TSTP Solution File: GEO541+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO541+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 05:27:04 EDT 2022
% Result : Theorem 53.72s 53.94s
% Output : CNFRefutation 53.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 30
% Syntax : Number of formulae : 384 ( 150 unt; 0 def)
% Number of atoms : 751 ( 0 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 655 ( 288 ~; 283 |; 52 &)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-6 aty)
% Number of variables : 885 ( 117 sgn 427 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ) ).
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,C)
& coll(A,B,D) )
=> coll(C,D,A) ) ).
fof(ruleD7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ) ).
fof(ruleD8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ) ).
fof(ruleD11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ) ).
fof(ruleD12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,B)
& cong(O,A,O,C) )
=> circle(O,A,B,C) ) ).
fof(ruleD13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,B)
& cong(O,A,O,C)
& cong(O,A,O,D) )
=> cyclic(A,B,C,D) ) ).
fof(ruleD14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ) ).
fof(ruleD15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ) ).
fof(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ) ).
fof(ruleD17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,D)
& cyclic(A,B,C,E) )
=> cyclic(B,C,D,E) ) ).
fof(ruleD19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ) ).
fof(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ) ).
fof(ruleD24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ) ).
fof(ruleD39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ) ).
fof(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ) ).
fof(ruleD41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ) ).
fof(ruleD52,axiom,
! [A,B,C,M] :
( ( perp(A,B,B,C)
& midp(M,A,C) )
=> cong(A,M,B,M) ) ).
fof(ruleD53,axiom,
! [A,B,C,O] :
( ( circle(O,A,B,C)
& coll(O,A,C) )
=> perp(A,B,B,C) ) ).
fof(ruleD56,axiom,
! [A,B,P,Q] :
( ( cong(A,P,B,P)
& cong(A,Q,B,Q) )
=> perp(A,B,P,Q) ) ).
fof(ruleD57,axiom,
! [A,B,P,Q] :
( ( cong(A,P,B,P)
& cong(A,Q,B,Q)
& cyclic(A,B,P,Q) )
=> perp(P,A,A,Q) ) ).
fof(ruleD64,axiom,
! [A,B,C,D,M] :
( ( midp(M,A,B)
& para(A,C,B,D)
& para(A,D,B,C) )
=> midp(M,C,D) ) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ) ).
fof(ruleD67,axiom,
! [A,B,C] :
( ( cong(A,B,A,C)
& coll(A,B,C) )
=> midp(A,B,C) ) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ) ).
fof(ruleD69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ) ).
fof(ruleX6,axiom,
! [A,B,C,D,M,N] :
? [P] :
( ( midp(M,A,B)
& midp(N,C,D) )
=> ( midp(P,A,D)
& para(P,M,B,D)
& para(P,N,A,C) ) ) ).
fof(ruleX7,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( midp(M,A,B)
& midp(N,C,D)
& coll(C,A,B)
& coll(D,A,B) )
=> midp(P,A,Q) ) ).
fof(exemplo6GDDFULL012001,conjecture,
! [A,B,C,D,E,F,G] :
( ( perp(D,C,A,B)
& coll(D,A,B)
& perp(E,B,A,C)
& coll(E,A,C)
& midp(F,C,B)
& midp(G,D,E) )
=> perp(F,G,D,E) ) ).
fof(subgoal_0,plain,
! [A,B,C,D,E,F,G] :
( ( perp(D,C,A,B)
& coll(D,A,B)
& perp(E,B,A,C)
& coll(E,A,C)
& midp(F,C,B)
& midp(G,D,E) )
=> perp(F,G,D,E) ),
inference(strip,[],[exemplo6GDDFULL012001]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D,E,F,G] :
( ( perp(D,C,A,B)
& coll(D,A,B)
& perp(E,B,A,C)
& coll(E,A,C)
& midp(F,C,B)
& midp(G,D,E) )
=> perp(F,G,D,E) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D,E,F,G] :
( ~ perp(F,G,D,E)
& coll(D,A,B)
& coll(E,A,C)
& midp(F,C,B)
& midp(G,D,E)
& perp(D,C,A,B)
& perp(E,B,A,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ perp(skolemFOFtoCNF_F,skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
& coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& coll(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
& midp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
& perp(skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& perp(skolemFOFtoCNF_E,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ perp(skolemFOFtoCNF_F,skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
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,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_27,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
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_C_1,skolemFOFtoCNF_B_1),
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,
midp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_46,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_47,plain,
! [A,B,C,D,M,N] :
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| ? [P] :
( midp(P,A,D)
& para(P,M,B,D)
& para(P,N,A,C) ) ),
inference(specialize,[],[normalize_0_46]) ).
fof(normalize_0_48,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_47]) ).
fof(normalize_0_49,plain,
! [A,B,C,D,M,N] :
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P(A,B,C,D,M,N),A,D) ),
inference(conjunct,[],[normalize_0_48]) ).
fof(normalize_0_50,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_51,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_50]) ).
fof(normalize_0_52,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_53,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_52]) ).
fof(normalize_0_54,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[ruleD12]) ).
fof(normalize_0_55,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(specialize,[],[normalize_0_54]) ).
fof(normalize_0_56,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[ruleD11]) ).
fof(normalize_0_57,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(specialize,[],[normalize_0_56]) ).
fof(normalize_0_58,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_59,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(specialize,[],[normalize_0_58]) ).
fof(normalize_0_60,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[ruleD2]) ).
fof(normalize_0_61,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(specialize,[],[normalize_0_60]) ).
fof(normalize_0_62,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD69]) ).
fof(normalize_0_63,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_62]) ).
fof(normalize_0_64,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[ruleD23]) ).
fof(normalize_0_65,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(specialize,[],[normalize_0_64]) ).
fof(normalize_0_66,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[ruleD24]) ).
fof(normalize_0_67,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(specialize,[],[normalize_0_66]) ).
cnf(refute_0_0,plain,
~ perp(skolemFOFtoCNF_F,skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
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_5904,X_5904)
| ~ perp(X_5904,X_5903,X_5903,X_5904)
| cong(X_5904,M,X_5903,M) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_5904)),bind(B,$fot(X_5903)),bind(C,$fot(X_5904))]]) ).
cnf(refute_0_4,plain,
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ cong(X_5901,X_5902,X_5901,X_5902)
| ~ cyclic(X_5901,X_5901,X_5902,X_5902)
| perp(X_5902,X_5901,X_5901,X_5902) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_5901)),bind(B,$fot(X_5901)),bind(P,$fot(X_5902)),bind(Q,$fot(X_5902))]]) ).
cnf(refute_0_6,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ cyclic(X_5899,X_5899,X_5899,X_5900)
| cyclic(X_5899,X_5899,X_5900,X_5900) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_5899)),bind(B,$fot(X_5899)),bind(C,$fot(X_5899)),bind(D,$fot(X_5900)),bind(E,$fot(X_5900))]]) ).
