TSTP Solution File: GEO616+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO616+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 05:27:41 EDT 2022
% Result : Theorem 49.71s 49.91s
% Output : CNFRefutation 49.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 28
% Syntax : Number of formulae : 276 ( 96 unt; 0 def)
% Number of atoms : 588 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 533 ( 221 ~; 216 |; 66 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-6 aty)
% Number of variables : 785 ( 77 sgn 415 !; 17 ?)
% 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(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(exemplo6GDDFULL618078,conjecture,
! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(O,A,B,C)
& midp(G,C,B)
& coll(E,O,G)
& circle(O,A,E,NWPNT1)
& perp(K,E,A,B)
& coll(K,A,B)
& perp(H,A,O,G)
& coll(H,O,G)
& circle(N,K,G,H) )
=> perp(E,K,K,N) ) ).
fof(subgoal_0,plain,
! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(O,A,B,C)
& midp(G,C,B)
& coll(E,O,G)
& circle(O,A,E,NWPNT1)
& perp(K,E,A,B)
& coll(K,A,B)
& perp(H,A,O,G)
& coll(H,O,G)
& circle(N,K,G,H) )
=> perp(E,K,K,N) ),
inference(strip,[],[exemplo6GDDFULL618078]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(O,A,B,C)
& midp(G,C,B)
& coll(E,O,G)
& circle(O,A,E,NWPNT1)
& perp(K,E,A,B)
& coll(K,A,B)
& perp(H,A,O,G)
& coll(H,O,G)
& circle(N,K,G,H) )
=> perp(E,K,K,N) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,E,G,H,K,N,O] :
( ~ perp(E,K,K,N)
& circle(N,K,G,H)
& circle(O,A,B,C)
& coll(E,O,G)
& coll(H,O,G)
& coll(K,A,B)
& midp(G,C,B)
& perp(H,A,O,G)
& perp(K,E,A,B)
& ? [NWPNT1] : circle(O,A,E,NWPNT1) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ perp(skolemFOFtoCNF_E,skolemFOFtoCNF_K,skolemFOFtoCNF_K,skolemFOFtoCNF_N)
& circle(skolemFOFtoCNF_N,skolemFOFtoCNF_K,skolemFOFtoCNF_G,skolemFOFtoCNF_H)
& circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_E,skolemFOFtoCNF_O_2,skolemFOFtoCNF_G)
& coll(skolemFOFtoCNF_H,skolemFOFtoCNF_O_2,skolemFOFtoCNF_G)
& coll(skolemFOFtoCNF_K,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& midp(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
& perp(skolemFOFtoCNF_H,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_G)
& perp(skolemFOFtoCNF_K,skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& ? [NWPNT1] : circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_E,NWPNT1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ perp(skolemFOFtoCNF_E,skolemFOFtoCNF_K,skolemFOFtoCNF_K,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,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_4,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[ruleD2]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
coll(skolemFOFtoCNF_K,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[ruleD1]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD66]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,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_15,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_14]) ).
fof(normalize_0_16,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_15]) ).
fof(normalize_0_17,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_18,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,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_20,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_19]) ).
fof(normalize_0_21,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_22,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_21]) ).
fof(normalize_0_23,plain,
midp(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_24,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[ruleD68]) ).
fof(normalize_0_25,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,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_27,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_26]) ).
fof(normalize_0_28,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_27]) ).
fof(normalize_0_29,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_30,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_29]) ).
fof(normalize_0_31,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_32,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[ruleD23]) ).
fof(normalize_0_34,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(specialize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[ruleD24]) ).
fof(normalize_0_36,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(specialize,[],[normalize_0_35]) ).
fof(normalize_0_37,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_38,plain,
! [A,B,C,M] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(specialize,[],[normalize_0_37]) ).
fof(normalize_0_39,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_40,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_39]) ).
fof(normalize_0_41,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[ruleD14]) ).
fof(normalize_0_42,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(specialize,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[ruleD15]) ).
fof(normalize_0_44,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[ruleD16]) ).
fof(normalize_0_46,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(specialize,[],[normalize_0_45]) ).
fof(normalize_0_47,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_48,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_47]) ).
fof(normalize_0_49,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_48]) ).
fof(normalize_0_50,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_51,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_50]) ).
fof(normalize_0_52,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[ruleD67]) ).
fof(normalize_0_53,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(specialize,[],[normalize_0_52]) ).
fof(normalize_0_54,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[ruleD11]) ).
fof(normalize_0_55,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(specialize,[],[normalize_0_54]) ).
fof(normalize_0_56,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_57,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_56]) ).
fof(normalize_0_58,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_57]) ).
fof(normalize_0_59,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_58]) ).
fof(normalize_0_60,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_61,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_60]) ).
fof(normalize_0_62,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_63,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_62]) ).
