$fot(X_4085))]]) ).
cnf(refute_0_197,plain,
( ~ cong(X_4084,X_4085,X_4084,X_4085)
| perp(X_4085,X_4084,X_4084,X_4085) ),
inference(resolve,[$cnf( cyclic(X_4084,X_4084,X_4085,X_4085) )],[refute_0_196,refute_0_5]) ).
cnf(refute_0_198,plain,
( ~ midp(X_1541,X_1540,X_1540)
| cong(X_1541,X_1540,X_1541,X_1540) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_1541)),bind(B,$fot(X_1540)),bind(C,$fot(X_1540))]]) ).
cnf(refute_0_199,plain,
cong(X_1541,X_1540,X_1541,X_1540),
inference(resolve,[$cnf( midp(X_1541,X_1540,X_1540) )],[refute_0_182,refute_0_198]) ).
cnf(refute_0_200,plain,
cong(X_4084,X_4085,X_4084,X_4085),
inference(subst,[],[refute_0_199:[bind(X_1540,$fot(X_4085)),bind(X_1541,$fot(X_4084))]]) ).
cnf(refute_0_201,plain,
perp(X_4085,X_4084,X_4084,X_4085),
inference(resolve,[$cnf( cong(X_4084,X_4085,X_4084,X_4085) )],[refute_0_200,refute_0_197]) ).
cnf(refute_0_202,plain,
perp(X_4087,X_4086,X_4086,X_4087),
inference(subst,[],[refute_0_201:[bind(X_4084,$fot(X_4086)),bind(X_4085,$fot(X_4087))]]) ).
cnf(refute_0_203,plain,
( ~ midp(M,X_4087,X_4087)
| cong(X_4087,M,X_4086,M) ),
inference(resolve,[$cnf( perp(X_4087,X_4086,X_4086,X_4087) )],[refute_0_202,refute_0_3]) ).
cnf(refute_0_204,plain,
( ~ midp(X_1529,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| midp(X_1529,X_1481,X_1481) ),
inference(subst,[],[refute_0_61:[bind(X_1480,$fot(skolemFOFtoCNF_F)),bind(X_1482,$fot(X_1529))]]) ).
cnf(refute_0_205,plain,
( ~ coll(X_1528,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| ~ cong(X_1528,skolemFOFtoCNF_F,X_1528,skolemFOFtoCNF_F)
| midp(X_1528,skolemFOFtoCNF_F,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_1528)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_206,plain,
( ~ cong(X_1527,skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_1527)
| cong(X_1527,skolemFOFtoCNF_F,X_1527,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_65:[bind(A,$fot(X_1527)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_F)),bind(D,$fot(X_1527))]]) ).
cnf(refute_0_207,plain,
( ~ cong(skolemFOFtoCNF_F,X_1522,X_1522,skolemFOFtoCNF_F)
| cong(X_1522,skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_1522) ),
inference(subst,[],[refute_0_67:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(X_1522)),bind(C,$fot(X_1522)),bind(D,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_208,plain,
( ~ cong(skolemFOFtoCNF_F,X_1510,skolemFOFtoCNF_F,X_1510)
| cong(skolemFOFtoCNF_F,X_1510,X_1510,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_65:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(X_1510)),bind(C,$fot(skolemFOFtoCNF_F)),bind(D,$fot(X_1510))]]) ).
cnf(refute_0_209,plain,
( ~ midp(skolemFOFtoCNF_F,X_1506,X_1506)
| cong(skolemFOFtoCNF_F,X_1506,skolemFOFtoCNF_F,X_1506) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(X_1506)),bind(C,$fot(X_1506))]]) ).
cnf(refute_0_210,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_F,X_1481,X_1481) ),
inference(subst,[],[refute_0_61:[bind(X_1480,$fot(skolemFOFtoCNF_A)),bind(X_1482,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_211,plain,
( ~ coll(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| ~ cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_212,plain,
( ~ cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_F)
| cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_65:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_213,plain,
( ~ cong(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_67:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_F)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_214,plain,
( ~ cong(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F)
| cong(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_65:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_215,plain,
cong(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F) )],[refute_0_163,refute_0_214]) ).
cnf(refute_0_216,plain,
cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_F),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_A) )],[refute_0_215,refute_0_213]) ).
cnf(refute_0_217,plain,
cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_F) )],[refute_0_216,refute_0_212]) ).
cnf(refute_0_218,plain,
( ~ coll(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_F,skolemFOFtoCNF_A) )],[refute_0_217,refute_0_211]) ).
cnf(refute_0_219,plain,
coll(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_153:[bind(C,$fot(skolemFOFtoCNF_F)),bind(X_1444,$fot(skolemFOFtoCNF_A)),bind(X_1445,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_220,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_219,refute_0_218]) ).
cnf(refute_0_221,plain,
midp(skolemFOFtoCNF_F,X_1481,X_1481),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_220,refute_0_210]) ).
