TSTP Solution File: GEO569+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO569+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 05:27:25 EDT 2022
% Result : Theorem 45.01s 45.23s
% Output : CNFRefutation 45.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 95
% Number of leaves : 29
% Syntax : Number of formulae : 422 ( 179 unt; 0 def)
% Number of atoms : 804 ( 0 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 682 ( 300 ~; 295 |; 56 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-6 aty)
% Number of variables : 996 ( 192 sgn 418 !; 14 ?)
% 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(ruleX6,axiom,
! [A,B,C,D,M,N] :
? [P] :
( ( midp(M,A,B)
& midp(N,C,D) )
=> ( midp(P,A,D)
& para(P,M,B,D)
& para(P,N,A,C) ) ) ).
fof(ruleX7,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( midp(M,A,B)
& midp(N,C,D)
& coll(C,A,B)
& coll(D,A,B) )
=> midp(P,A,Q) ) ).
fof(exemplo6GDDFULL214031,conjecture,
! [A,B,C,O,C1,B1,P,Q] :
( ( circle(O,A,B,C)
& midp(C1,B,A)
& midp(B1,C,A)
& coll(P,O,C1)
& coll(P,A,C)
& coll(Q,O,B1)
& coll(Q,A,B) )
=> cyclic(Q,B,C,P) ) ).
fof(subgoal_0,plain,
! [A,B,C,O,C1,B1,P,Q] :
( ( circle(O,A,B,C)
& midp(C1,B,A)
& midp(B1,C,A)
& coll(P,O,C1)
& coll(P,A,C)
& coll(Q,O,B1)
& coll(Q,A,B) )
=> cyclic(Q,B,C,P) ),
inference(strip,[],[exemplo6GDDFULL214031]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,O,C1,B1,P,Q] :
( ( circle(O,A,B,C)
& midp(C1,B,A)
& midp(B1,C,A)
& coll(P,O,C1)
& coll(P,A,C)
& coll(Q,O,B1)
& coll(Q,A,B) )
=> cyclic(Q,B,C,P) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,B1,C,C1,O,P,Q] :
( ~ cyclic(Q,B,C,P)
& circle(O,A,B,C)
& coll(P,A,C)
& coll(P,O,C1)
& coll(Q,A,B)
& coll(Q,O,B1)
& midp(B1,C,A)
& midp(C1,B,A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ cyclic(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_8)
& circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1)
& coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_O_2,skolemFOFtoCNF_B1)
& midp(skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A)
& midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ cyclic(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_8),
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_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A),
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] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_44,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,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_46,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_45]) ).
fof(normalize_0_47,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[ruleD67]) ).
fof(normalize_0_48,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(specialize,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_50,plain,
! [A,B,C,D,M,N] :
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| ? [P] :
( midp(P,A,D)
& para(P,M,B,D)
& para(P,N,A,C) ) ),
inference(canonicalize,[],[ruleX6]) ).
fof(normalize_0_51,plain,
! [A,B,C,D,M,N] :
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| ? [P] :
( midp(P,A,D)
& para(P,M,B,D)
& para(P,N,A,C) ) ),
inference(specialize,[],[normalize_0_50]) ).
fof(normalize_0_52,plain,
! [A,B,C,D,M,N] :
( ( ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P(A,B,C,D,M,N),A,D) )
& ( ~ midp(M,A,B)
| ~ midp(N,C,D)
| para(skolemFOFtoCNF_P(A,B,C,D,M,N),M,B,D) )
& ( ~ midp(M,A,B)
| ~ midp(N,C,D)
| para(skolemFOFtoCNF_P(A,B,C,D,M,N),N,A,C) ) ),
inference(clausify,[],[normalize_0_51]) ).
fof(normalize_0_53,plain,
! [A,B,C,D,M,N] :
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P(A,B,C,D,M,N),A,D) ),
inference(conjunct,[],[normalize_0_52]) ).
fof(normalize_0_54,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_55,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_54]) ).
fof(normalize_0_56,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_57,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_56]) ).
fof(normalize_0_58,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_59,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(specialize,[],[normalize_0_58]) ).
fof(normalize_0_60,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_61,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(specialize,[],[normalize_0_60]) ).
fof(normalize_0_62,plain,
coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_63,plain,
coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_64,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[ruleD11]) ).
fof(normalize_0_65,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(specialize,[],[normalize_0_64]) ).
fof(normalize_0_66,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD69]) ).
fof(normalize_0_67,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_66]) ).
cnf(refute_0_0,plain,
~ cyclic(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_8),
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_11548,X_11547,X_11548,X_11549)
| cyclic(X_11548,X_11548,X_11547,X_11549) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_11548)),bind(B,$fot(X_11547)),bind(C,$fot(X_11548)),bind(D,$fot(X_11549))]]) ).
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_11544,X_11545,X_11545,X_11546)
| cyclic(X_11545,X_11544,X_11545,X_11546) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_11544)),bind(B,$fot(X_11545)),bind(C,$fot(X_11545)),bind(D,$fot(X_11546))]]) ).
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,$fot(C))]]) ).
cnf(refute_0_7,plain,
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ cong(X_3795,X_3796,X_3797,X_3795)
| cong(X_3795,X_3796,X_3795,X_3797) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_3795)),bind(B,$fot(X_3796)),bind(C,$fot(X_3797)),bind(D,$fot(X_3795))]]) ).
cnf(refute_0_9,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ cong(X_3778,X_3776,X_3776,X_3777)
| cong(X_3776,X_3777,X_3778,X_3776) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_3778)),bind(B,$fot(X_3776)),bind(C,$fot(X_3776)),bind(D,$fot(X_3777))]]) ).
cnf(refute_0_11,plain,
( ~ cong(X_3775,X_3773,X_3774,X_3773)
| cong(X_3775,X_3773,X_3773,X_3774) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_3775)),bind(B,$fot(X_3773)),bind(C,$fot(X_3774)),bind(D,$fot(X_3773))]]) ).
cnf(refute_0_12,plain,
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
( ~ midp(M,X_3756,X_3756)
| ~ perp(X_3756,X_3755,X_3755,X_3756)
| cong(X_3756,M,X_3755,M) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_3756)),bind(B,$fot(X_3755)),bind(C,$fot(X_3756))]]) ).
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_3753,X_3754,X_3753,X_3754)
| ~ cyclic(X_3753,X_3753,X_3754,X_3754)
| perp(X_3754,X_3753,X_3753,X_3754) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_3753)),bind(B,$fot(X_3753)),bind(P,$fot(X_3754)),bind(Q,$fot(X_3754))]]) ).
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_3751,X_3751,X_3751,X_3752)
| cyclic(X_3751,X_3751,X_3752,X_3752) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_3751)),bind(B,$fot(X_3751)),bind(C,$fot(X_3751)),bind(D,$fot(X_3752)),bind(E,$fot(X_3752))]]) ).
cnf(refute_0_18,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_19,plain,
( ~ cyclic(X_3749,X_3749,X_3750,X_3749)
| cyclic(X_3749,X_3749,X_3749,X_3750) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(X_3749)),bind(B,$fot(X_3749)),bind(C,$fot(X_3750)),bind(D,$fot(X_3749))]]) ).
cnf(refute_0_20,plain,
( ~ cyclic(X_3747,X_3748,X_3747,X_3747)
| cyclic(X_3747,X_3747,X_3748,X_3747) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_3747)),bind(B,$fot(X_3748)),bind(C,$fot(X_3747)),bind(D,$fot(X_3747))]]) ).
cnf(refute_0_21,plain,
( ~ cyclic(X_3746,X_3745,X_3745,X_3745)
| cyclic(X_3745,X_3746,X_3745,X_3745) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_3746)),bind(B,$fot(X_3745)),bind(C,$fot(X_3745)),bind(D,$fot(X_3745))]]) ).
cnf(refute_0_22,plain,
( ~ cong(skolemFOFtoCNF_P_1(X_3744,X_3743),X_3744,skolemFOFtoCNF_P_1(X_3744,X_3743),X_3743)
| cyclic(X_3744,X_3743,X_3743,X_3743) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_3744)),bind(B,$fot(X_3743)),bind(C,$fot(X_3743)),bind(D,$fot(X_3743)),bind(O,$fot(skolemFOFtoCNF_P_1(X_3744,X_3743)))]]) ).