cnf(refute_0_0,plain,
~ perp(skolemFOFtoCNF_E,skolemFOFtoCNF_K,skolemFOFtoCNF_K,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ coll(X_1537,skolemFOFtoCNF_K,C)
| ~ coll(X_1537,skolemFOFtoCNF_K,X_1538)
| coll(C,X_1538,X_1537) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_1537)),bind(B,$fot(skolemFOFtoCNF_K)),bind(D,$fot(X_1538))]]) ).
cnf(refute_0_4,plain,
( ~ coll(X_1509,skolemFOFtoCNF_A,C)
| ~ coll(X_1509,skolemFOFtoCNF_A,skolemFOFtoCNF_K)
| coll(C,skolemFOFtoCNF_K,X_1509) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_1509)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_K))]]) ).
cnf(refute_0_5,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
( ~ coll(skolemFOFtoCNF_A,X_1495,skolemFOFtoCNF_K)
| coll(X_1495,skolemFOFtoCNF_A,skolemFOFtoCNF_K) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_1495)),bind(C,$fot(skolemFOFtoCNF_K))]]) ).
cnf(refute_0_7,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_K)
| coll(skolemFOFtoCNF_K,skolemFOFtoCNF_K,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_K)),bind(D,$fot(skolemFOFtoCNF_K))]]) ).
cnf(refute_0_8,plain,
coll(skolemFOFtoCNF_K,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( ~ coll(skolemFOFtoCNF_K,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_K,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_K)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_10,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_K,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_K,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_K,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_K) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_K)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_13,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_K),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_K,skolemFOFtoCNF_B_1) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
coll(skolemFOFtoCNF_K,skolemFOFtoCNF_K,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_K) )],[refute_0_13,refute_0_7]) ).
cnf(refute_0_15,plain,
( ~ coll(skolemFOFtoCNF_K,skolemFOFtoCNF_K,X_1470)
| ~ coll(skolemFOFtoCNF_K,skolemFOFtoCNF_K,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,X_1470,skolemFOFtoCNF_K) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_K)),bind(B,$fot(skolemFOFtoCNF_K)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_1470))]]) ).
cnf(refute_0_16,plain,
( ~ coll(skolemFOFtoCNF_K,skolemFOFtoCNF_K,X_1470)
| coll(skolemFOFtoCNF_A,X_1470,skolemFOFtoCNF_K) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_K,skolemFOFtoCNF_K,skolemFOFtoCNF_A) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ coll(X_365,X_366,X_366)
| coll(X_366,X_366,X_365) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_365)),bind(B,$fot(X_366)),bind(C,$fot(X_366)),bind(D,$fot(X_366))]]) ).
cnf(refute_0_18,plain,
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_19,plain,
( ~ para(X_363,X_364,X_363,X_364)
| coll(X_363,X_364,X_364) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(X_363)),bind(B,$fot(X_364)),bind(C,$fot(X_364))]]) ).
cnf(refute_0_20,plain,
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_21,plain,
( ~ eqangle(X_361,X_362,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_361,X_362,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| para(X_361,X_362,X_361,X_362) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(X_361)),bind(B,$fot(X_362)),bind(C,$fot(X_361)),bind(D,$fot(X_362)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_22,plain,
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_23,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_22:[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_24,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_25,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_24:[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,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_26,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_27,plain,
( ~ cong(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_26:[bind(A,$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_G))]]) ).
cnf(refute_0_28,plain,
midp(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_29,plain,
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_30,plain,
( ~ midp(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_31,plain,
cong(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1) )],[refute_0_31,refute_0_27]) ).
cnf(refute_0_33,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_32,refute_0_25]) ).
cnf(refute_0_34,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,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_33,refute_0_23]) ).
cnf(refute_0_35,plain,
( ~ eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_20:[bind(A,$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,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_36,plain,
para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$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_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_38,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_37:[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_39,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_36,refute_0_38]) ).
cnf(refute_0_40,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_359,X_360,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_359,X_360),
inference(subst,[],[refute_0_39:[bind(X_153,$fot(X_359)),bind(X_154,$fot(X_360))]]) ).
cnf(refute_0_41,plain,
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_42,plain,
( ~ eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_359,X_360,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_359,X_360)
| eqangle(X_359,X_360,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_359,X_360,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_41:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_359)),bind(D,$fot(X_360)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1)),bind(U,$fot(X_359)),bind(V,$fot(X_360))]]) ).
cnf(refute_0_43,plain,
eqangle(X_359,X_360,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_359,X_360,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_359,X_360,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_359,X_360) )],[refute_0_40,refute_0_42]) ).
cnf(refute_0_44,plain,
eqangle(X_361,X_362,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_361,X_362,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_43:[bind(X_359,$fot(X_361)),bind(X_360,$fot(X_362))]]) ).
cnf(refute_0_45,plain,
para(X_361,X_362,X_361,X_362),
inference(resolve,[$cnf( eqangle(X_361,X_362,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_361,X_362,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_44,refute_0_21]) ).