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_5897,X_5897,X_5898,X_5897)
| cyclic(X_5897,X_5897,X_5897,X_5898) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_5897)),bind(B,$fot(X_5897)),bind(C,$fot(X_5898)),bind(D,$fot(X_5897))]]) ).
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_5895,X_5896,X_5895,X_5895)
| cyclic(X_5895,X_5895,X_5896,X_5895) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_5895)),bind(B,$fot(X_5896)),bind(C,$fot(X_5895)),bind(D,$fot(X_5895))]]) ).
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_5894,X_5893,X_5893,X_5893)
| cyclic(X_5893,X_5894,X_5893,X_5893) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_5894)),bind(B,$fot(X_5893)),bind(C,$fot(X_5893)),bind(D,$fot(X_5893))]]) ).
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_5892,X_5891),X_5892,skolemFOFtoCNF_P_1(X_5892,X_5891),X_5891)
| cyclic(X_5892,X_5891,X_5891,X_5891) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_5892)),bind(B,$fot(X_5891)),bind(C,$fot(X_5891)),bind(D,$fot(X_5891)),bind(O,$fot(skolemFOFtoCNF_P_1(X_5892,X_5891)))]]) ).
cnf(refute_0_16,plain,
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_17,plain,
( ~ midp(skolemFOFtoCNF_P_1(X_4191,X_4190),X_4191,X_4190)
| cong(skolemFOFtoCNF_P_1(X_4191,X_4190),X_4191,skolemFOFtoCNF_P_1(X_4191,X_4190),X_4190) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_P_1(X_4191,X_4190))),bind(B,$fot(X_4191)),bind(C,$fot(X_4190))]]) ).
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_484,X_484,X_483)
| coll(X_484,X_483,X_484) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(X_484)),bind(B,$fot(X_484)),bind(C,$fot(X_483))]]) ).
cnf(refute_0_22,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_23,plain,
( ~ coll(X_481,X_482,X_482)
| coll(X_482,X_482,X_481) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_481)),bind(B,$fot(X_482)),bind(C,$fot(X_482)),bind(D,$fot(X_482))]]) ).
cnf(refute_0_24,plain,
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_25,plain,
( ~ para(X_476,X_477,X_476,X_477)
| coll(X_476,X_477,X_477) ),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_476)),bind(B,$fot(X_477)),bind(C,$fot(X_477))]]) ).
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_474,X_475,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_474,X_475,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| para(X_474,X_475,X_474,X_475) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_474)),bind(B,$fot(X_475)),bind(C,$fot(X_474)),bind(D,$fot(X_475)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1))]]) ).
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_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_28:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_30,plain,
( ~ cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1)),bind(E,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_31,plain,
( ~ cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1)),bind(O,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_32,plain,
midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_33,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_34,plain,
cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1) )],[refute_0_34,refute_0_31]) ).
cnf(refute_0_36,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_35,refute_0_30]) ).
cnf(refute_0_37,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_36,refute_0_29]) ).
cnf(refute_0_38,plain,
( ~ eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_39,plain,
para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_41,plain,
( ~ para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154) ),
inference(subst,[],[refute_0_40:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1)),bind(P,$fot(X_153)),bind(Q,$fot(X_154))]]) ).
cnf(refute_0_42,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_472,X_473,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_472,X_473),
inference(subst,[],[refute_0_42:[bind(X_153,$fot(X_472)),bind(X_154,$fot(X_473))]]) ).
cnf(refute_0_44,plain,
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_45,plain,
( ~ eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_472,X_473,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_472,X_473)
| eqangle(X_472,X_473,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_472,X_473,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_44:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_472)),bind(D,$fot(X_473)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1)),bind(U,$fot(X_472)),bind(V,$fot(X_473))]]) ).
cnf(refute_0_46,plain,
eqangle(X_472,X_473,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_472,X_473,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_472,X_473,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_472,X_473) )],[refute_0_43,refute_0_45]) ).
cnf(refute_0_47,plain,
eqangle(X_474,X_475,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_474,X_475,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_46:[bind(X_472,$fot(X_474)),bind(X_473,$fot(X_475))]]) ).
cnf(refute_0_48,plain,
para(X_474,X_475,X_474,X_475),
inference(resolve,[$cnf( eqangle(X_474,X_475,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_474,X_475,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_47,refute_0_27]) ).
cnf(refute_0_49,plain,
para(X_476,X_477,X_476,X_477),
inference(subst,[],[refute_0_48:[bind(X_474,$fot(X_476)),bind(X_475,$fot(X_477))]]) ).
cnf(refute_0_50,plain,
coll(X_476,X_477,X_477),
inference(resolve,[$cnf( para(X_476,X_477,X_476,X_477) )],[refute_0_49,refute_0_25]) ).
cnf(refute_0_51,plain,
coll(X_481,X_482,X_482),
inference(subst,[],[refute_0_50:[bind(X_476,$fot(X_481)),bind(X_477,$fot(X_482))]]) ).
cnf(refute_0_52,plain,
coll(X_482,X_482,X_481),
inference(resolve,[$cnf( coll(X_481,X_482,X_482) )],[refute_0_51,refute_0_23]) ).
cnf(refute_0_53,plain,
coll(X_484,X_484,X_483),
inference(subst,[],[refute_0_52:[bind(X_481,$fot(X_483)),bind(X_482,$fot(X_484))]]) ).
cnf(refute_0_54,plain,
coll(X_484,X_483,X_484),
inference(resolve,[$cnf( coll(X_484,X_484,X_483) )],[refute_0_53,refute_0_21]) ).
cnf(refute_0_55,plain,
coll(D,D,D),
inference(subst,[],[refute_0_54:[bind(X_483,$fot(D)),bind(X_484,$fot(D))]]) ).
cnf(refute_0_56,plain,
( ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(resolve,[$cnf( coll(D,D,D) )],[refute_0_55,refute_0_19]) ).
cnf(refute_0_57,plain,
( ~ midp(skolemFOFtoCNF_D,X_4148,X_4148)
| midp(skolemFOFtoCNF_P_1(X_4148,Q),X_4148,Q) ),
inference(subst,[],[refute_0_56:[bind(D,$fot(X_4148)),bind(N,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_58,plain,
para(X_3773,X_3774,X_3773,X_3774),
inference(subst,[],[refute_0_48:[bind(X_474,$fot(X_3773)),bind(X_475,$fot(X_3774))]]) ).
cnf(refute_0_59,plain,
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_60,plain,
( ~ midp(X_3775,X_3773,X_3773)
| ~ para(X_3773,X_3774,X_3773,X_3774)
| midp(X_3775,X_3774,X_3774) ),
inference(subst,[],[refute_0_59:[bind(A,$fot(X_3773)),bind(B,$fot(X_3773)),bind(C,$fot(X_3774)),bind(D,$fot(X_3774)),bind(M,$fot(X_3775))]]) ).