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_2772,X_2771),X_2772,X_2771)
| cong(skolemFOFtoCNF_P_1(X_2772,X_2771),X_2772,skolemFOFtoCNF_P_1(X_2772,X_2771),X_2771) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_P_1(X_2772,X_2771))),bind(B,$fot(X_2772)),bind(C,$fot(X_2771))]]) ).
cnf(refute_0_25,plain,
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P_1(A,Q),A,Q) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_26,plain,
( ~ coll(X_2595,X_2595,X_2595)
| ~ midp(N,X_2595,X_2595)
| midp(skolemFOFtoCNF_P_1(X_2595,Q),X_2595,Q) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_2595)),bind(B,$fot(X_2595)),bind(C,$fot(X_2595)),bind(D,$fot(X_2595)),bind(M,$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_467,X_466,X_467)
| coll(X_467,X_467,X_466) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_467)),bind(B,$fot(X_466)),bind(C,$fot(X_467))]]) ).
cnf(refute_0_29,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_30,plain,
( ~ coll(X_462,X_463,X_463)
| coll(X_463,X_462,X_463) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_462)),bind(B,$fot(X_463)),bind(C,$fot(X_463))]]) ).
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_460,X_461,X_460,X_461)
| coll(X_460,X_461,X_461) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(X_460)),bind(B,$fot(X_461)),bind(C,$fot(X_461))]]) ).
cnf(refute_0_33,plain,
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_34,plain,
( ~ eqangle(X_458,X_459,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_458,X_459,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(X_458,X_459,X_458,X_459) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(X_458)),bind(B,$fot(X_459)),bind(C,$fot(X_458)),bind(D,$fot(X_459)),bind(P,$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_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B1,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,$fot(skolemFOFtoCNF_B1))]]) ).
cnf(refute_0_39,plain,
midp(skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_40,plain,
( ~ midp(skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_B1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_41,plain,
cong(skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B1,skolemFOFtoCNF_A) )],[refute_0_41,refute_0_38]) ).
cnf(refute_0_43,plain,
cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_42,refute_0_37]) ).
cnf(refute_0_44,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_43,refute_0_36]) ).
cnf(refute_0_45,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_46,plain,
para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_48,plain,
( ~ para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154) ),
inference(subst,[],[refute_0_47:[bind(A,$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,$fot(X_154))]]) ).
cnf(refute_0_49,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_46,refute_0_48]) ).
cnf(refute_0_50,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_456,X_457,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_456,X_457),
inference(subst,[],[refute_0_49:[bind(X_153,$fot(X_456)),bind(X_154,$fot(X_457))]]) ).
cnf(refute_0_51,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_52,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_456,X_457,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_456,X_457)
| eqangle(X_456,X_457,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_456,X_457,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_51:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(X_456)),bind(D,$fot(X_457)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A)),bind(U,$fot(X_456)),bind(V,$fot(X_457))]]) ).
cnf(refute_0_53,plain,
eqangle(X_456,X_457,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_456,X_457,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_456,X_457,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_456,X_457) )],[refute_0_50,refute_0_52]) ).
cnf(refute_0_54,plain,
eqangle(X_458,X_459,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_458,X_459,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_53:[bind(X_456,$fot(X_458)),bind(X_457,$fot(X_459))]]) ).
cnf(refute_0_55,plain,
para(X_458,X_459,X_458,X_459),
inference(resolve,[$cnf( eqangle(X_458,X_459,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_458,X_459,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_54,refute_0_34]) ).
cnf(refute_0_56,plain,
para(X_460,X_461,X_460,X_461),
inference(subst,[],[refute_0_55:[bind(X_458,$fot(X_460)),bind(X_459,$fot(X_461))]]) ).
cnf(refute_0_57,plain,
coll(X_460,X_461,X_461),
inference(resolve,[$cnf( para(X_460,X_461,X_460,X_461) )],[refute_0_56,refute_0_32]) ).
cnf(refute_0_58,plain,
coll(X_462,X_463,X_463),
inference(subst,[],[refute_0_57:[bind(X_460,$fot(X_462)),bind(X_461,$fot(X_463))]]) ).
cnf(refute_0_59,plain,
coll(X_463,X_462,X_463),
inference(resolve,[$cnf( coll(X_462,X_463,X_463) )],[refute_0_58,refute_0_30]) ).
cnf(refute_0_60,plain,
coll(X_467,X_466,X_467),
inference(subst,[],[refute_0_59:[bind(X_462,$fot(X_466)),bind(X_463,$fot(X_467))]]) ).
cnf(refute_0_61,plain,
coll(X_467,X_467,X_466),
inference(resolve,[$cnf( coll(X_467,X_466,X_467) )],[refute_0_60,refute_0_28]) ).
cnf(refute_0_62,plain,
coll(X_2473,X_2473,X_2474),
inference(subst,[],[refute_0_61:[bind(X_466,$fot(X_2474)),bind(X_467,$fot(X_2473))]]) ).
cnf(refute_0_63,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_64,plain,
( ~ coll(X_2473,X_2473,X_2474)
| ~ coll(X_2473,X_2473,X_2475)
| coll(X_2474,X_2475,X_2473) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_2473)),bind(B,$fot(X_2473)),bind(C,$fot(X_2474)),bind(D,$fot(X_2475))]]) ).
cnf(refute_0_65,plain,
( ~ coll(X_2473,X_2473,X_2475)
| coll(X_2474,X_2475,X_2473) ),
inference(resolve,[$cnf( coll(X_2473,X_2473,X_2474) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
coll(X_2473,X_2473,X_2475),
inference(subst,[],[refute_0_61:[bind(X_466,$fot(X_2475)),bind(X_467,$fot(X_2473))]]) ).
cnf(refute_0_67,plain,
coll(X_2474,X_2475,X_2473),
inference(resolve,[$cnf( coll(X_2473,X_2473,X_2475) )],[refute_0_66,refute_0_65]) ).
cnf(refute_0_68,plain,
coll(X_2595,X_2595,X_2595),
inference(subst,[],[refute_0_67:[bind(X_2473,$fot(X_2595)),bind(X_2474,$fot(X_2595)),bind(X_2475,$fot(X_2595))]]) ).
cnf(refute_0_69,plain,
( ~ midp(N,X_2595,X_2595)
| midp(skolemFOFtoCNF_P_1(X_2595,Q),X_2595,Q) ),
inference(resolve,[$cnf( coll(X_2595,X_2595,X_2595) )],[refute_0_68,refute_0_26]) ).
cnf(refute_0_70,plain,
( ~ midp(skolemFOFtoCNF_B_1,X_2716,X_2716)
| midp(skolemFOFtoCNF_P_1(X_2716,Q),X_2716,Q) ),
inference(subst,[],[refute_0_69:[bind(N,$fot(skolemFOFtoCNF_B_1)),bind(X_2595,$fot(X_2716))]]) ).
cnf(refute_0_71,plain,
para(X_2605,X_2606,X_2605,X_2606),
inference(subst,[],[refute_0_55:[bind(X_458,$fot(X_2605)),bind(X_459,$fot(X_2606))]]) ).