cnf(refute_0_46,plain,
para(X_363,X_364,X_363,X_364),
inference(subst,[],[refute_0_45:[bind(X_361,$fot(X_363)),bind(X_362,$fot(X_364))]]) ).
cnf(refute_0_47,plain,
coll(X_363,X_364,X_364),
inference(resolve,[$cnf( para(X_363,X_364,X_363,X_364) )],[refute_0_46,refute_0_19]) ).
cnf(refute_0_48,plain,
coll(X_365,X_366,X_366),
inference(subst,[],[refute_0_47:[bind(X_363,$fot(X_365)),bind(X_364,$fot(X_366))]]) ).
cnf(refute_0_49,plain,
coll(X_366,X_366,X_365),
inference(resolve,[$cnf( coll(X_365,X_366,X_366) )],[refute_0_48,refute_0_17]) ).
cnf(refute_0_50,plain,
coll(skolemFOFtoCNF_K,skolemFOFtoCNF_K,X_1470),
inference(subst,[],[refute_0_49:[bind(X_365,$fot(X_1470)),bind(X_366,$fot(skolemFOFtoCNF_K))]]) ).
cnf(refute_0_51,plain,
coll(skolemFOFtoCNF_A,X_1470,skolemFOFtoCNF_K),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_K,skolemFOFtoCNF_K,X_1470) )],[refute_0_50,refute_0_16]) ).
cnf(refute_0_52,plain,
coll(skolemFOFtoCNF_A,X_1495,skolemFOFtoCNF_K),
inference(subst,[],[refute_0_51:[bind(X_1470,$fot(X_1495))]]) ).
cnf(refute_0_53,plain,
coll(X_1495,skolemFOFtoCNF_A,skolemFOFtoCNF_K),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_1495,skolemFOFtoCNF_K) )],[refute_0_52,refute_0_6]) ).
cnf(refute_0_54,plain,
coll(X_1509,skolemFOFtoCNF_A,skolemFOFtoCNF_K),
inference(subst,[],[refute_0_53:[bind(X_1495,$fot(X_1509))]]) ).
cnf(refute_0_55,plain,
( ~ coll(X_1509,skolemFOFtoCNF_A,C)
| coll(C,skolemFOFtoCNF_K,X_1509) ),
inference(resolve,[$cnf( coll(X_1509,skolemFOFtoCNF_A,skolemFOFtoCNF_K) )],[refute_0_54,refute_0_4]) ).
cnf(refute_0_56,plain,
coll(X_1468,X_1468,X_1469),
inference(subst,[],[refute_0_49:[bind(X_365,$fot(X_1469)),bind(X_366,$fot(X_1468))]]) ).
cnf(refute_0_57,plain,
( ~ coll(X_1468,X_1468,X_1469)
| ~ coll(X_1468,X_1468,X_1470)
| coll(X_1469,X_1470,X_1468) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_1468)),bind(B,$fot(X_1468)),bind(C,$fot(X_1469)),bind(D,$fot(X_1470))]]) ).
cnf(refute_0_58,plain,
( ~ coll(X_1468,X_1468,X_1470)
| coll(X_1469,X_1470,X_1468) ),
inference(resolve,[$cnf( coll(X_1468,X_1468,X_1469) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
coll(X_1468,X_1468,X_1470),
inference(subst,[],[refute_0_49:[bind(X_365,$fot(X_1470)),bind(X_366,$fot(X_1468))]]) ).
cnf(refute_0_60,plain,
coll(X_1469,X_1470,X_1468),
inference(resolve,[$cnf( coll(X_1468,X_1468,X_1470) )],[refute_0_59,refute_0_58]) ).
cnf(refute_0_61,plain,
coll(X_1509,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_60:[bind(X_1468,$fot(C)),bind(X_1469,$fot(X_1509)),bind(X_1470,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_62,plain,
coll(C,skolemFOFtoCNF_K,X_1509),
inference(resolve,[$cnf( coll(X_1509,skolemFOFtoCNF_A,C) )],[refute_0_61,refute_0_55]) ).
cnf(refute_0_63,plain,
coll(X_1537,skolemFOFtoCNF_K,X_1538),
inference(subst,[],[refute_0_62:[bind(C,$fot(X_1537)),bind(X_1509,$fot(X_1538))]]) ).
cnf(refute_0_64,plain,
( ~ coll(X_1537,skolemFOFtoCNF_K,C)
| coll(C,X_1538,X_1537) ),
inference(resolve,[$cnf( coll(X_1537,skolemFOFtoCNF_K,X_1538) )],[refute_0_63,refute_0_3]) ).
cnf(refute_0_65,plain,
coll(X_1537,skolemFOFtoCNF_K,C),
inference(subst,[],[refute_0_60:[bind(X_1468,$fot(C)),bind(X_1469,$fot(X_1537)),bind(X_1470,$fot(skolemFOFtoCNF_K))]]) ).