cnf(refute_0_61,plain,
( ~ midp(X_3775,X_3773,X_3773)
| midp(X_3775,X_3774,X_3774) ),
inference(resolve,[$cnf( para(X_3773,X_3774,X_3773,X_3774) )],[refute_0_58,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| midp(skolemFOFtoCNF_D,X_3774,X_3774) ),
inference(subst,[],[refute_0_61:[bind(X_3773,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G))),bind(X_3775,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_63,plain,
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_64,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| ~ cong(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| midp(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G))),bind(C,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_65,plain,
midp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_66,plain,
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P(A,B,C,D,M,N),A,D) ),
inference(canonicalize,[],[normalize_0_49]) ).
cnf(refute_0_67,plain,
( ~ midp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
| midp(skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_D,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_66:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_G)),bind(N,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_68,plain,
midp(skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_65,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ midp(skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_D,skolemFOFtoCNF_E)
| ~ perp(skolemFOFtoCNF_D,X_4072,X_4072,skolemFOFtoCNF_E)
| cong(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),X_4072,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_4072)),bind(C,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_70,plain,
( ~ perp(skolemFOFtoCNF_D,X_4072,X_4072,skolemFOFtoCNF_E)
| cong(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),X_4072,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
| cong(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(subst,[],[refute_0_70:[bind(X_4072,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_72,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_73,plain,
( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D)
| perp(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_72:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_74,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_53]) ).
cnf(refute_0_75,plain,
( ~ perp(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| perp(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_74:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_76,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_77,plain,
( ~ cong(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_D)
| circle(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D)),bind(O,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_78,plain,
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_79,plain,
( ~ midp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
| midp(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_78:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_D)),bind(M,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_80,plain,
midp(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_65,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ midp(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_82,plain,
cong(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
circle(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_D) )],[refute_0_82,refute_0_77]) ).
cnf(refute_0_84,plain,
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[normalize_0_59]) ).
cnf(refute_0_85,plain,
( ~ coll(X_2673,skolemFOFtoCNF_D,C)
| ~ coll(X_2673,skolemFOFtoCNF_D,X_2674)
| coll(C,X_2674,X_2673) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2673)),bind(B,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_2674))]]) ).
cnf(refute_0_86,plain,
( ~ coll(X_2641,skolemFOFtoCNF_E,C)
| ~ coll(X_2641,skolemFOFtoCNF_E,skolemFOFtoCNF_D)
| coll(C,skolemFOFtoCNF_D,X_2641) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2641)),bind(B,$fot(skolemFOFtoCNF_E)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_87,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_61]) ).
cnf(refute_0_88,plain,
( ~ coll(skolemFOFtoCNF_E,X_2639,skolemFOFtoCNF_D)
| coll(X_2639,skolemFOFtoCNF_E,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_87:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(X_2639)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_89,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_90,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_87:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_91,plain,
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_63]) ).
cnf(refute_0_92,plain,
( ~ midp(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_91:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_93,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D) )],[refute_0_80,refute_0_92]) ).
cnf(refute_0_94,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D) )],[refute_0_93,refute_0_90]) ).
cnf(refute_0_95,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_D) )],[refute_0_94,refute_0_89]) ).
cnf(refute_0_96,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_2603)
| ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
| coll(skolemFOFtoCNF_E,X_2603,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(X_2603))]]) ).
cnf(refute_0_97,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_2603)
| coll(skolemFOFtoCNF_E,X_2603,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_2603),
inference(subst,[],[refute_0_52:[bind(X_481,$fot(X_2603)),bind(X_482,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_99,plain,
coll(skolemFOFtoCNF_E,X_2603,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_2603) )],[refute_0_98,refute_0_97]) ).
cnf(refute_0_100,plain,
coll(skolemFOFtoCNF_E,X_2639,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_99:[bind(X_2603,$fot(X_2639))]]) ).
cnf(refute_0_101,plain,
coll(X_2639,skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,X_2639,skolemFOFtoCNF_D) )],[refute_0_100,refute_0_88]) ).
cnf(refute_0_102,plain,
coll(X_2641,skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_101:[bind(X_2639,$fot(X_2641))]]) ).
cnf(refute_0_103,plain,
( ~ coll(X_2641,skolemFOFtoCNF_E,C)
| coll(C,skolemFOFtoCNF_D,X_2641) ),
inference(resolve,[$cnf( coll(X_2641,skolemFOFtoCNF_E,skolemFOFtoCNF_D) )],[refute_0_102,refute_0_86]) ).
cnf(refute_0_104,plain,
coll(X_2601,X_2601,X_2602),
inference(subst,[],[refute_0_52:[bind(X_481,$fot(X_2602)),bind(X_482,$fot(X_2601))]]) ).
cnf(refute_0_105,plain,
( ~ coll(X_2601,X_2601,X_2602)
| ~ coll(X_2601,X_2601,X_2603)
| coll(X_2602,X_2603,X_2601) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2601)),bind(B,$fot(X_2601)),bind(C,$fot(X_2602)),bind(D,$fot(X_2603))]]) ).
cnf(refute_0_106,plain,
( ~ coll(X_2601,X_2601,X_2603)
| coll(X_2602,X_2603,X_2601) ),
inference(resolve,[$cnf( coll(X_2601,X_2601,X_2602) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
coll(X_2601,X_2601,X_2603),
inference(subst,[],[refute_0_52:[bind(X_481,$fot(X_2603)),bind(X_482,$fot(X_2601))]]) ).
cnf(refute_0_108,plain,
coll(X_2602,X_2603,X_2601),
inference(resolve,[$cnf( coll(X_2601,X_2601,X_2603) )],[refute_0_107,refute_0_106]) ).
cnf(refute_0_109,plain,
coll(X_2641,skolemFOFtoCNF_E,C),
inference(subst,[],[refute_0_108:[bind(X_2601,$fot(C)),bind(X_2602,$fot(X_2641)),bind(X_2603,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_110,plain,
coll(C,skolemFOFtoCNF_D,X_2641),
inference(resolve,[$cnf( coll(X_2641,skolemFOFtoCNF_E,C) )],[refute_0_109,refute_0_103]) ).
cnf(refute_0_111,plain,
coll(X_2673,skolemFOFtoCNF_D,X_2674),
inference(subst,[],[refute_0_110:[bind(C,$fot(X_2673)),bind(X_2641,$fot(X_2674))]]) ).
cnf(refute_0_112,plain,
( ~ coll(X_2673,skolemFOFtoCNF_D,C)
| coll(C,X_2674,X_2673) ),
inference(resolve,[$cnf( coll(X_2673,skolemFOFtoCNF_D,X_2674) )],[refute_0_111,refute_0_85]) ).