cnf(refute_0_72,plain,
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_73,plain,
( ~ midp(X_2607,X_2605,X_2605)
| ~ para(X_2605,X_2606,X_2605,X_2606)
| midp(X_2607,X_2606,X_2606) ),
inference(subst,[],[refute_0_72:[bind(A,$fot(X_2605)),bind(B,$fot(X_2605)),bind(C,$fot(X_2606)),bind(D,$fot(X_2606)),bind(M,$fot(X_2607))]]) ).
cnf(refute_0_74,plain,
( ~ midp(X_2607,X_2605,X_2605)
| midp(X_2607,X_2606,X_2606) ),
inference(resolve,[$cnf( para(X_2605,X_2606,X_2605,X_2606) )],[refute_0_71,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1))
| midp(skolemFOFtoCNF_B_1,X_2606,X_2606) ),
inference(subst,[],[refute_0_74:[bind(X_2605,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1))),bind(X_2607,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_76,plain,
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_77,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1))
| ~ cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1))
| midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1))),bind(C,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)))]]) ).
cnf(refute_0_78,plain,
midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_49]) ).
cnf(refute_0_79,plain,
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P(A,B,C,D,M,N),A,D) ),
inference(canonicalize,[],[normalize_0_53]) ).
cnf(refute_0_80,plain,
( ~ midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_79:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_A)),bind(M,$fot(skolemFOFtoCNF_C1)),bind(N,$fot(skolemFOFtoCNF_C1))]]) ).
cnf(refute_0_81,plain,
midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_78,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| ~ perp(skolemFOFtoCNF_B_1,X_2640,X_2640,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),X_2640,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_2640)),bind(C,$fot(skolemFOFtoCNF_A)),bind(M,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)))]]) ).
cnf(refute_0_83,plain,
( ~ perp(skolemFOFtoCNF_B_1,X_2640,X_2640,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),X_2640,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)) ),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)) ),
inference(subst,[],[refute_0_83:[bind(X_2640,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_85,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_86,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_85:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_87,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_88,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_87:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_89,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[normalize_0_59]) ).
cnf(refute_0_90,plain,
( ~ cong(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1)
| circle(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_89:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(O,$fot(skolemFOFtoCNF_C1))]]) ).
cnf(refute_0_91,plain,
( ~ cong(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_C1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C1)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_92,plain,
( ~ midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_C1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_93,plain,
cong(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_78,refute_0_92]) ).
cnf(refute_0_94,plain,
cong(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C1,skolemFOFtoCNF_A) )],[refute_0_93,refute_0_91]) ).
cnf(refute_0_95,plain,
circle(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1) )],[refute_0_94,refute_0_90]) ).
cnf(refute_0_96,plain,
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[normalize_0_61]) ).
cnf(refute_0_97,plain,
( ~ coll(X_2589,skolemFOFtoCNF_Q_3,C)
| ~ coll(X_2589,skolemFOFtoCNF_Q_3,X_2590)
| coll(C,X_2590,X_2589) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_2589)),bind(B,$fot(skolemFOFtoCNF_Q_3)),bind(D,$fot(X_2590))]]) ).
cnf(refute_0_98,plain,
( ~ coll(X_2509,X_2510,skolemFOFtoCNF_Q_3)
| coll(X_2509,skolemFOFtoCNF_Q_3,X_2510) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_2509)),bind(B,$fot(X_2510)),bind(C,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_99,plain,
( ~ coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,C)
| ~ coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,X_2508)
| coll(C,X_2508,skolemFOFtoCNF_Q_3) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_Q_3)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_2508))]]) ).
cnf(refute_0_100,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,X_2505)
| coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,X_2505) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_Q_3)),bind(C,$fot(X_2505))]]) ).
cnf(refute_0_101,plain,
( ~ coll(skolemFOFtoCNF_A,X_2500,skolemFOFtoCNF_Q_3)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,X_2500) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_2500)),bind(C,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_102,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_Q_3) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_Q_3)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_103,plain,
coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_62]) ).
cnf(refute_0_104,plain,
( ~ coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_Q_3)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_105,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_Q_3),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_B_1) )],[refute_0_105,refute_0_102]) ).
cnf(refute_0_107,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_Q_3)
| coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_Q_3)),bind(D,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_108,plain,
coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_Q_3) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
( ~ coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,X_2475)
| ~ coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,X_2475,skolemFOFtoCNF_Q_3) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_Q_3)),bind(B,$fot(skolemFOFtoCNF_Q_3)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_2475))]]) ).
cnf(refute_0_110,plain,
( ~ coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,X_2475)
| coll(skolemFOFtoCNF_A,X_2475,skolemFOFtoCNF_Q_3) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,X_2475),
inference(subst,[],[refute_0_61:[bind(X_466,$fot(X_2475)),bind(X_467,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_112,plain,
coll(skolemFOFtoCNF_A,X_2475,skolemFOFtoCNF_Q_3),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_Q_3,X_2475) )],[refute_0_111,refute_0_110]) ).
cnf(refute_0_113,plain,
coll(skolemFOFtoCNF_A,X_2500,skolemFOFtoCNF_Q_3),
inference(subst,[],[refute_0_112:[bind(X_2475,$fot(X_2500))]]) ).
cnf(refute_0_114,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,X_2500),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_2500,skolemFOFtoCNF_Q_3) )],[refute_0_113,refute_0_101]) ).
cnf(refute_0_115,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,X_2505),
inference(subst,[],[refute_0_114:[bind(X_2500,$fot(X_2505))]]) ).
cnf(refute_0_116,plain,
coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,X_2505),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,X_2505) )],[refute_0_115,refute_0_100]) ).
cnf(refute_0_117,plain,
coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,X_2508),
inference(subst,[],[refute_0_116:[bind(X_2505,$fot(X_2508))]]) ).
cnf(refute_0_118,plain,
( ~ coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,C)
| coll(C,X_2508,skolemFOFtoCNF_Q_3) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,X_2508) )],[refute_0_117,refute_0_99]) ).
cnf(refute_0_119,plain,
coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_67:[bind(X_2473,$fot(C)),bind(X_2474,$fot(skolemFOFtoCNF_Q_3)),bind(X_2475,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_120,plain,
coll(C,X_2508,skolemFOFtoCNF_Q_3),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,C) )],[refute_0_119,refute_0_118]) ).
cnf(refute_0_121,plain,
coll(X_2509,X_2510,skolemFOFtoCNF_Q_3),
inference(subst,[],[refute_0_120:[bind(C,$fot(X_2509)),bind(X_2508,$fot(X_2510))]]) ).
cnf(refute_0_122,plain,
coll(X_2509,skolemFOFtoCNF_Q_3,X_2510),
inference(resolve,[$cnf( coll(X_2509,X_2510,skolemFOFtoCNF_Q_3) )],[refute_0_121,refute_0_98]) ).
cnf(refute_0_123,plain,
coll(X_2589,skolemFOFtoCNF_Q_3,X_2590),
inference(subst,[],[refute_0_122:[bind(X_2509,$fot(X_2589)),bind(X_2510,$fot(X_2590))]]) ).
cnf(refute_0_124,plain,
( ~ coll(X_2589,skolemFOFtoCNF_Q_3,C)
| coll(C,X_2590,X_2589) ),
inference(resolve,[$cnf( coll(X_2589,skolemFOFtoCNF_Q_3,X_2590) )],[refute_0_123,refute_0_97]) ).
cnf(refute_0_125,plain,
( ~ coll(X_2587,skolemFOFtoCNF_A,C)
| ~ coll(X_2587,skolemFOFtoCNF_A,X_2588)
| coll(C,X_2588,X_2587) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_2587)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_2588))]]) ).