cnf(refute_0_66,plain,
coll(C,X_1538,X_1537),
inference(resolve,[$cnf( coll(X_1537,skolemFOFtoCNF_K,C) )],[refute_0_65,refute_0_64]) ).
cnf(refute_0_67,plain,
coll(O,A,C),
inference(subst,[],[refute_0_66:[bind(C,$fot(O)),bind(X_1537,$fot(C)),bind(X_1538,$fot(A))]]) ).
cnf(refute_0_68,plain,
( ~ circle(O,A,B,C)
| perp(A,B,B,C) ),
inference(resolve,[$cnf( coll(O,A,C) )],[refute_0_67,refute_0_1]) ).
cnf(refute_0_69,plain,
( ~ circle(X_18451,X_18448,X_18449,X_18450)
| perp(X_18448,X_18449,X_18449,X_18450) ),
inference(subst,[],[refute_0_68:[bind(A,$fot(X_18448)),bind(B,$fot(X_18449)),bind(C,$fot(X_18450)),bind(O,$fot(X_18451))]]) ).
cnf(refute_0_70,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_71,plain,
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_72,plain,
( ~ cong(X_4107,X_4108,X_4109,X_4107)
| cong(X_4107,X_4108,X_4107,X_4109) ),
inference(subst,[],[refute_0_71:[bind(A,$fot(X_4107)),bind(B,$fot(X_4108)),bind(C,$fot(X_4109)),bind(D,$fot(X_4107))]]) ).
cnf(refute_0_73,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_74,plain,
( ~ cong(X_4084,X_4082,X_4082,X_4083)
| cong(X_4082,X_4083,X_4084,X_4082) ),
inference(subst,[],[refute_0_73:[bind(A,$fot(X_4084)),bind(B,$fot(X_4082)),bind(C,$fot(X_4082)),bind(D,$fot(X_4083))]]) ).
cnf(refute_0_75,plain,
( ~ cong(X_4081,X_4079,X_4080,X_4079)
| cong(X_4081,X_4079,X_4079,X_4080) ),
inference(subst,[],[refute_0_71:[bind(A,$fot(X_4081)),bind(B,$fot(X_4079)),bind(C,$fot(X_4080)),bind(D,$fot(X_4079))]]) ).
cnf(refute_0_76,plain,
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_77,plain,
( ~ midp(M,X_4062,X_4062)
| ~ perp(X_4062,X_4061,X_4061,X_4062)
| cong(X_4062,M,X_4061,M) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(X_4062)),bind(B,$fot(X_4061)),bind(C,$fot(X_4062))]]) ).
cnf(refute_0_78,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_40]) ).
cnf(refute_0_79,plain,
( ~ cong(X_4059,X_4060,X_4059,X_4060)
| ~ cyclic(X_4059,X_4059,X_4060,X_4060)
| perp(X_4060,X_4059,X_4059,X_4060) ),
inference(subst,[],[refute_0_78:[bind(A,$fot(X_4059)),bind(B,$fot(X_4059)),bind(P,$fot(X_4060)),bind(Q,$fot(X_4060))]]) ).
cnf(refute_0_80,plain,
( ~ cyclic(X_4057,X_4057,X_4057,X_4058)
| cyclic(X_4057,X_4057,X_4058,X_4058) ),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_4057)),bind(B,$fot(X_4057)),bind(C,$fot(X_4057)),bind(D,$fot(X_4058)),bind(E,$fot(X_4058))]]) ).
cnf(refute_0_81,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_82,plain,
( ~ cyclic(X_4055,X_4055,X_4056,X_4055)
| cyclic(X_4055,X_4055,X_4055,X_4056) ),
inference(subst,[],[refute_0_81:[bind(A,$fot(X_4055)),bind(B,$fot(X_4055)),bind(C,$fot(X_4056)),bind(D,$fot(X_4055))]]) ).
cnf(refute_0_83,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_84,plain,
( ~ cyclic(X_4053,X_4054,X_4053,X_4053)
| cyclic(X_4053,X_4053,X_4054,X_4053) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(X_4053)),bind(B,$fot(X_4054)),bind(C,$fot(X_4053)),bind(D,$fot(X_4053))]]) ).
cnf(refute_0_85,plain,
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_86,plain,
( ~ cyclic(X_4052,X_4051,X_4051,X_4051)
| cyclic(X_4051,X_4052,X_4051,X_4051) ),
inference(subst,[],[refute_0_85:[bind(A,$fot(X_4052)),bind(B,$fot(X_4051)),bind(C,$fot(X_4051)),bind(D,$fot(X_4051))]]) ).
cnf(refute_0_87,plain,
( ~ cong(skolemFOFtoCNF_P_1(X_4050,X_4049),X_4050,skolemFOFtoCNF_P_1(X_4050,X_4049),X_4049)
| cyclic(X_4050,X_4049,X_4049,X_4049) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_4050)),bind(B,$fot(X_4049)),bind(C,$fot(X_4049)),bind(D,$fot(X_4049)),bind(O,$fot(skolemFOFtoCNF_P_1(X_4050,X_4049)))]]) ).