cnf(refute_0_113,plain,
( ~ coll(X_2669,skolemFOFtoCNF_E,C)
| ~ coll(X_2669,skolemFOFtoCNF_E,X_2670)
| coll(C,X_2670,X_2669) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2669)),bind(B,$fot(skolemFOFtoCNF_E)),bind(D,$fot(X_2670))]]) ).
cnf(refute_0_114,plain,
( ~ coll(X_2625,skolemFOFtoCNF_G,C)
| ~ coll(X_2625,skolemFOFtoCNF_G,skolemFOFtoCNF_E)
| coll(C,skolemFOFtoCNF_E,X_2625) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2625)),bind(B,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_115,plain,
( ~ coll(skolemFOFtoCNF_E,X_2611,C)
| ~ coll(skolemFOFtoCNF_E,X_2611,skolemFOFtoCNF_G)
| coll(C,skolemFOFtoCNF_G,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(X_2611)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_116,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_117,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_87:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_118,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_119,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_87:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_120,plain,
( ~ midp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
| coll(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_91:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_121,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_65,refute_0_120]) ).
cnf(refute_0_122,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_121,refute_0_119]) ).
cnf(refute_0_123,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E) )],[refute_0_122,refute_0_118]) ).
cnf(refute_0_124,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G) )],[refute_0_123,refute_0_117]) ).
cnf(refute_0_125,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G) )],[refute_0_124,refute_0_116]) ).
cnf(refute_0_126,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_2603)
| ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E)
| coll(skolemFOFtoCNF_E,X_2603,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(X_2603))]]) ).
cnf(refute_0_127,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_2603)
| coll(skolemFOFtoCNF_E,X_2603,skolemFOFtoCNF_G) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,skolemFOFtoCNF_E) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_2603),
inference(subst,[],[refute_0_52:[bind(X_481,$fot(X_2603)),bind(X_482,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_129,plain,
coll(skolemFOFtoCNF_E,X_2603,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_G,X_2603) )],[refute_0_128,refute_0_127]) ).
cnf(refute_0_130,plain,
coll(skolemFOFtoCNF_E,X_2611,skolemFOFtoCNF_G),
inference(subst,[],[refute_0_129:[bind(X_2603,$fot(X_2611))]]) ).
cnf(refute_0_131,plain,
( ~ coll(skolemFOFtoCNF_E,X_2611,C)
| coll(C,skolemFOFtoCNF_G,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,X_2611,skolemFOFtoCNF_G) )],[refute_0_130,refute_0_115]) ).
cnf(refute_0_132,plain,
coll(skolemFOFtoCNF_E,X_2611,C),
inference(subst,[],[refute_0_108:[bind(X_2601,$fot(C)),bind(X_2602,$fot(skolemFOFtoCNF_E)),bind(X_2603,$fot(X_2611))]]) ).
cnf(refute_0_133,plain,
coll(C,skolemFOFtoCNF_G,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,X_2611,C) )],[refute_0_132,refute_0_131]) ).
cnf(refute_0_134,plain,
coll(X_2625,skolemFOFtoCNF_G,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_133:[bind(C,$fot(X_2625))]]) ).
cnf(refute_0_135,plain,
( ~ coll(X_2625,skolemFOFtoCNF_G,C)
| coll(C,skolemFOFtoCNF_E,X_2625) ),
inference(resolve,[$cnf( coll(X_2625,skolemFOFtoCNF_G,skolemFOFtoCNF_E) )],[refute_0_134,refute_0_114]) ).
cnf(refute_0_136,plain,
coll(X_2625,skolemFOFtoCNF_G,C),
inference(subst,[],[refute_0_108:[bind(X_2601,$fot(C)),bind(X_2602,$fot(X_2625)),bind(X_2603,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_137,plain,
coll(C,skolemFOFtoCNF_E,X_2625),
inference(resolve,[$cnf( coll(X_2625,skolemFOFtoCNF_G,C) )],[refute_0_136,refute_0_135]) ).
cnf(refute_0_138,plain,
coll(X_2669,skolemFOFtoCNF_E,X_2670),
inference(subst,[],[refute_0_137:[bind(C,$fot(X_2669)),bind(X_2625,$fot(X_2670))]]) ).
cnf(refute_0_139,plain,
( ~ coll(X_2669,skolemFOFtoCNF_E,C)
| coll(C,X_2670,X_2669) ),
inference(resolve,[$cnf( coll(X_2669,skolemFOFtoCNF_E,X_2670) )],[refute_0_138,refute_0_113]) ).
cnf(refute_0_140,plain,
( ~ coll(X_2662,skolemFOFtoCNF_F,C)
| ~ coll(X_2662,skolemFOFtoCNF_F,X_2663)
| coll(C,X_2663,X_2662) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2662)),bind(B,$fot(skolemFOFtoCNF_F)),bind(D,$fot(X_2663))]]) ).
cnf(refute_0_141,plain,
( ~ coll(X_2628,skolemFOFtoCNF_B_1,C)
| ~ coll(X_2628,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F)
| coll(C,skolemFOFtoCNF_F,X_2628) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2628)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_142,plain,
( ~ coll(skolemFOFtoCNF_B_1,X_2618,skolemFOFtoCNF_F)
| coll(X_2618,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_87:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_2618)),bind(C,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_143,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F)
| coll(skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_F)),bind(D,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_144,plain,
( ~ coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_145,plain,
( ~ midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_91:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_146,plain,
coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_32,refute_0_145]) ).
cnf(refute_0_147,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_146,refute_0_144]) ).
cnf(refute_0_148,plain,
coll(skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F) )],[refute_0_147,refute_0_143]) ).
cnf(refute_0_149,plain,
( ~ coll(skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_2603)
| ~ coll(skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,X_2603,skolemFOFtoCNF_F) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_2603))]]) ).
cnf(refute_0_150,plain,
( ~ coll(skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_2603)
| coll(skolemFOFtoCNF_B_1,X_2603,skolemFOFtoCNF_F) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_F,skolemFOFtoCNF_F,skolemFOFtoCNF_B_1) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
coll(skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_2603),
inference(subst,[],[refute_0_52:[bind(X_481,$fot(X_2603)),bind(X_482,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_152,plain,
coll(skolemFOFtoCNF_B_1,X_2603,skolemFOFtoCNF_F),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_F,skolemFOFtoCNF_F,X_2603) )],[refute_0_151,refute_0_150]) ).
cnf(refute_0_153,plain,
coll(skolemFOFtoCNF_B_1,X_2618,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_152:[bind(X_2603,$fot(X_2618))]]) ).