cnf(refute_0_126,plain,
( ~ coll(X_2506,X_2507,skolemFOFtoCNF_A)
| coll(X_2506,skolemFOFtoCNF_A,X_2507) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_2506)),bind(B,$fot(X_2507)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_127,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,C)
| ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,X_2505)
| coll(C,X_2505,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_Q_3)),bind(D,$fot(X_2505))]]) ).
cnf(refute_0_128,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,C)
| coll(C,X_2505,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,X_2505) )],[refute_0_115,refute_0_127]) ).
cnf(refute_0_129,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,C),
inference(subst,[],[refute_0_67:[bind(X_2473,$fot(C)),bind(X_2474,$fot(skolemFOFtoCNF_A)),bind(X_2475,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_130,plain,
coll(C,X_2505,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_Q_3,C) )],[refute_0_129,refute_0_128]) ).
cnf(refute_0_131,plain,
coll(X_2506,X_2507,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_130:[bind(C,$fot(X_2506)),bind(X_2505,$fot(X_2507))]]) ).
cnf(refute_0_132,plain,
coll(X_2506,skolemFOFtoCNF_A,X_2507),
inference(resolve,[$cnf( coll(X_2506,X_2507,skolemFOFtoCNF_A) )],[refute_0_131,refute_0_126]) ).
cnf(refute_0_133,plain,
coll(X_2587,skolemFOFtoCNF_A,X_2588),
inference(subst,[],[refute_0_132:[bind(X_2506,$fot(X_2587)),bind(X_2507,$fot(X_2588))]]) ).
cnf(refute_0_134,plain,
( ~ coll(X_2587,skolemFOFtoCNF_A,C)
| coll(C,X_2588,X_2587) ),
inference(resolve,[$cnf( coll(X_2587,skolemFOFtoCNF_A,X_2588) )],[refute_0_133,refute_0_125]) ).
cnf(refute_0_135,plain,
( ~ coll(X_2576,skolemFOFtoCNF_O_2,C)
| ~ coll(X_2576,skolemFOFtoCNF_O_2,X_2577)
| coll(C,X_2577,X_2576) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_2576)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(X_2577))]]) ).
cnf(refute_0_136,plain,
( ~ coll(X_2546,X_2547,skolemFOFtoCNF_O_2)
| coll(X_2546,skolemFOFtoCNF_O_2,X_2547) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_2546)),bind(B,$fot(X_2547)),bind(C,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_137,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1,C)
| ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1,X_2545)
| coll(C,X_2545,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(skolemFOFtoCNF_C1)),bind(D,$fot(X_2545))]]) ).
cnf(refute_0_138,plain,
( ~ coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2,X_2544)
| coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1,X_2544) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_C1)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(C,$fot(X_2544))]]) ).
cnf(refute_0_139,plain,
( ~ coll(skolemFOFtoCNF_C1,X_2535,skolemFOFtoCNF_O_2)
| coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2,X_2535) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_C1)),bind(B,$fot(X_2535)),bind(C,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_140,plain,
coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1),
inference(canonicalize,[],[normalize_0_63]) ).
cnf(refute_0_141,plain,
( ~ coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1)
| coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_P_8)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(C,$fot(skolemFOFtoCNF_C1))]]) ).
cnf(refute_0_142,plain,
coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
( ~ coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2)
| coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_P_8)),bind(B,$fot(skolemFOFtoCNF_C1)),bind(C,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_144,plain,
coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
( ~ coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_O_2)
| coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_C1)),bind(B,$fot(skolemFOFtoCNF_P_8)),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_146,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_P_8,skolemFOFtoCNF_O_2) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_2475)
| ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1)
| coll(skolemFOFtoCNF_C1,X_2475,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(C,$fot(skolemFOFtoCNF_C1)),bind(D,$fot(X_2475))]]) ).
cnf(refute_0_148,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_2475)
| coll(skolemFOFtoCNF_C1,X_2475,skolemFOFtoCNF_O_2) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_2475),
inference(subst,[],[refute_0_61:[bind(X_466,$fot(X_2475)),bind(X_467,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_150,plain,
coll(skolemFOFtoCNF_C1,X_2475,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_2475) )],[refute_0_149,refute_0_148]) ).
cnf(refute_0_151,plain,
coll(skolemFOFtoCNF_C1,X_2535,skolemFOFtoCNF_O_2),
inference(subst,[],[refute_0_150:[bind(X_2475,$fot(X_2535))]]) ).
cnf(refute_0_152,plain,
coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2,X_2535),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C1,X_2535,skolemFOFtoCNF_O_2) )],[refute_0_151,refute_0_139]) ).
cnf(refute_0_153,plain,
coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2,X_2544),
inference(subst,[],[refute_0_152:[bind(X_2535,$fot(X_2544))]]) ).
cnf(refute_0_154,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1,X_2544),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2,X_2544) )],[refute_0_153,refute_0_138]) ).
cnf(refute_0_155,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1,X_2545),
inference(subst,[],[refute_0_154:[bind(X_2544,$fot(X_2545))]]) ).
cnf(refute_0_156,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1,C)
| coll(C,X_2545,skolemFOFtoCNF_O_2) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1,X_2545) )],[refute_0_155,refute_0_137]) ).
cnf(refute_0_157,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1,C),
inference(subst,[],[refute_0_67:[bind(X_2473,$fot(C)),bind(X_2474,$fot(skolemFOFtoCNF_O_2)),bind(X_2475,$fot(skolemFOFtoCNF_C1))]]) ).
cnf(refute_0_158,plain,
coll(C,X_2545,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_C1,C) )],[refute_0_157,refute_0_156]) ).
cnf(refute_0_159,plain,
coll(X_2546,X_2547,skolemFOFtoCNF_O_2),
inference(subst,[],[refute_0_158:[bind(C,$fot(X_2546)),bind(X_2545,$fot(X_2547))]]) ).
cnf(refute_0_160,plain,
coll(X_2546,skolemFOFtoCNF_O_2,X_2547),
inference(resolve,[$cnf( coll(X_2546,X_2547,skolemFOFtoCNF_O_2) )],[refute_0_159,refute_0_136]) ).
cnf(refute_0_161,plain,
coll(X_2576,skolemFOFtoCNF_O_2,X_2577),
inference(subst,[],[refute_0_160:[bind(X_2546,$fot(X_2576)),bind(X_2547,$fot(X_2577))]]) ).
cnf(refute_0_162,plain,
( ~ coll(X_2576,skolemFOFtoCNF_O_2,C)
| coll(C,X_2577,X_2576) ),
inference(resolve,[$cnf( coll(X_2576,skolemFOFtoCNF_O_2,X_2577) )],[refute_0_161,refute_0_135]) ).
cnf(refute_0_163,plain,
( ~ coll(X_2557,skolemFOFtoCNF_P_8,C)
| ~ coll(X_2557,skolemFOFtoCNF_P_8,X_2558)
| coll(C,X_2558,X_2557) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_2557)),bind(B,$fot(skolemFOFtoCNF_P_8)),bind(D,$fot(X_2558))]]) ).
cnf(refute_0_164,plain,
( ~ coll(X_2556,skolemFOFtoCNF_O_2,C)
| ~ coll(X_2556,skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_8)
| coll(C,skolemFOFtoCNF_P_8,X_2556) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_2556)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(skolemFOFtoCNF_P_8))]]) ).
cnf(refute_0_165,plain,
( ~ coll(skolemFOFtoCNF_P_8,X_2536,C)
| ~ coll(skolemFOFtoCNF_P_8,X_2536,skolemFOFtoCNF_O_2)
| coll(C,skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_8) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_P_8)),bind(B,$fot(X_2536)),bind(D,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_166,plain,
( ~ coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2)
| coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_8) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_P_8)),bind(B,$fot(skolemFOFtoCNF_C1)),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_167,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_8),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_C1,skolemFOFtoCNF_O_2) )],[refute_0_142,refute_0_166]) ).