cnf(refute_0_88,plain,
( ~ midp(skolemFOFtoCNF_P_1(X_2466,X_2465),X_2466,X_2465)
| cong(skolemFOFtoCNF_P_1(X_2466,X_2465),X_2466,skolemFOFtoCNF_P_1(X_2466,X_2465),X_2465) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_P_1(X_2466,X_2465))),bind(B,$fot(X_2466)),bind(C,$fot(X_2465))]]) ).
cnf(refute_0_89,plain,
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P_1(A,Q),A,Q) ),
inference(canonicalize,[],[normalize_0_49]) ).
cnf(refute_0_90,plain,
( ~ coll(X_2338,X_2338,X_2338)
| ~ midp(skolemFOFtoCNF_B_1,X_2338,X_2338)
| midp(skolemFOFtoCNF_P_1(X_2338,Q),X_2338,Q) ),
inference(subst,[],[refute_0_89:[bind(A,$fot(X_2338)),bind(B,$fot(X_2338)),bind(C,$fot(X_2338)),bind(D,$fot(X_2338)),bind(M,$fot(skolemFOFtoCNF_B_1)),bind(N,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_91,plain,
para(X_2230,X_2231,X_2230,X_2231),
inference(subst,[],[refute_0_45:[bind(X_361,$fot(X_2230)),bind(X_362,$fot(X_2231))]]) ).
cnf(refute_0_92,plain,
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_93,plain,
( ~ midp(X_2232,X_2230,X_2230)
| ~ para(X_2230,X_2231,X_2230,X_2231)
| midp(X_2232,X_2231,X_2231) ),
inference(subst,[],[refute_0_92:[bind(A,$fot(X_2230)),bind(B,$fot(X_2230)),bind(C,$fot(X_2231)),bind(D,$fot(X_2231)),bind(M,$fot(X_2232))]]) ).
cnf(refute_0_94,plain,
( ~ midp(X_2232,X_2230,X_2230)
| midp(X_2232,X_2231,X_2231) ),
inference(resolve,[$cnf( para(X_2230,X_2231,X_2230,X_2231) )],[refute_0_91,refute_0_93]) ).
cnf(refute_0_95,plain,
( ~ midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| midp(skolemFOFtoCNF_B_1,X_2231,X_2231) ),
inference(subst,[],[refute_0_94:[bind(X_2230,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G))),bind(X_2232,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_96,plain,
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[normalize_0_53]) ).
cnf(refute_0_97,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| ~ cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(subst,[],[refute_0_96:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G))),bind(C,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_98,plain,
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_99,plain,
( ~ midp(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| midp(skolemFOFtoCNF_G,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_98:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(M,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_100,plain,
midp(skolemFOFtoCNF_G,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_28,refute_0_99]) ).
cnf(refute_0_101,plain,
( ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P(A,B,C,D,M,N),A,D) ),
inference(canonicalize,[],[normalize_0_59]) ).
cnf(refute_0_102,plain,
( ~ midp(skolemFOFtoCNF_G,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_101:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_C_1)),bind(M,$fot(skolemFOFtoCNF_G)),bind(N,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_103,plain,
midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_G,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_100,refute_0_102]) ).
cnf(refute_0_104,plain,
( ~ midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| ~ perp(skolemFOFtoCNF_B_1,X_2276,X_2276,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),X_2276,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_2276)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(M,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_105,plain,
( ~ perp(skolemFOFtoCNF_B_1,X_2276,X_2276,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),X_2276,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(subst,[],[refute_0_105:[bind(X_2276,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_107,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_61]) ).
cnf(refute_0_108,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_107:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_109,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_63]) ).
cnf(refute_0_110,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_109:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_111,plain,
( ~ cong(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1)
| circle(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_70:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(O,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_112,plain,
circle(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_B_1) )],[refute_0_31,refute_0_111]) ).
cnf(refute_0_113,plain,
( ~ circle(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_68:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(O,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_114,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_G,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_114,refute_0_110]) ).
cnf(refute_0_116,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_115,refute_0_108]) ).
cnf(refute_0_117,plain,
cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_116,refute_0_106]) ).
cnf(refute_0_118,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G))
| midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) )],[refute_0_117,refute_0_97]) ).
cnf(refute_0_119,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)),
inference(subst,[],[refute_0_66:[bind(C,$fot(skolemFOFtoCNF_B_1)),bind(X_1537,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G))),bind(X_1538,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_120,plain,
midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) )],[refute_0_119,refute_0_118]) ).
cnf(refute_0_121,plain,
midp(skolemFOFtoCNF_B_1,X_2231,X_2231),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G),skolemFOFtoCNF_P(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_G,skolemFOFtoCNF_G)) )],[refute_0_120,refute_0_95]) ).
cnf(refute_0_122,plain,
midp(skolemFOFtoCNF_B_1,X_2338,X_2338),
inference(subst,[],[refute_0_121:[bind(X_2231,$fot(X_2338))]]) ).