cnf(refute_0_154,plain,
coll(X_2618,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,X_2618,skolemFOFtoCNF_F) )],[refute_0_153,refute_0_142]) ).
cnf(refute_0_155,plain,
coll(X_2628,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F),
inference(subst,[],[refute_0_154:[bind(X_2618,$fot(X_2628))]]) ).
cnf(refute_0_156,plain,
( ~ coll(X_2628,skolemFOFtoCNF_B_1,C)
| coll(C,skolemFOFtoCNF_F,X_2628) ),
inference(resolve,[$cnf( coll(X_2628,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F) )],[refute_0_155,refute_0_141]) ).
cnf(refute_0_157,plain,
coll(X_2628,skolemFOFtoCNF_B_1,C),
inference(subst,[],[refute_0_108:[bind(X_2601,$fot(C)),bind(X_2602,$fot(X_2628)),bind(X_2603,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_158,plain,
coll(C,skolemFOFtoCNF_F,X_2628),
inference(resolve,[$cnf( coll(X_2628,skolemFOFtoCNF_B_1,C) )],[refute_0_157,refute_0_156]) ).
cnf(refute_0_159,plain,
coll(X_2662,skolemFOFtoCNF_F,X_2663),
inference(subst,[],[refute_0_158:[bind(C,$fot(X_2662)),bind(X_2628,$fot(X_2663))]]) ).
cnf(refute_0_160,plain,
( ~ coll(X_2662,skolemFOFtoCNF_F,C)
| coll(C,X_2663,X_2662) ),
inference(resolve,[$cnf( coll(X_2662,skolemFOFtoCNF_F,X_2663) )],[refute_0_159,refute_0_140]) ).
cnf(refute_0_161,plain,
( ~ coll(X_2660,skolemFOFtoCNF_G,C)
| ~ coll(X_2660,skolemFOFtoCNF_G,X_2661)
| coll(C,X_2661,X_2660) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2660)),bind(B,$fot(skolemFOFtoCNF_G)),bind(D,$fot(X_2661))]]) ).
cnf(refute_0_162,plain,
( ~ coll(X_2626,skolemFOFtoCNF_E,C)
| ~ coll(X_2626,skolemFOFtoCNF_E,skolemFOFtoCNF_G)
| coll(C,skolemFOFtoCNF_G,X_2626) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2626)),bind(B,$fot(skolemFOFtoCNF_E)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_163,plain,
( ~ coll(skolemFOFtoCNF_E,X_2611,skolemFOFtoCNF_G)
| coll(X_2611,skolemFOFtoCNF_E,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_87:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(X_2611)),bind(C,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_164,plain,
coll(X_2611,skolemFOFtoCNF_E,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,X_2611,skolemFOFtoCNF_G) )],[refute_0_130,refute_0_163]) ).
cnf(refute_0_165,plain,
coll(X_2626,skolemFOFtoCNF_E,skolemFOFtoCNF_G),
inference(subst,[],[refute_0_164:[bind(X_2611,$fot(X_2626))]]) ).
cnf(refute_0_166,plain,
( ~ coll(X_2626,skolemFOFtoCNF_E,C)
| coll(C,skolemFOFtoCNF_G,X_2626) ),
inference(resolve,[$cnf( coll(X_2626,skolemFOFtoCNF_E,skolemFOFtoCNF_G) )],[refute_0_165,refute_0_162]) ).
cnf(refute_0_167,plain,
coll(X_2626,skolemFOFtoCNF_E,C),
inference(subst,[],[refute_0_108:[bind(X_2601,$fot(C)),bind(X_2602,$fot(X_2626)),bind(X_2603,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_168,plain,
coll(C,skolemFOFtoCNF_G,X_2626),
inference(resolve,[$cnf( coll(X_2626,skolemFOFtoCNF_E,C) )],[refute_0_167,refute_0_166]) ).
cnf(refute_0_169,plain,
coll(X_2660,skolemFOFtoCNF_G,X_2661),
inference(subst,[],[refute_0_168:[bind(C,$fot(X_2660)),bind(X_2626,$fot(X_2661))]]) ).
cnf(refute_0_170,plain,
( ~ coll(X_2660,skolemFOFtoCNF_G,C)
| coll(C,X_2661,X_2660) ),
inference(resolve,[$cnf( coll(X_2660,skolemFOFtoCNF_G,X_2661) )],[refute_0_169,refute_0_161]) ).
cnf(refute_0_171,plain,
coll(X_2660,skolemFOFtoCNF_G,C),
inference(subst,[],[refute_0_108:[bind(X_2601,$fot(C)),bind(X_2602,$fot(X_2660)),bind(X_2603,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_172,plain,
coll(C,X_2661,X_2660),
inference(resolve,[$cnf( coll(X_2660,skolemFOFtoCNF_G,C) )],[refute_0_171,refute_0_170]) ).
cnf(refute_0_173,plain,
coll(X_2662,skolemFOFtoCNF_F,C),
inference(subst,[],[refute_0_172:[bind(C,$fot(X_2662)),bind(X_2660,$fot(C)),bind(X_2661,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_174,plain,
coll(C,X_2663,X_2662),
inference(resolve,[$cnf( coll(X_2662,skolemFOFtoCNF_F,C) )],[refute_0_173,refute_0_160]) ).
cnf(refute_0_175,plain,
coll(X_2669,skolemFOFtoCNF_E,C),
inference(subst,[],[refute_0_174:[bind(C,$fot(X_2669)),bind(X_2662,$fot(C)),bind(X_2663,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_176,plain,
coll(C,X_2670,X_2669),
inference(resolve,[$cnf( coll(X_2669,skolemFOFtoCNF_E,C) )],[refute_0_175,refute_0_139]) ).
cnf(refute_0_177,plain,
coll(X_2673,skolemFOFtoCNF_D,C),
inference(subst,[],[refute_0_176:[bind(C,$fot(X_2673)),bind(X_2669,$fot(C)),bind(X_2670,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_178,plain,
coll(C,X_2674,X_2673),
inference(resolve,[$cnf( coll(X_2673,skolemFOFtoCNF_D,C) )],[refute_0_177,refute_0_112]) ).
cnf(refute_0_179,plain,
coll(O,A,C),
inference(subst,[],[refute_0_178:[bind(C,$fot(O)),bind(X_2673,$fot(C)),bind(X_2674,$fot(A))]]) ).
cnf(refute_0_180,plain,
( ~ circle(O,A,B,C)
| perp(A,B,B,C) ),
inference(resolve,[$cnf( coll(O,A,C) )],[refute_0_179,refute_0_84]) ).
cnf(refute_0_181,plain,
( ~ circle(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| perp(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_180:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D)),bind(O,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_182,plain,
perp(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_83,refute_0_181]) ).
cnf(refute_0_183,plain,
perp(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_182,refute_0_75]) ).