cnf(refute_0_168,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_2475)
| ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_8)
| coll(skolemFOFtoCNF_P_8,X_2475,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(C,$fot(skolemFOFtoCNF_P_8)),bind(D,$fot(X_2475))]]) ).
cnf(refute_0_169,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_2475)
| coll(skolemFOFtoCNF_P_8,X_2475,skolemFOFtoCNF_O_2) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_8) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
coll(skolemFOFtoCNF_P_8,X_2475,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_O_2,X_2475) )],[refute_0_149,refute_0_169]) ).
cnf(refute_0_171,plain,
coll(skolemFOFtoCNF_P_8,X_2536,skolemFOFtoCNF_O_2),
inference(subst,[],[refute_0_170:[bind(X_2475,$fot(X_2536))]]) ).
cnf(refute_0_172,plain,
( ~ coll(skolemFOFtoCNF_P_8,X_2536,C)
| coll(C,skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_8) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_8,X_2536,skolemFOFtoCNF_O_2) )],[refute_0_171,refute_0_165]) ).
cnf(refute_0_173,plain,
coll(skolemFOFtoCNF_P_8,X_2536,C),
inference(subst,[],[refute_0_67:[bind(X_2473,$fot(C)),bind(X_2474,$fot(skolemFOFtoCNF_P_8)),bind(X_2475,$fot(X_2536))]]) ).
cnf(refute_0_174,plain,
coll(C,skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_8),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_8,X_2536,C) )],[refute_0_173,refute_0_172]) ).
cnf(refute_0_175,plain,
coll(X_2556,skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_8),
inference(subst,[],[refute_0_174:[bind(C,$fot(X_2556))]]) ).
cnf(refute_0_176,plain,
( ~ coll(X_2556,skolemFOFtoCNF_O_2,C)
| coll(C,skolemFOFtoCNF_P_8,X_2556) ),
inference(resolve,[$cnf( coll(X_2556,skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_8) )],[refute_0_175,refute_0_164]) ).
cnf(refute_0_177,plain,
( ~ coll(X_2554,skolemFOFtoCNF_C_1,C)
| ~ coll(X_2554,skolemFOFtoCNF_C_1,X_2555)
| coll(C,X_2555,X_2554) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_2554)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_2555))]]) ).
cnf(refute_0_178,plain,
( ~ coll(X_2528,X_2529,skolemFOFtoCNF_C_1)
| coll(X_2528,skolemFOFtoCNF_C_1,X_2529) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_2528)),bind(B,$fot(X_2529)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_179,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,C)
| ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,X_2527)
| coll(C,X_2527,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_2527))]]) ).
cnf(refute_0_180,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,X_2518)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,X_2518) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(X_2518))]]) ).
cnf(refute_0_181,plain,
( ~ coll(skolemFOFtoCNF_A,X_2495,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,X_2495) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_2495)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_182,plain,
( ~ coll(skolemFOFtoCNF_B1,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_B1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_183,plain,
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[normalize_0_65]) ).
cnf(refute_0_184,plain,
( ~ midp(skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_B1,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_183:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(M,$fot(skolemFOFtoCNF_B1))]]) ).
cnf(refute_0_185,plain,
midp(skolemFOFtoCNF_B1,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) )],[refute_0_39,refute_0_184]) ).
cnf(refute_0_186,plain,
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_67]) ).
cnf(refute_0_187,plain,
( ~ midp(skolemFOFtoCNF_B1,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_B1,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_186:[bind(A,$fot(skolemFOFtoCNF_B1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_188,plain,
coll(skolemFOFtoCNF_B1,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B1,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) )],[refute_0_185,refute_0_187]) ).
cnf(refute_0_189,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B1,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) )],[refute_0_188,refute_0_182]) ).
cnf(refute_0_190,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_191,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B1,skolemFOFtoCNF_C_1) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2475)
| ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,X_2475,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_2475))]]) ).
cnf(refute_0_193,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2475)
| coll(skolemFOFtoCNF_A,X_2475,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2475),
inference(subst,[],[refute_0_61:[bind(X_466,$fot(X_2475)),bind(X_467,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_195,plain,
coll(skolemFOFtoCNF_A,X_2475,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_2475) )],[refute_0_194,refute_0_193]) ).
cnf(refute_0_196,plain,
coll(skolemFOFtoCNF_A,X_2495,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_195:[bind(X_2475,$fot(X_2495))]]) ).
cnf(refute_0_197,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,X_2495),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_2495,skolemFOFtoCNF_C_1) )],[refute_0_196,refute_0_181]) ).
cnf(refute_0_198,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,X_2518),
inference(subst,[],[refute_0_197:[bind(X_2495,$fot(X_2518))]]) ).
cnf(refute_0_199,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,X_2518),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,X_2518) )],[refute_0_198,refute_0_180]) ).
cnf(refute_0_200,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,X_2527),
inference(subst,[],[refute_0_199:[bind(X_2518,$fot(X_2527))]]) ).
cnf(refute_0_201,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,C)
| coll(C,X_2527,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,X_2527) )],[refute_0_200,refute_0_179]) ).
cnf(refute_0_202,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_67:[bind(X_2473,$fot(C)),bind(X_2474,$fot(skolemFOFtoCNF_C_1)),bind(X_2475,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_203,plain,
coll(C,X_2527,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,C) )],[refute_0_202,refute_0_201]) ).
cnf(refute_0_204,plain,
coll(X_2528,X_2529,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_203:[bind(C,$fot(X_2528)),bind(X_2527,$fot(X_2529))]]) ).
cnf(refute_0_205,plain,
coll(X_2528,skolemFOFtoCNF_C_1,X_2529),
inference(resolve,[$cnf( coll(X_2528,X_2529,skolemFOFtoCNF_C_1) )],[refute_0_204,refute_0_178]) ).
cnf(refute_0_206,plain,
coll(X_2554,skolemFOFtoCNF_C_1,X_2555),
inference(subst,[],[refute_0_205:[bind(X_2528,$fot(X_2554)),bind(X_2529,$fot(X_2555))]]) ).
cnf(refute_0_207,plain,
( ~ coll(X_2554,skolemFOFtoCNF_C_1,C)
| coll(C,X_2555,X_2554) ),
inference(resolve,[$cnf( coll(X_2554,skolemFOFtoCNF_C_1,X_2555) )],[refute_0_206,refute_0_177]) ).
cnf(refute_0_208,plain,
( ~ coll(X_2550,skolemFOFtoCNF_B_1,C)
| ~ coll(X_2550,skolemFOFtoCNF_B_1,X_2551)
| coll(C,X_2551,X_2550) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_2550)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_2551))]]) ).
cnf(refute_0_209,plain,
( ~ coll(X_2515,skolemFOFtoCNF_A,C)
| ~ coll(X_2515,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(C,skolemFOFtoCNF_B_1,X_2515) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_2515)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_210,plain,
( ~ coll(skolemFOFtoCNF_A,X_2489,skolemFOFtoCNF_B_1)
| coll(X_2489,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_2489)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_211,plain,
( ~ coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_C1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_212,plain,
( ~ midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_183:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(M,$fot(skolemFOFtoCNF_C1))]]) ).
cnf(refute_0_213,plain,
midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_78,refute_0_212]) ).
cnf(refute_0_214,plain,
( ~ midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_186:[bind(A,$fot(skolemFOFtoCNF_C1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_215,plain,
coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_215,refute_0_211]) ).
cnf(refute_0_217,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_C1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_218,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_B_1) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2475)
| ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,X_2475,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_2475))]]) ).