cnf(refute_0_123,plain,
( ~ coll(X_2338,X_2338,X_2338)
| midp(skolemFOFtoCNF_P_1(X_2338,Q),X_2338,Q) ),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,X_2338,X_2338) )],[refute_0_122,refute_0_90]) ).
cnf(refute_0_124,plain,
coll(X_2338,X_2338,X_2338),
inference(subst,[],[refute_0_66:[bind(C,$fot(X_2338)),bind(X_1537,$fot(X_2338)),bind(X_1538,$fot(X_2338))]]) ).
cnf(refute_0_125,plain,
midp(skolemFOFtoCNF_P_1(X_2338,Q),X_2338,Q),
inference(resolve,[$cnf( coll(X_2338,X_2338,X_2338) )],[refute_0_124,refute_0_123]) ).
cnf(refute_0_126,plain,
midp(skolemFOFtoCNF_P_1(X_2466,X_2465),X_2466,X_2465),
inference(subst,[],[refute_0_125:[bind(Q,$fot(X_2465)),bind(X_2338,$fot(X_2466))]]) ).
cnf(refute_0_127,plain,
cong(skolemFOFtoCNF_P_1(X_2466,X_2465),X_2466,skolemFOFtoCNF_P_1(X_2466,X_2465),X_2465),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(X_2466,X_2465),X_2466,X_2465) )],[refute_0_126,refute_0_88]) ).
cnf(refute_0_128,plain,
cong(skolemFOFtoCNF_P_1(X_4050,X_4049),X_4050,skolemFOFtoCNF_P_1(X_4050,X_4049),X_4049),
inference(subst,[],[refute_0_127:[bind(X_2465,$fot(X_4049)),bind(X_2466,$fot(X_4050))]]) ).
cnf(refute_0_129,plain,
cyclic(X_4050,X_4049,X_4049,X_4049),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_P_1(X_4050,X_4049),X_4050,skolemFOFtoCNF_P_1(X_4050,X_4049),X_4049) )],[refute_0_128,refute_0_87]) ).
cnf(refute_0_130,plain,
cyclic(X_4052,X_4051,X_4051,X_4051),
inference(subst,[],[refute_0_129:[bind(X_4049,$fot(X_4051)),bind(X_4050,$fot(X_4052))]]) ).
cnf(refute_0_131,plain,
cyclic(X_4051,X_4052,X_4051,X_4051),
inference(resolve,[$cnf( cyclic(X_4052,X_4051,X_4051,X_4051) )],[refute_0_130,refute_0_86]) ).
cnf(refute_0_132,plain,
cyclic(X_4053,X_4054,X_4053,X_4053),
inference(subst,[],[refute_0_131:[bind(X_4051,$fot(X_4053)),bind(X_4052,$fot(X_4054))]]) ).
cnf(refute_0_133,plain,
cyclic(X_4053,X_4053,X_4054,X_4053),
inference(resolve,[$cnf( cyclic(X_4053,X_4054,X_4053,X_4053) )],[refute_0_132,refute_0_84]) ).
cnf(refute_0_134,plain,
cyclic(X_4055,X_4055,X_4056,X_4055),
inference(subst,[],[refute_0_133:[bind(X_4053,$fot(X_4055)),bind(X_4054,$fot(X_4056))]]) ).
cnf(refute_0_135,plain,
cyclic(X_4055,X_4055,X_4055,X_4056),
inference(resolve,[$cnf( cyclic(X_4055,X_4055,X_4056,X_4055) )],[refute_0_134,refute_0_82]) ).
cnf(refute_0_136,plain,
cyclic(X_4057,X_4057,X_4057,X_4058),
inference(subst,[],[refute_0_135:[bind(X_4055,$fot(X_4057)),bind(X_4056,$fot(X_4058))]]) ).
cnf(refute_0_137,plain,
cyclic(X_4057,X_4057,X_4058,X_4058),
inference(resolve,[$cnf( cyclic(X_4057,X_4057,X_4057,X_4058) )],[refute_0_136,refute_0_80]) ).
cnf(refute_0_138,plain,
cyclic(X_4059,X_4059,X_4060,X_4060),
inference(subst,[],[refute_0_137:[bind(X_4057,$fot(X_4059)),bind(X_4058,$fot(X_4060))]]) ).
cnf(refute_0_139,plain,
( ~ cong(X_4059,X_4060,X_4059,X_4060)
| perp(X_4060,X_4059,X_4059,X_4060) ),
inference(resolve,[$cnf( cyclic(X_4059,X_4059,X_4060,X_4060) )],[refute_0_138,refute_0_79]) ).
cnf(refute_0_140,plain,
( ~ midp(X_2352,X_2351,X_2351)
| cong(X_2352,X_2351,X_2352,X_2351) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_2352)),bind(B,$fot(X_2351)),bind(C,$fot(X_2351))]]) ).