cnf(refute_0_184,plain,
perp(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D) )],[refute_0_183,refute_0_73]) ).
cnf(refute_0_185,plain,
cong(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_184,refute_0_71]) ).
cnf(refute_0_186,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| midp(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) )],[refute_0_185,refute_0_64]) ).
cnf(refute_0_187,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)),
inference(subst,[],[refute_0_178:[bind(C,$fot(skolemFOFtoCNF_D)),bind(X_2673,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G))),bind(X_2674,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_188,plain,
midp(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) )],[refute_0_187,refute_0_186]) ).
cnf(refute_0_189,plain,
midp(skolemFOFtoCNF_D,X_3774,X_3774),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) )],[refute_0_188,refute_0_62]) ).
cnf(refute_0_190,plain,
midp(skolemFOFtoCNF_D,X_4148,X_4148),
inference(subst,[],[refute_0_189:[bind(X_3774,$fot(X_4148))]]) ).
cnf(refute_0_191,plain,
midp(skolemFOFtoCNF_P_1(X_4148,Q),X_4148,Q),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,X_4148,X_4148) )],[refute_0_190,refute_0_57]) ).
cnf(refute_0_192,plain,
midp(skolemFOFtoCNF_P_1(X_4191,X_4190),X_4191,X_4190),
inference(subst,[],[refute_0_191:[bind(Q,$fot(X_4190)),bind(X_4148,$fot(X_4191))]]) ).
cnf(refute_0_193,plain,
cong(skolemFOFtoCNF_P_1(X_4191,X_4190),X_4191,skolemFOFtoCNF_P_1(X_4191,X_4190),X_4190),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(X_4191,X_4190),X_4191,X_4190) )],[refute_0_192,refute_0_17]) ).
cnf(refute_0_194,plain,
cong(skolemFOFtoCNF_P_1(X_5892,X_5891),X_5892,skolemFOFtoCNF_P_1(X_5892,X_5891),X_5891),
inference(subst,[],[refute_0_193:[bind(X_4190,$fot(X_5891)),bind(X_4191,$fot(X_5892))]]) ).
cnf(refute_0_195,plain,
cyclic(X_5892,X_5891,X_5891,X_5891),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_P_1(X_5892,X_5891),X_5892,skolemFOFtoCNF_P_1(X_5892,X_5891),X_5891) )],[refute_0_194,refute_0_15]) ).
cnf(refute_0_196,plain,
cyclic(X_5894,X_5893,X_5893,X_5893),
inference(subst,[],[refute_0_195:[bind(X_5891,$fot(X_5893)),bind(X_5892,$fot(X_5894))]]) ).
cnf(refute_0_197,plain,
cyclic(X_5893,X_5894,X_5893,X_5893),
inference(resolve,[$cnf( cyclic(X_5894,X_5893,X_5893,X_5893) )],[refute_0_196,refute_0_13]) ).
cnf(refute_0_198,plain,
cyclic(X_5895,X_5896,X_5895,X_5895),
inference(subst,[],[refute_0_197:[bind(X_5893,$fot(X_5895)),bind(X_5894,$fot(X_5896))]]) ).
cnf(refute_0_199,plain,
cyclic(X_5895,X_5895,X_5896,X_5895),
inference(resolve,[$cnf( cyclic(X_5895,X_5896,X_5895,X_5895) )],[refute_0_198,refute_0_11]) ).
cnf(refute_0_200,plain,
cyclic(X_5897,X_5897,X_5898,X_5897),
inference(subst,[],[refute_0_199:[bind(X_5895,$fot(X_5897)),bind(X_5896,$fot(X_5898))]]) ).
cnf(refute_0_201,plain,
cyclic(X_5897,X_5897,X_5897,X_5898),
inference(resolve,[$cnf( cyclic(X_5897,X_5897,X_5898,X_5897) )],[refute_0_200,refute_0_9]) ).
cnf(refute_0_202,plain,
cyclic(X_5899,X_5899,X_5899,X_5900),
inference(subst,[],[refute_0_201:[bind(X_5897,$fot(X_5899)),bind(X_5898,$fot(X_5900))]]) ).
cnf(refute_0_203,plain,
cyclic(X_5899,X_5899,X_5900,X_5900),
inference(resolve,[$cnf( cyclic(X_5899,X_5899,X_5899,X_5900) )],[refute_0_202,refute_0_7]) ).
cnf(refute_0_204,plain,
cyclic(X_5901,X_5901,X_5902,X_5902),
inference(subst,[],[refute_0_203:[bind(X_5899,$fot(X_5901)),bind(X_5900,$fot(X_5902))]]) ).
cnf(refute_0_205,plain,
( ~ cong(X_5901,X_5902,X_5901,X_5902)
| perp(X_5902,X_5901,X_5901,X_5902) ),
inference(resolve,[$cnf( cyclic(X_5901,X_5901,X_5902,X_5902) )],[refute_0_204,refute_0_5]) ).
cnf(refute_0_206,plain,
( ~ midp(X_4177,X_4176,X_4176)
| cong(X_4177,X_4176,X_4177,X_4176) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_4177)),bind(B,$fot(X_4176)),bind(C,$fot(X_4176))]]) ).
cnf(refute_0_207,plain,
( ~ midp(X_4168,skolemFOFtoCNF_E,skolemFOFtoCNF_E)
| midp(X_4168,X_3774,X_3774) ),
inference(subst,[],[refute_0_61:[bind(X_3773,$fot(skolemFOFtoCNF_E)),bind(X_3775,$fot(X_4168))]]) ).
cnf(refute_0_208,plain,
( ~ coll(X_4167,skolemFOFtoCNF_E,skolemFOFtoCNF_E)
| ~ cong(X_4167,skolemFOFtoCNF_E,X_4167,skolemFOFtoCNF_E)
| midp(X_4167,skolemFOFtoCNF_E,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_4167)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_209,plain,
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_65]) ).
cnf(refute_0_210,plain,
( ~ cong(X_4166,skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_4166)
| cong(X_4166,skolemFOFtoCNF_E,X_4166,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_209:[bind(A,$fot(X_4166)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(X_4166))]]) ).
cnf(refute_0_211,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_67]) ).
cnf(refute_0_212,plain,
( ~ cong(skolemFOFtoCNF_E,X_4154,X_4154,skolemFOFtoCNF_E)
| cong(X_4154,skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_4154) ),
inference(subst,[],[refute_0_211:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(X_4154)),bind(C,$fot(X_4154)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_213,plain,
( ~ cong(skolemFOFtoCNF_E,X_4152,skolemFOFtoCNF_E,X_4152)
| cong(skolemFOFtoCNF_E,X_4152,X_4152,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_209:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(X_4152)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(X_4152))]]) ).