cnf(refute_0_222,plain,
midp(skolemFOFtoCNF_F,X_1506,X_1506),
inference(subst,[],[refute_0_221:[bind(X_1481,$fot(X_1506))]]) ).
cnf(refute_0_223,plain,
cong(skolemFOFtoCNF_F,X_1506,skolemFOFtoCNF_F,X_1506),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,X_1506,X_1506) )],[refute_0_222,refute_0_209]) ).
cnf(refute_0_224,plain,
cong(skolemFOFtoCNF_F,X_1510,skolemFOFtoCNF_F,X_1510),
inference(subst,[],[refute_0_223:[bind(X_1506,$fot(X_1510))]]) ).
cnf(refute_0_225,plain,
cong(skolemFOFtoCNF_F,X_1510,X_1510,skolemFOFtoCNF_F),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,X_1510,skolemFOFtoCNF_F,X_1510) )],[refute_0_224,refute_0_208]) ).
cnf(refute_0_226,plain,
cong(skolemFOFtoCNF_F,X_1522,X_1522,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_225:[bind(X_1510,$fot(X_1522))]]) ).
cnf(refute_0_227,plain,
cong(X_1522,skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_1522),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,X_1522,X_1522,skolemFOFtoCNF_F) )],[refute_0_226,refute_0_207]) ).
cnf(refute_0_228,plain,
cong(X_1527,skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_1527),
inference(subst,[],[refute_0_227:[bind(X_1522,$fot(X_1527))]]) ).
cnf(refute_0_229,plain,
cong(X_1527,skolemFOFtoCNF_F,X_1527,skolemFOFtoCNF_F),
inference(resolve,[$cnf( cong(X_1527,skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_1527) )],[refute_0_228,refute_0_206]) ).
cnf(refute_0_230,plain,
cong(X_1528,skolemFOFtoCNF_F,X_1528,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_229:[bind(X_1527,$fot(X_1528))]]) ).
cnf(refute_0_231,plain,
( ~ coll(X_1528,skolemFOFtoCNF_F,skolemFOFtoCNF_F)
| midp(X_1528,skolemFOFtoCNF_F,skolemFOFtoCNF_F) ),
inference(resolve,[$cnf( cong(X_1528,skolemFOFtoCNF_F,X_1528,skolemFOFtoCNF_F) )],[refute_0_230,refute_0_205]) ).
cnf(refute_0_232,plain,
coll(X_1528,skolemFOFtoCNF_F,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_153:[bind(C,$fot(X_1528)),bind(X_1444,$fot(skolemFOFtoCNF_F)),bind(X_1445,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_233,plain,
midp(X_1528,skolemFOFtoCNF_F,skolemFOFtoCNF_F),
inference(resolve,[$cnf( coll(X_1528,skolemFOFtoCNF_F,skolemFOFtoCNF_F) )],[refute_0_232,refute_0_231]) ).
cnf(refute_0_234,plain,
midp(X_1529,skolemFOFtoCNF_F,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_233:[bind(X_1528,$fot(X_1529))]]) ).
cnf(refute_0_235,plain,
midp(X_1529,X_1481,X_1481),
inference(resolve,[$cnf( midp(X_1529,skolemFOFtoCNF_F,skolemFOFtoCNF_F) )],[refute_0_234,refute_0_204]) ).
cnf(refute_0_236,plain,
midp(M,X_4087,X_4087),
inference(subst,[],[refute_0_235:[bind(X_1481,$fot(X_4087)),bind(X_1529,$fot(M))]]) ).
cnf(refute_0_237,plain,
cong(X_4087,M,X_4086,M),
inference(resolve,[$cnf( midp(M,X_4087,X_4087) )],[refute_0_236,refute_0_203]) ).
cnf(refute_0_238,plain,
cong(A,P,B,P),
inference(subst,[],[refute_0_237:[bind(M,$fot(P)),bind(X_4086,$fot(B)),bind(X_4087,$fot(A))]]) ).
cnf(refute_0_239,plain,
( ~ cong(A,Q,B,Q)
| perp(A,B,P,Q) ),
inference(resolve,[$cnf( cong(A,P,B,P) )],[refute_0_238,refute_0_1]) ).
cnf(refute_0_240,plain,
cong(A,Q,B,Q),
inference(subst,[],[refute_0_237:[bind(M,$fot(Q)),bind(X_4086,$fot(B)),bind(X_4087,$fot(A))]]) ).
cnf(refute_0_241,plain,
perp(A,B,P,Q),
inference(resolve,[$cnf( cong(A,Q,B,Q) )],[refute_0_240,refute_0_239]) ).
cnf(refute_0_242,plain,
perp(skolemFOFtoCNF_F,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_241:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_E)),bind(P,$fot(skolemFOFtoCNF_C_1)),bind(Q,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_243,plain,
$false,
inference(resolve,[$cnf( perp(skolemFOFtoCNF_F,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D) )],[refute_0_242,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO552+1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 11:35:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 36.31/36.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.31/36.50
% 36.31/36.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.36/36.52
%------------------------------------------------------------------------------