cnf(refute_0_141,plain,
( ~ midp(X_2350,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| midp(X_2350,X_2231,X_2231) ),
inference(subst,[],[refute_0_94:[bind(X_2230,$fot(skolemFOFtoCNF_B_1)),bind(X_2232,$fot(X_2350))]]) ).
cnf(refute_0_142,plain,
( ~ coll(X_2349,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| ~ cong(X_2349,skolemFOFtoCNF_B_1,X_2349,skolemFOFtoCNF_B_1)
| midp(X_2349,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_96:[bind(A,$fot(X_2349)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_143,plain,
( ~ cong(X_2348,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2348)
| cong(X_2348,skolemFOFtoCNF_B_1,X_2348,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_71:[bind(A,$fot(X_2348)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_2348))]]) ).
cnf(refute_0_144,plain,
( ~ cong(skolemFOFtoCNF_B_1,X_2342,X_2342,skolemFOFtoCNF_B_1)
| cong(X_2342,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2342) ),
inference(subst,[],[refute_0_73:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_2342)),bind(C,$fot(X_2342)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_145,plain,
( ~ cong(skolemFOFtoCNF_B_1,X_2339,skolemFOFtoCNF_B_1,X_2339)
| cong(skolemFOFtoCNF_B_1,X_2339,X_2339,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_71:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_2339)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_2339))]]) ).
cnf(refute_0_146,plain,
( ~ midp(skolemFOFtoCNF_B_1,X_2338,X_2338)
| cong(skolemFOFtoCNF_B_1,X_2338,skolemFOFtoCNF_B_1,X_2338) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_2338)),bind(C,$fot(X_2338))]]) ).
cnf(refute_0_147,plain,
cong(skolemFOFtoCNF_B_1,X_2338,skolemFOFtoCNF_B_1,X_2338),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,X_2338,X_2338) )],[refute_0_122,refute_0_146]) ).
cnf(refute_0_148,plain,
cong(skolemFOFtoCNF_B_1,X_2339,skolemFOFtoCNF_B_1,X_2339),
inference(subst,[],[refute_0_147:[bind(X_2338,$fot(X_2339))]]) ).
cnf(refute_0_149,plain,
cong(skolemFOFtoCNF_B_1,X_2339,X_2339,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,X_2339,skolemFOFtoCNF_B_1,X_2339) )],[refute_0_148,refute_0_145]) ).
cnf(refute_0_150,plain,
cong(skolemFOFtoCNF_B_1,X_2342,X_2342,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_149:[bind(X_2339,$fot(X_2342))]]) ).
cnf(refute_0_151,plain,
cong(X_2342,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2342),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,X_2342,X_2342,skolemFOFtoCNF_B_1) )],[refute_0_150,refute_0_144]) ).
cnf(refute_0_152,plain,
cong(X_2348,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2348),
inference(subst,[],[refute_0_151:[bind(X_2342,$fot(X_2348))]]) ).
cnf(refute_0_153,plain,
cong(X_2348,skolemFOFtoCNF_B_1,X_2348,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(X_2348,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_2348) )],[refute_0_152,refute_0_143]) ).
cnf(refute_0_154,plain,
cong(X_2349,skolemFOFtoCNF_B_1,X_2349,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_153:[bind(X_2348,$fot(X_2349))]]) ).
cnf(refute_0_155,plain,
( ~ coll(X_2349,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| midp(X_2349,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( cong(X_2349,skolemFOFtoCNF_B_1,X_2349,skolemFOFtoCNF_B_1) )],[refute_0_154,refute_0_142]) ).
cnf(refute_0_156,plain,
coll(X_2349,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_66:[bind(C,$fot(X_2349)),bind(X_1537,$fot(skolemFOFtoCNF_B_1)),bind(X_1538,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_157,plain,
midp(X_2349,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(X_2349,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_156,refute_0_155]) ).
cnf(refute_0_158,plain,
midp(X_2350,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_157:[bind(X_2349,$fot(X_2350))]]) ).
cnf(refute_0_159,plain,
midp(X_2350,X_2231,X_2231),
inference(resolve,[$cnf( midp(X_2350,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_158,refute_0_141]) ).
cnf(refute_0_160,plain,
midp(X_2352,X_2351,X_2351),
inference(subst,[],[refute_0_159:[bind(X_2231,$fot(X_2351)),bind(X_2350,$fot(X_2352))]]) ).
cnf(refute_0_161,plain,
cong(X_2352,X_2351,X_2352,X_2351),
inference(resolve,[$cnf( midp(X_2352,X_2351,X_2351) )],[refute_0_160,refute_0_140]) ).
cnf(refute_0_162,plain,
cong(X_4059,X_4060,X_4059,X_4060),
inference(subst,[],[refute_0_161:[bind(X_2351,$fot(X_4060)),bind(X_2352,$fot(X_4059))]]) ).