cnf(refute_0_214,plain,
( ~ midp(skolemFOFtoCNF_E,X_4149,X_4149)
| cong(skolemFOFtoCNF_E,X_4149,skolemFOFtoCNF_E,X_4149) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(X_4149)),bind(C,$fot(X_4149))]]) ).
cnf(refute_0_215,plain,
( ~ midp(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| midp(skolemFOFtoCNF_E,X_3774,X_3774) ),
inference(subst,[],[refute_0_61:[bind(X_3773,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G))),bind(X_3775,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_216,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| ~ cong(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| midp(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G))),bind(C,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_217,plain,
( ~ midp(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D)
| midp(skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_E,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_66:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(skolemFOFtoCNF_D)),bind(M,$fot(skolemFOFtoCNF_G)),bind(N,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_218,plain,
midp(skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_D) )],[refute_0_80,refute_0_217]) ).
cnf(refute_0_219,plain,
( ~ midp(skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_E,skolemFOFtoCNF_D)
| ~ perp(skolemFOFtoCNF_E,X_4072,X_4072,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),X_4072,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(X_4072)),bind(C,$fot(skolemFOFtoCNF_D)),bind(M,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_220,plain,
( ~ perp(skolemFOFtoCNF_E,X_4072,X_4072,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),X_4072,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_E,skolemFOFtoCNF_D) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
( ~ perp(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(subst,[],[refute_0_220:[bind(X_4072,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_222,plain,
( ~ perp(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E)
| perp(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_72:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_223,plain,
( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_E)
| perp(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_74:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_224,plain,
( ~ cong(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E)
| circle(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_E)),bind(O,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_225,plain,
( ~ cong(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_211:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_226,plain,
cong(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_D) )],[refute_0_82,refute_0_225]) ).
cnf(refute_0_227,plain,
circle(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_E),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_E) )],[refute_0_226,refute_0_224]) ).
cnf(refute_0_228,plain,
( ~ circle(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_E)
| perp(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_180:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_E)),bind(O,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_229,plain,
perp(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_E),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_E) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
perp(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_E) )],[refute_0_229,refute_0_223]) ).
cnf(refute_0_231,plain,
perp(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_230,refute_0_222]) ).
cnf(refute_0_232,plain,
cong(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_D) )],[refute_0_231,refute_0_221]) ).
cnf(refute_0_233,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| midp(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) )],[refute_0_232,refute_0_216]) ).
cnf(refute_0_234,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)),
inference(subst,[],[refute_0_178:[bind(C,$fot(skolemFOFtoCNF_E)),bind(X_2673,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G))),bind(X_2674,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_235,plain,
midp(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) )],[refute_0_234,refute_0_233]) ).
cnf(refute_0_236,plain,
midp(skolemFOFtoCNF_E,X_3774,X_3774),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_E,skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) )],[refute_0_235,refute_0_215]) ).
cnf(refute_0_237,plain,
midp(skolemFOFtoCNF_E,X_4149,X_4149),
inference(subst,[],[refute_0_236:[bind(X_3774,$fot(X_4149))]]) ).
cnf(refute_0_238,plain,
cong(skolemFOFtoCNF_E,X_4149,skolemFOFtoCNF_E,X_4149),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_E,X_4149,X_4149) )],[refute_0_237,refute_0_214]) ).
cnf(refute_0_239,plain,
cong(skolemFOFtoCNF_E,X_4152,skolemFOFtoCNF_E,X_4152),
inference(subst,[],[refute_0_238:[bind(X_4149,$fot(X_4152))]]) ).
cnf(refute_0_240,plain,
cong(skolemFOFtoCNF_E,X_4152,X_4152,skolemFOFtoCNF_E),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_E,X_4152,skolemFOFtoCNF_E,X_4152) )],[refute_0_239,refute_0_213]) ).
cnf(refute_0_241,plain,
cong(skolemFOFtoCNF_E,X_4154,X_4154,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_240:[bind(X_4152,$fot(X_4154))]]) ).
cnf(refute_0_242,plain,
cong(X_4154,skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_4154),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_E,X_4154,X_4154,skolemFOFtoCNF_E) )],[refute_0_241,refute_0_212]) ).
cnf(refute_0_243,plain,
cong(X_4166,skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_4166),
inference(subst,[],[refute_0_242:[bind(X_4154,$fot(X_4166))]]) ).
cnf(refute_0_244,plain,
cong(X_4166,skolemFOFtoCNF_E,X_4166,skolemFOFtoCNF_E),
inference(resolve,[$cnf( cong(X_4166,skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_4166) )],[refute_0_243,refute_0_210]) ).
cnf(refute_0_245,plain,
cong(X_4167,skolemFOFtoCNF_E,X_4167,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_244:[bind(X_4166,$fot(X_4167))]]) ).
cnf(refute_0_246,plain,
( ~ coll(X_4167,skolemFOFtoCNF_E,skolemFOFtoCNF_E)
| midp(X_4167,skolemFOFtoCNF_E,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( cong(X_4167,skolemFOFtoCNF_E,X_4167,skolemFOFtoCNF_E) )],[refute_0_245,refute_0_208]) ).
cnf(refute_0_247,plain,
coll(X_4167,skolemFOFtoCNF_E,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_178:[bind(C,$fot(X_4167)),bind(X_2673,$fot(skolemFOFtoCNF_E)),bind(X_2674,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_248,plain,
midp(X_4167,skolemFOFtoCNF_E,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(X_4167,skolemFOFtoCNF_E,skolemFOFtoCNF_E) )],[refute_0_247,refute_0_246]) ).
cnf(refute_0_249,plain,
midp(X_4168,skolemFOFtoCNF_E,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_248:[bind(X_4167,$fot(X_4168))]]) ).
cnf(refute_0_250,plain,
midp(X_4168,X_3774,X_3774),
inference(resolve,[$cnf( midp(X_4168,skolemFOFtoCNF_E,skolemFOFtoCNF_E) )],[refute_0_249,refute_0_207]) ).
cnf(refute_0_251,plain,
midp(X_4177,X_4176,X_4176),
inference(subst,[],[refute_0_250:[bind(X_3774,$fot(X_4176)),bind(X_4168,$fot(X_4177))]]) ).
cnf(refute_0_252,plain,
cong(X_4177,X_4176,X_4177,X_4176),
inference(resolve,[$cnf( midp(X_4177,X_4176,X_4176) )],[refute_0_251,refute_0_206]) ).
cnf(refute_0_253,plain,
cong(X_5901,X_5902,X_5901,X_5902),
inference(subst,[],[refute_0_252:[bind(X_4176,$fot(X_5902)),bind(X_4177,$fot(X_5901))]]) ).