cnf(refute_0_220,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2475)
| coll(skolemFOFtoCNF_A,X_2475,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2475),
inference(subst,[],[refute_0_61:[bind(X_466,$fot(X_2475)),bind(X_467,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_222,plain,
coll(skolemFOFtoCNF_A,X_2475,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2475) )],[refute_0_221,refute_0_220]) ).
cnf(refute_0_223,plain,
coll(skolemFOFtoCNF_A,X_2489,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_222:[bind(X_2475,$fot(X_2489))]]) ).
cnf(refute_0_224,plain,
coll(X_2489,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_2489,skolemFOFtoCNF_B_1) )],[refute_0_223,refute_0_210]) ).
cnf(refute_0_225,plain,
coll(X_2515,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_224:[bind(X_2489,$fot(X_2515))]]) ).
cnf(refute_0_226,plain,
( ~ coll(X_2515,skolemFOFtoCNF_A,C)
| coll(C,skolemFOFtoCNF_B_1,X_2515) ),
inference(resolve,[$cnf( coll(X_2515,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_225,refute_0_209]) ).
cnf(refute_0_227,plain,
coll(X_2515,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_67:[bind(X_2473,$fot(C)),bind(X_2474,$fot(X_2515)),bind(X_2475,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_228,plain,
coll(C,skolemFOFtoCNF_B_1,X_2515),
inference(resolve,[$cnf( coll(X_2515,skolemFOFtoCNF_A,C) )],[refute_0_227,refute_0_226]) ).
cnf(refute_0_229,plain,
coll(X_2550,skolemFOFtoCNF_B_1,X_2551),
inference(subst,[],[refute_0_228:[bind(C,$fot(X_2550)),bind(X_2515,$fot(X_2551))]]) ).
cnf(refute_0_230,plain,
( ~ coll(X_2550,skolemFOFtoCNF_B_1,C)
| coll(C,X_2551,X_2550) ),
inference(resolve,[$cnf( coll(X_2550,skolemFOFtoCNF_B_1,X_2551) )],[refute_0_229,refute_0_208]) ).
cnf(refute_0_231,plain,
coll(X_2550,skolemFOFtoCNF_B_1,C),
inference(subst,[],[refute_0_67:[bind(X_2473,$fot(C)),bind(X_2474,$fot(X_2550)),bind(X_2475,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_232,plain,
coll(C,X_2551,X_2550),
inference(resolve,[$cnf( coll(X_2550,skolemFOFtoCNF_B_1,C) )],[refute_0_231,refute_0_230]) ).
cnf(refute_0_233,plain,
coll(X_2554,skolemFOFtoCNF_C_1,C),
inference(subst,[],[refute_0_232:[bind(C,$fot(X_2554)),bind(X_2550,$fot(C)),bind(X_2551,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_234,plain,
coll(C,X_2555,X_2554),
inference(resolve,[$cnf( coll(X_2554,skolemFOFtoCNF_C_1,C) )],[refute_0_233,refute_0_207]) ).
cnf(refute_0_235,plain,
coll(X_2556,skolemFOFtoCNF_O_2,C),
inference(subst,[],[refute_0_234:[bind(C,$fot(X_2556)),bind(X_2554,$fot(C)),bind(X_2555,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_236,plain,
coll(C,skolemFOFtoCNF_P_8,X_2556),
inference(resolve,[$cnf( coll(X_2556,skolemFOFtoCNF_O_2,C) )],[refute_0_235,refute_0_176]) ).
cnf(refute_0_237,plain,
coll(X_2557,skolemFOFtoCNF_P_8,X_2558),
inference(subst,[],[refute_0_236:[bind(C,$fot(X_2557)),bind(X_2556,$fot(X_2558))]]) ).
cnf(refute_0_238,plain,
( ~ coll(X_2557,skolemFOFtoCNF_P_8,C)
| coll(C,X_2558,X_2557) ),
inference(resolve,[$cnf( coll(X_2557,skolemFOFtoCNF_P_8,X_2558) )],[refute_0_237,refute_0_163]) ).
cnf(refute_0_239,plain,
coll(X_2557,skolemFOFtoCNF_P_8,C),
inference(subst,[],[refute_0_234:[bind(C,$fot(X_2557)),bind(X_2554,$fot(C)),bind(X_2555,$fot(skolemFOFtoCNF_P_8))]]) ).
cnf(refute_0_240,plain,
coll(C,X_2558,X_2557),
inference(resolve,[$cnf( coll(X_2557,skolemFOFtoCNF_P_8,C) )],[refute_0_239,refute_0_238]) ).
cnf(refute_0_241,plain,
coll(X_2576,skolemFOFtoCNF_O_2,C),
inference(subst,[],[refute_0_240:[bind(C,$fot(X_2576)),bind(X_2557,$fot(C)),bind(X_2558,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_242,plain,
coll(C,X_2577,X_2576),
inference(resolve,[$cnf( coll(X_2576,skolemFOFtoCNF_O_2,C) )],[refute_0_241,refute_0_162]) ).
cnf(refute_0_243,plain,
coll(X_2587,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_242:[bind(C,$fot(X_2587)),bind(X_2576,$fot(C)),bind(X_2577,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_244,plain,
coll(C,X_2588,X_2587),
inference(resolve,[$cnf( coll(X_2587,skolemFOFtoCNF_A,C) )],[refute_0_243,refute_0_134]) ).
cnf(refute_0_245,plain,
coll(X_2589,skolemFOFtoCNF_Q_3,C),
inference(subst,[],[refute_0_244:[bind(C,$fot(X_2589)),bind(X_2587,$fot(C)),bind(X_2588,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_246,plain,
coll(C,X_2590,X_2589),
inference(resolve,[$cnf( coll(X_2589,skolemFOFtoCNF_Q_3,C) )],[refute_0_245,refute_0_124]) ).
cnf(refute_0_247,plain,
coll(O,A,C),
inference(subst,[],[refute_0_246:[bind(C,$fot(O)),bind(X_2589,$fot(C)),bind(X_2590,$fot(A))]]) ).
cnf(refute_0_248,plain,
( ~ circle(O,A,B,C)
| perp(A,B,B,C) ),
inference(resolve,[$cnf( coll(O,A,C) )],[refute_0_247,refute_0_96]) ).
cnf(refute_0_249,plain,
( ~ circle(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_248:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(O,$fot(skolemFOFtoCNF_C1))]]) ).
cnf(refute_0_250,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_C1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_95,refute_0_249]) ).
cnf(refute_0_251,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_250,refute_0_88]) ).
cnf(refute_0_252,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_251,refute_0_86]) ).
cnf(refute_0_253,plain,
cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_252,refute_0_84]) ).
cnf(refute_0_254,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1))
| midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)) )],[refute_0_253,refute_0_77]) ).
cnf(refute_0_255,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)),
inference(subst,[],[refute_0_246:[bind(C,$fot(skolemFOFtoCNF_B_1)),bind(X_2589,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1))),bind(X_2590,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)))]]) ).
cnf(refute_0_256,plain,
midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)) )],[refute_0_255,refute_0_254]) ).
cnf(refute_0_257,plain,
midp(skolemFOFtoCNF_B_1,X_2606,X_2606),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C1,skolemFOFtoCNF_C1)) )],[refute_0_256,refute_0_75]) ).
cnf(refute_0_258,plain,
midp(skolemFOFtoCNF_B_1,X_2716,X_2716),
inference(subst,[],[refute_0_257:[bind(X_2606,$fot(X_2716))]]) ).
cnf(refute_0_259,plain,
midp(skolemFOFtoCNF_P_1(X_2716,Q),X_2716,Q),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,X_2716,X_2716) )],[refute_0_258,refute_0_70]) ).