cnf(refute_0_163,plain,
perp(X_4060,X_4059,X_4059,X_4060),
inference(resolve,[$cnf( cong(X_4059,X_4060,X_4059,X_4060) )],[refute_0_162,refute_0_139]) ).
cnf(refute_0_164,plain,
perp(X_4062,X_4061,X_4061,X_4062),
inference(subst,[],[refute_0_163:[bind(X_4059,$fot(X_4061)),bind(X_4060,$fot(X_4062))]]) ).
cnf(refute_0_165,plain,
( ~ midp(M,X_4062,X_4062)
| cong(X_4062,M,X_4061,M) ),
inference(resolve,[$cnf( perp(X_4062,X_4061,X_4061,X_4062) )],[refute_0_164,refute_0_77]) ).
cnf(refute_0_166,plain,
midp(M,X_4062,X_4062),
inference(subst,[],[refute_0_159:[bind(X_2231,$fot(X_4062)),bind(X_2350,$fot(M))]]) ).
cnf(refute_0_167,plain,
cong(X_4062,M,X_4061,M),
inference(resolve,[$cnf( midp(M,X_4062,X_4062) )],[refute_0_166,refute_0_165]) ).
cnf(refute_0_168,plain,
cong(X_4081,X_4079,X_4080,X_4079),
inference(subst,[],[refute_0_167:[bind(M,$fot(X_4079)),bind(X_4061,$fot(X_4080)),bind(X_4062,$fot(X_4081))]]) ).
cnf(refute_0_169,plain,
cong(X_4081,X_4079,X_4079,X_4080),
inference(resolve,[$cnf( cong(X_4081,X_4079,X_4080,X_4079) )],[refute_0_168,refute_0_75]) ).
cnf(refute_0_170,plain,
cong(X_4084,X_4082,X_4082,X_4083),
inference(subst,[],[refute_0_169:[bind(X_4079,$fot(X_4082)),bind(X_4080,$fot(X_4083)),bind(X_4081,$fot(X_4084))]]) ).
cnf(refute_0_171,plain,
cong(X_4082,X_4083,X_4084,X_4082),
inference(resolve,[$cnf( cong(X_4084,X_4082,X_4082,X_4083) )],[refute_0_170,refute_0_74]) ).
cnf(refute_0_172,plain,
cong(X_4107,X_4108,X_4109,X_4107),
inference(subst,[],[refute_0_171:[bind(X_4082,$fot(X_4107)),bind(X_4083,$fot(X_4108)),bind(X_4084,$fot(X_4109))]]) ).
cnf(refute_0_173,plain,
cong(X_4107,X_4108,X_4107,X_4109),
inference(resolve,[$cnf( cong(X_4107,X_4108,X_4109,X_4107) )],[refute_0_172,refute_0_72]) ).
cnf(refute_0_174,plain,
cong(O,A,O,B),
inference(subst,[],[refute_0_173:[bind(X_4107,$fot(O)),bind(X_4108,$fot(A)),bind(X_4109,$fot(B))]]) ).
cnf(refute_0_175,plain,
( ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(resolve,[$cnf( cong(O,A,O,B) )],[refute_0_174,refute_0_70]) ).
cnf(refute_0_176,plain,
cong(O,A,O,C),
inference(subst,[],[refute_0_173:[bind(X_4107,$fot(O)),bind(X_4108,$fot(A)),bind(X_4109,$fot(C))]]) ).
cnf(refute_0_177,plain,
circle(O,A,B,C),
inference(resolve,[$cnf( cong(O,A,O,C) )],[refute_0_176,refute_0_175]) ).
cnf(refute_0_178,plain,
circle(X_18451,X_18448,X_18449,X_18450),
inference(subst,[],[refute_0_177:[bind(A,$fot(X_18448)),bind(B,$fot(X_18449)),bind(C,$fot(X_18450)),bind(O,$fot(X_18451))]]) ).
cnf(refute_0_179,plain,
perp(X_18448,X_18449,X_18449,X_18450),
inference(resolve,[$cnf( circle(X_18451,X_18448,X_18449,X_18450) )],[refute_0_178,refute_0_69]) ).
cnf(refute_0_180,plain,
perp(skolemFOFtoCNF_E,skolemFOFtoCNF_K,skolemFOFtoCNF_K,skolemFOFtoCNF_N),
inference(subst,[],[refute_0_179:[bind(X_18448,$fot(skolemFOFtoCNF_E)),bind(X_18449,$fot(skolemFOFtoCNF_K)),bind(X_18450,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_181,plain,
$false,
inference(resolve,[$cnf( perp(skolemFOFtoCNF_E,skolemFOFtoCNF_K,skolemFOFtoCNF_K,skolemFOFtoCNF_N) )],[refute_0_180,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO616+1 : TPTP v8.1.0. Released v7.5.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Fri Jun 17 18:35:28 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 49.71/49.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.71/49.91
% 49.71/49.91 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.71/49.93
%------------------------------------------------------------------------------