cnf(refute_0_254,plain,
perp(X_5902,X_5901,X_5901,X_5902),
inference(resolve,[$cnf( cong(X_5901,X_5902,X_5901,X_5902) )],[refute_0_253,refute_0_205]) ).
cnf(refute_0_255,plain,
perp(X_5904,X_5903,X_5903,X_5904),
inference(subst,[],[refute_0_254:[bind(X_5901,$fot(X_5903)),bind(X_5902,$fot(X_5904))]]) ).
cnf(refute_0_256,plain,
( ~ midp(M,X_5904,X_5904)
| cong(X_5904,M,X_5903,M) ),
inference(resolve,[$cnf( perp(X_5904,X_5903,X_5903,X_5904) )],[refute_0_255,refute_0_3]) ).
cnf(refute_0_257,plain,
( ~ midp(X_4171,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| midp(X_4171,X_3774,X_3774) ),
inference(subst,[],[refute_0_61:[bind(X_3773,$fot(skolemFOFtoCNF_D)),bind(X_3775,$fot(X_4171))]]) ).
cnf(refute_0_258,plain,
( ~ coll(X_4170,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| ~ cong(X_4170,skolemFOFtoCNF_D,X_4170,skolemFOFtoCNF_D)
| midp(X_4170,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(X_4170)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_259,plain,
( ~ cong(X_4169,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_4169)
| cong(X_4169,skolemFOFtoCNF_D,X_4169,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_209:[bind(A,$fot(X_4169)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_4169))]]) ).
cnf(refute_0_260,plain,
( ~ cong(skolemFOFtoCNF_D,X_4158,X_4158,skolemFOFtoCNF_D)
| cong(X_4158,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_4158) ),
inference(subst,[],[refute_0_211:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_4158)),bind(C,$fot(X_4158)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_261,plain,
( ~ cong(skolemFOFtoCNF_D,X_4150,skolemFOFtoCNF_D,X_4150)
| cong(skolemFOFtoCNF_D,X_4150,X_4150,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_209:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_4150)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_4150))]]) ).
cnf(refute_0_262,plain,
( ~ midp(skolemFOFtoCNF_D,X_4148,X_4148)
| cong(skolemFOFtoCNF_D,X_4148,skolemFOFtoCNF_D,X_4148) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_4148)),bind(C,$fot(X_4148))]]) ).
cnf(refute_0_263,plain,
cong(skolemFOFtoCNF_D,X_4148,skolemFOFtoCNF_D,X_4148),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,X_4148,X_4148) )],[refute_0_190,refute_0_262]) ).
cnf(refute_0_264,plain,
cong(skolemFOFtoCNF_D,X_4150,skolemFOFtoCNF_D,X_4150),
inference(subst,[],[refute_0_263:[bind(X_4148,$fot(X_4150))]]) ).
cnf(refute_0_265,plain,
cong(skolemFOFtoCNF_D,X_4150,X_4150,skolemFOFtoCNF_D),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,X_4150,skolemFOFtoCNF_D,X_4150) )],[refute_0_264,refute_0_261]) ).
cnf(refute_0_266,plain,
cong(skolemFOFtoCNF_D,X_4158,X_4158,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_265:[bind(X_4150,$fot(X_4158))]]) ).
cnf(refute_0_267,plain,
cong(X_4158,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_4158),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,X_4158,X_4158,skolemFOFtoCNF_D) )],[refute_0_266,refute_0_260]) ).
cnf(refute_0_268,plain,
cong(X_4169,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_4169),
inference(subst,[],[refute_0_267:[bind(X_4158,$fot(X_4169))]]) ).
cnf(refute_0_269,plain,
cong(X_4169,skolemFOFtoCNF_D,X_4169,skolemFOFtoCNF_D),
inference(resolve,[$cnf( cong(X_4169,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_4169) )],[refute_0_268,refute_0_259]) ).
cnf(refute_0_270,plain,
cong(X_4170,skolemFOFtoCNF_D,X_4170,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_269:[bind(X_4169,$fot(X_4170))]]) ).
cnf(refute_0_271,plain,
( ~ coll(X_4170,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| midp(X_4170,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( cong(X_4170,skolemFOFtoCNF_D,X_4170,skolemFOFtoCNF_D) )],[refute_0_270,refute_0_258]) ).
cnf(refute_0_272,plain,
coll(X_4170,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_178:[bind(C,$fot(X_4170)),bind(X_2673,$fot(skolemFOFtoCNF_D)),bind(X_2674,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_273,plain,
midp(X_4170,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(X_4170,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_272,refute_0_271]) ).
cnf(refute_0_274,plain,
midp(X_4171,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_273:[bind(X_4170,$fot(X_4171))]]) ).
cnf(refute_0_275,plain,
midp(X_4171,X_3774,X_3774),
inference(resolve,[$cnf( midp(X_4171,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_274,refute_0_257]) ).
cnf(refute_0_276,plain,
midp(M,X_5904,X_5904),
inference(subst,[],[refute_0_275:[bind(X_3774,$fot(X_5904)),bind(X_4171,$fot(M))]]) ).
cnf(refute_0_277,plain,
cong(X_5904,M,X_5903,M),
inference(resolve,[$cnf( midp(M,X_5904,X_5904) )],[refute_0_276,refute_0_256]) ).
cnf(refute_0_278,plain,
cong(A,P,B,P),
inference(subst,[],[refute_0_277:[bind(M,$fot(P)),bind(X_5903,$fot(B)),bind(X_5904,$fot(A))]]) ).
cnf(refute_0_279,plain,
( ~ cong(A,Q,B,Q)
| perp(A,B,P,Q) ),
inference(resolve,[$cnf( cong(A,P,B,P) )],[refute_0_278,refute_0_1]) ).
cnf(refute_0_280,plain,
cong(A,Q,B,Q),
inference(subst,[],[refute_0_277:[bind(M,$fot(Q)),bind(X_5903,$fot(B)),bind(X_5904,$fot(A))]]) ).
cnf(refute_0_281,plain,
perp(A,B,P,Q),
inference(resolve,[$cnf( cong(A,Q,B,Q) )],[refute_0_280,refute_0_279]) ).
cnf(refute_0_282,plain,
perp(skolemFOFtoCNF_F,skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_281:[bind(A,$fot(skolemFOFtoCNF_F)),bind(B,$fot(skolemFOFtoCNF_G)),bind(P,$fot(skolemFOFtoCNF_D)),bind(Q,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_283,plain,
$false,
inference(resolve,[$cnf( perp(skolemFOFtoCNF_F,skolemFOFtoCNF_G,skolemFOFtoCNF_D,skolemFOFtoCNF_E) )],[refute_0_282,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO541+1 : TPTP v8.1.0. Released v7.5.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 12:38:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 53.72/53.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.72/53.94
% 53.72/53.94 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.72/53.97
%------------------------------------------------------------------------------