cnf(refute_0_260,plain,
midp(skolemFOFtoCNF_P_1(X_2772,X_2771),X_2772,X_2771),
inference(subst,[],[refute_0_259:[bind(Q,$fot(X_2771)),bind(X_2716,$fot(X_2772))]]) ).
cnf(refute_0_261,plain,
cong(skolemFOFtoCNF_P_1(X_2772,X_2771),X_2772,skolemFOFtoCNF_P_1(X_2772,X_2771),X_2771),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(X_2772,X_2771),X_2772,X_2771) )],[refute_0_260,refute_0_24]) ).
cnf(refute_0_262,plain,
cong(skolemFOFtoCNF_P_1(X_3744,X_3743),X_3744,skolemFOFtoCNF_P_1(X_3744,X_3743),X_3743),
inference(subst,[],[refute_0_261:[bind(X_2771,$fot(X_3743)),bind(X_2772,$fot(X_3744))]]) ).
cnf(refute_0_263,plain,
cyclic(X_3744,X_3743,X_3743,X_3743),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_P_1(X_3744,X_3743),X_3744,skolemFOFtoCNF_P_1(X_3744,X_3743),X_3743) )],[refute_0_262,refute_0_22]) ).
cnf(refute_0_264,plain,
cyclic(X_3746,X_3745,X_3745,X_3745),
inference(subst,[],[refute_0_263:[bind(X_3743,$fot(X_3745)),bind(X_3744,$fot(X_3746))]]) ).
cnf(refute_0_265,plain,
cyclic(X_3745,X_3746,X_3745,X_3745),
inference(resolve,[$cnf( cyclic(X_3746,X_3745,X_3745,X_3745) )],[refute_0_264,refute_0_21]) ).
cnf(refute_0_266,plain,
cyclic(X_3747,X_3748,X_3747,X_3747),
inference(subst,[],[refute_0_265:[bind(X_3745,$fot(X_3747)),bind(X_3746,$fot(X_3748))]]) ).
cnf(refute_0_267,plain,
cyclic(X_3747,X_3747,X_3748,X_3747),
inference(resolve,[$cnf( cyclic(X_3747,X_3748,X_3747,X_3747) )],[refute_0_266,refute_0_20]) ).
cnf(refute_0_268,plain,
cyclic(X_3749,X_3749,X_3750,X_3749),
inference(subst,[],[refute_0_267:[bind(X_3747,$fot(X_3749)),bind(X_3748,$fot(X_3750))]]) ).
cnf(refute_0_269,plain,
cyclic(X_3749,X_3749,X_3749,X_3750),
inference(resolve,[$cnf( cyclic(X_3749,X_3749,X_3750,X_3749) )],[refute_0_268,refute_0_19]) ).
cnf(refute_0_270,plain,
cyclic(X_3751,X_3751,X_3751,X_3752),
inference(subst,[],[refute_0_269:[bind(X_3749,$fot(X_3751)),bind(X_3750,$fot(X_3752))]]) ).
cnf(refute_0_271,plain,
cyclic(X_3751,X_3751,X_3752,X_3752),
inference(resolve,[$cnf( cyclic(X_3751,X_3751,X_3751,X_3752) )],[refute_0_270,refute_0_17]) ).
cnf(refute_0_272,plain,
cyclic(X_3753,X_3753,X_3754,X_3754),
inference(subst,[],[refute_0_271:[bind(X_3751,$fot(X_3753)),bind(X_3752,$fot(X_3754))]]) ).
cnf(refute_0_273,plain,
( ~ cong(X_3753,X_3754,X_3753,X_3754)
| perp(X_3754,X_3753,X_3753,X_3754) ),
inference(resolve,[$cnf( cyclic(X_3753,X_3753,X_3754,X_3754) )],[refute_0_272,refute_0_15]) ).
cnf(refute_0_274,plain,
( ~ midp(X_2738,X_2737,X_2737)
| cong(X_2738,X_2737,X_2738,X_2737) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_2738)),bind(B,$fot(X_2737)),bind(C,$fot(X_2737))]]) ).
cnf(refute_0_275,plain,
( ~ midp(X_2736,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| midp(X_2736,X_2606,X_2606) ),
inference(subst,[],[refute_0_74:[bind(X_2605,$fot(skolemFOFtoCNF_B_1)),bind(X_2607,$fot(X_2736))]]) ).
cnf(refute_0_276,plain,
( ~ coll(X_2735,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| ~ cong(X_2735,skolemFOFtoCNF_B_1,X_2735,skolemFOFtoCNF_B_1)
| midp(X_2735,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(X_2735)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_277,plain,
( ~ cong(X_2731,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2731)
| cong(X_2731,skolemFOFtoCNF_B_1,X_2731,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_2731)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_2731))]]) ).
cnf(refute_0_278,plain,
( ~ cong(skolemFOFtoCNF_B_1,X_2724,X_2724,skolemFOFtoCNF_B_1)
| cong(X_2724,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2724) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_2724)),bind(C,$fot(X_2724)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_279,plain,
( ~ cong(skolemFOFtoCNF_B_1,X_2719,skolemFOFtoCNF_B_1,X_2719)
| cong(skolemFOFtoCNF_B_1,X_2719,X_2719,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_2719)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_2719))]]) ).
cnf(refute_0_280,plain,
( ~ midp(skolemFOFtoCNF_B_1,X_2716,X_2716)
| cong(skolemFOFtoCNF_B_1,X_2716,skolemFOFtoCNF_B_1,X_2716) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_2716)),bind(C,$fot(X_2716))]]) ).
cnf(refute_0_281,plain,
cong(skolemFOFtoCNF_B_1,X_2716,skolemFOFtoCNF_B_1,X_2716),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,X_2716,X_2716) )],[refute_0_258,refute_0_280]) ).
cnf(refute_0_282,plain,
cong(skolemFOFtoCNF_B_1,X_2719,skolemFOFtoCNF_B_1,X_2719),
inference(subst,[],[refute_0_281:[bind(X_2716,$fot(X_2719))]]) ).
cnf(refute_0_283,plain,
cong(skolemFOFtoCNF_B_1,X_2719,X_2719,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,X_2719,skolemFOFtoCNF_B_1,X_2719) )],[refute_0_282,refute_0_279]) ).
cnf(refute_0_284,plain,
cong(skolemFOFtoCNF_B_1,X_2724,X_2724,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_283:[bind(X_2719,$fot(X_2724))]]) ).
cnf(refute_0_285,plain,
cong(X_2724,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2724),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,X_2724,X_2724,skolemFOFtoCNF_B_1) )],[refute_0_284,refute_0_278]) ).
cnf(refute_0_286,plain,
cong(X_2731,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2731),
inference(subst,[],[refute_0_285:[bind(X_2724,$fot(X_2731))]]) ).
cnf(refute_0_287,plain,
cong(X_2731,skolemFOFtoCNF_B_1,X_2731,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(X_2731,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2731) )],[refute_0_286,refute_0_277]) ).
cnf(refute_0_288,plain,
cong(X_2735,skolemFOFtoCNF_B_1,X_2735,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_287:[bind(X_2731,$fot(X_2735))]]) ).
cnf(refute_0_289,plain,
( ~ coll(X_2735,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| midp(X_2735,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( cong(X_2735,skolemFOFtoCNF_B_1,X_2735,skolemFOFtoCNF_B_1) )],[refute_0_288,refute_0_276]) ).
cnf(refute_0_290,plain,
coll(X_2735,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_246:[bind(C,$fot(X_2735)),bind(X_2589,$fot(skolemFOFtoCNF_B_1)),bind(X_2590,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_291,plain,
midp(X_2735,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(X_2735,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_290,refute_0_289]) ).
cnf(refute_0_292,plain,
midp(X_2736,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_291:[bind(X_2735,$fot(X_2736))]]) ).
cnf(refute_0_293,plain,
midp(X_2736,X_2606,X_2606),
inference(resolve,[$cnf( midp(X_2736,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_292,refute_0_275]) ).
cnf(refute_0_294,plain,
midp(X_2738,X_2737,X_2737),
inference(subst,[],[refute_0_293:[bind(X_2606,$fot(X_2737)),bind(X_2736,$fot(X_2738))]]) ).
cnf(refute_0_295,plain,
cong(X_2738,X_2737,X_2738,X_2737),
inference(resolve,[$cnf( midp(X_2738,X_2737,X_2737) )],[refute_0_294,refute_0_274]) ).
cnf(refute_0_296,plain,
cong(X_3753,X_3754,X_3753,X_3754),
inference(subst,[],[refute_0_295:[bind(X_2737,$fot(X_3754)),bind(X_2738,$fot(X_3753))]]) ).
cnf(refute_0_297,plain,
perp(X_3754,X_3753,X_3753,X_3754),
inference(resolve,[$cnf( cong(X_3753,X_3754,X_3753,X_3754) )],[refute_0_296,refute_0_273]) ).
cnf(refute_0_298,plain,
perp(X_3756,X_3755,X_3755,X_3756),
inference(subst,[],[refute_0_297:[bind(X_3753,$fot(X_3755)),bind(X_3754,$fot(X_3756))]]) ).
cnf(refute_0_299,plain,
( ~ midp(M,X_3756,X_3756)
| cong(X_3756,M,X_3755,M) ),
inference(resolve,[$cnf( perp(X_3756,X_3755,X_3755,X_3756) )],[refute_0_298,refute_0_13]) ).
cnf(refute_0_300,plain,
midp(M,X_3756,X_3756),
inference(subst,[],[refute_0_293:[bind(X_2606,$fot(X_3756)),bind(X_2736,$fot(M))]]) ).
cnf(refute_0_301,plain,
cong(X_3756,M,X_3755,M),
inference(resolve,[$cnf( midp(M,X_3756,X_3756) )],[refute_0_300,refute_0_299]) ).
cnf(refute_0_302,plain,
cong(X_3775,X_3773,X_3774,X_3773),
inference(subst,[],[refute_0_301:[bind(M,$fot(X_3773)),bind(X_3755,$fot(X_3774)),bind(X_3756,$fot(X_3775))]]) ).
cnf(refute_0_303,plain,
cong(X_3775,X_3773,X_3773,X_3774),
inference(resolve,[$cnf( cong(X_3775,X_3773,X_3774,X_3773) )],[refute_0_302,refute_0_11]) ).
cnf(refute_0_304,plain,
cong(X_3778,X_3776,X_3776,X_3777),
inference(subst,[],[refute_0_303:[bind(X_3773,$fot(X_3776)),bind(X_3774,$fot(X_3777)),bind(X_3775,$fot(X_3778))]]) ).
cnf(refute_0_305,plain,
cong(X_3776,X_3777,X_3778,X_3776),
inference(resolve,[$cnf( cong(X_3778,X_3776,X_3776,X_3777) )],[refute_0_304,refute_0_10]) ).
cnf(refute_0_306,plain,
cong(X_3795,X_3796,X_3797,X_3795),
inference(subst,[],[refute_0_305:[bind(X_3776,$fot(X_3795)),bind(X_3777,$fot(X_3796)),bind(X_3778,$fot(X_3797))]]) ).
cnf(refute_0_307,plain,
cong(X_3795,X_3796,X_3795,X_3797),
inference(resolve,[$cnf( cong(X_3795,X_3796,X_3797,X_3795) )],[refute_0_306,refute_0_8]) ).
cnf(refute_0_308,plain,
cong(O,A,O,C),
inference(subst,[],[refute_0_307:[bind(X_3795,$fot(O)),bind(X_3796,$fot(A)),bind(X_3797,$fot(C))]]) ).
cnf(refute_0_309,plain,
( ~ cong(O,A,O,D)
| cyclic(A,C,C,D) ),
inference(resolve,[$cnf( cong(O,A,O,C) )],[refute_0_308,refute_0_6]) ).
cnf(refute_0_310,plain,
cong(O,A,O,D),
inference(subst,[],[refute_0_307:[bind(X_3795,$fot(O)),bind(X_3796,$fot(A)),bind(X_3797,$fot(D))]]) ).
cnf(refute_0_311,plain,
cyclic(A,C,C,D),
inference(resolve,[$cnf( cong(O,A,O,D) )],[refute_0_310,refute_0_309]) ).
cnf(refute_0_312,plain,
cyclic(X_11544,X_11545,X_11545,X_11546),
inference(subst,[],[refute_0_311:[bind(A,$fot(X_11544)),bind(C,$fot(X_11545)),bind(D,$fot(X_11546))]]) ).
cnf(refute_0_313,plain,
cyclic(X_11545,X_11544,X_11545,X_11546),
inference(resolve,[$cnf( cyclic(X_11544,X_11545,X_11545,X_11546) )],[refute_0_312,refute_0_4]) ).
cnf(refute_0_314,plain,
cyclic(X_11548,X_11547,X_11548,X_11549),
inference(subst,[],[refute_0_313:[bind(X_11544,$fot(X_11547)),bind(X_11545,$fot(X_11548)),bind(X_11546,$fot(X_11549))]]) ).
cnf(refute_0_315,plain,
cyclic(X_11548,X_11548,X_11547,X_11549),
inference(resolve,[$cnf( cyclic(X_11548,X_11547,X_11548,X_11549) )],[refute_0_314,refute_0_2]) ).
cnf(refute_0_316,plain,
cyclic(X_12021,X_12021,X_12022,X_12023),
inference(subst,[],[refute_0_315:[bind(X_11547,$fot(X_12022)),bind(X_11548,$fot(X_12021)),bind(X_11549,$fot(X_12023))]]) ).
cnf(refute_0_317,plain,
( ~ cyclic(X_12021,X_12021,X_12022,X_12023)
| ~ cyclic(X_12021,X_12021,X_12022,X_12024)
| cyclic(X_12021,X_12022,X_12023,X_12024) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_12021)),bind(B,$fot(X_12021)),bind(C,$fot(X_12022)),bind(D,$fot(X_12023)),bind(E,$fot(X_12024))]]) ).
cnf(refute_0_318,plain,
( ~ cyclic(X_12021,X_12021,X_12022,X_12024)
| cyclic(X_12021,X_12022,X_12023,X_12024) ),
inference(resolve,[$cnf( cyclic(X_12021,X_12021,X_12022,X_12023) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
cyclic(X_12021,X_12021,X_12022,X_12024),
inference(subst,[],[refute_0_315:[bind(X_11547,$fot(X_12022)),bind(X_11548,$fot(X_12021)),bind(X_11549,$fot(X_12024))]]) ).
cnf(refute_0_320,plain,
cyclic(X_12021,X_12022,X_12023,X_12024),
inference(resolve,[$cnf( cyclic(X_12021,X_12021,X_12022,X_12024) )],[refute_0_319,refute_0_318]) ).
cnf(refute_0_321,plain,
cyclic(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_8),
inference(subst,[],[refute_0_320:[bind(X_12021,$fot(skolemFOFtoCNF_Q_3)),bind(X_12022,$fot(skolemFOFtoCNF_B_1)),bind(X_12023,$fot(skolemFOFtoCNF_C_1)),bind(X_12024,$fot(skolemFOFtoCNF_P_8))]]) ).
cnf(refute_0_322,plain,
$false,
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_8) )],[refute_0_321,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO569+1 : TPTP v8.1.0. Released v7.5.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 18 16:53:09 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 45.01/45.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.01/45.23
% 45.01/45.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 45.07/45.26
%------------------------------------------------------------------------------