TSTP Solution File: GEO656+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO656+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 05:28:06 EDT 2022
% Result : Theorem 32.98s 33.20s
% Output : CNFRefutation 33.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 29
% Syntax : Number of formulae : 300 ( 107 unt; 0 def)
% Number of atoms : 584 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 514 ( 230 ~; 225 |; 28 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 790 ( 93 sgn 397 !; 9 ?)
% 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(ruleD44,axiom,
! [A,B,C,E,F] :
( ( midp(E,A,B)
& midp(F,A,C) )
=> para(E,F,B,C) ) ).
fof(ruleD52,axiom,
! [A,B,C,M] :
( ( perp(A,B,B,C)
& midp(M,A,C) )
=> cong(A,M,B,M) ) ).
fof(ruleD53,axiom,
! [A,B,C,O] :
( ( circle(O,A,B,C)
& coll(O,A,C) )
=> perp(A,B,B,C) ) ).
fof(ruleD57,axiom,
! [A,B,P,Q] :
( ( cong(A,P,B,P)
& cong(A,Q,B,Q)
& cyclic(A,B,P,Q) )
=> perp(P,A,A,Q) ) ).
fof(ruleD64,axiom,
! [A,B,C,D,M] :
( ( midp(M,A,B)
& para(A,C,B,D)
& para(A,D,B,C) )
=> midp(M,C,D) ) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ) ).
fof(ruleD67,axiom,
! [A,B,C] :
( ( cong(A,B,A,C)
& coll(A,B,C) )
=> midp(A,B,C) ) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ) ).
fof(ruleD69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ) ).
fof(ruleX7,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( midp(M,A,B)
& midp(N,C,D)
& coll(C,A,B)
& coll(D,A,B) )
=> midp(P,A,Q) ) ).
fof(exemplo6GDDFULLmoreE02314,conjecture,
! [A,B,C,D,E,F] :
( ( midp(D,B,A)
& eqangle(E,D,D,A,E,D,D,C)
& eqangle(F,D,D,B,F,D,D,C) )
=> para(E,F,A,B) ) ).
fof(subgoal_0,plain,
! [A,B,C,D,E,F] :
( ( midp(D,B,A)
& eqangle(E,D,D,A,E,D,D,C)
& eqangle(F,D,D,B,F,D,D,C) )
=> para(E,F,A,B) ),
inference(strip,[],[exemplo6GDDFULLmoreE02314]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D,E,F] :
( ( midp(D,B,A)
& eqangle(E,D,D,A,E,D,D,C)
& eqangle(F,D,D,B,F,D,D,C) )
=> para(E,F,A,B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D,E,F] :
( ~ para(E,F,A,B)
& eqangle(E,D,D,A,E,D,D,C)
& eqangle(F,D,D,B,F,D,D,C)
& midp(D,B,A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ para(skolemFOFtoCNF_E,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& eqangle(skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1)
& eqangle(skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_F,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1)
& midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ para(skolemFOFtoCNF_E,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C,E,F] :
( ~ midp(E,A,B)
| ~ midp(F,A,C)
| para(E,F,B,C) ),
inference(canonicalize,[],[ruleD44]) ).
fof(normalize_0_4,plain,
! [A,B,C,E,F] :
( ~ midp(E,A,B)
| ~ midp(F,A,C)
| para(E,F,B,C) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[ruleD67]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[ruleD23]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[ruleD24]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,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_12,plain,
! [A,B,C,M] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,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_14,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_13]) ).
fof(normalize_0_15,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_16,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_15]) ).
fof(normalize_0_17,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[ruleD14]) ).
fof(normalize_0_18,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[ruleD15]) ).
fof(normalize_0_20,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[ruleD16]) ).
fof(normalize_0_22,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,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_24,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_23]) ).
fof(normalize_0_25,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[ruleD68]) ).
fof(normalize_0_26,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,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_28,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_27]) ).
fof(normalize_0_29,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_28]) ).
fof(normalize_0_30,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[ruleD1]) ).
fof(normalize_0_31,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_33,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD66]) ).
fof(normalize_0_35,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_34]) ).
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,[],[ruleD39]) ).
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] :
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,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_40,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(specialize,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_42,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_43,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_42]) ).
fof(normalize_0_44,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_43]) ).
fof(normalize_0_45,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_46,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_45]) ).
fof(normalize_0_47,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_48,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_47]) ).
fof(normalize_0_49,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_50,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_49]) ).
fof(normalize_0_51,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_52,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_51]) ).
fof(normalize_0_53,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_54,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(specialize,[],[normalize_0_53]) ).
fof(normalize_0_55,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[ruleD11]) ).
fof(normalize_0_56,plain,
! [A,B,M] :
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(specialize,[],[normalize_0_55]) ).
fof(normalize_0_57,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[ruleD53]) ).
fof(normalize_0_58,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(specialize,[],[normalize_0_57]) ).
fof(normalize_0_59,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[ruleD2]) ).
fof(normalize_0_60,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(specialize,[],[normalize_0_59]) ).
fof(normalize_0_61,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD69]) ).
fof(normalize_0_62,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_61]) ).
cnf(refute_0_0,plain,
~ para(skolemFOFtoCNF_E,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ midp(E,A,B)
| ~ midp(F,A,C)
| para(E,F,B,C) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ coll(X_3162,X_3163,X_3164)
| ~ cong(X_3162,X_3163,X_3162,X_3164)
| midp(X_3162,X_3163,X_3164) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_3162)),bind(B,$fot(X_3163)),bind(C,$fot(X_3164))]]) ).
cnf(refute_0_4,plain,
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ cong(X_3157,X_3158,X_3159,X_3157)
| cong(X_3157,X_3158,X_3157,X_3159) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_3157)),bind(B,$fot(X_3158)),bind(C,$fot(X_3159)),bind(D,$fot(X_3157))]]) ).
cnf(refute_0_6,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ cong(X_3134,X_3132,X_3132,X_3133)
| cong(X_3132,X_3133,X_3134,X_3132) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_3134)),bind(B,$fot(X_3132)),bind(C,$fot(X_3132)),bind(D,$fot(X_3133))]]) ).
cnf(refute_0_8,plain,
( ~ cong(X_3131,X_3129,X_3130,X_3129)
| cong(X_3131,X_3129,X_3129,X_3130) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_3131)),bind(B,$fot(X_3129)),bind(C,$fot(X_3130)),bind(D,$fot(X_3129))]]) ).
cnf(refute_0_9,plain,
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ midp(M,X_3112,X_3112)
| ~ perp(X_3112,X_3111,X_3111,X_3112)
| cong(X_3112,M,X_3111,M) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_3112)),bind(B,$fot(X_3111)),bind(C,$fot(X_3112))]]) ).
cnf(refute_0_11,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_14]) ).
cnf(refute_0_12,plain,
( ~ cong(X_3109,X_3110,X_3109,X_3110)
| ~ cyclic(X_3109,X_3109,X_3110,X_3110)
| perp(X_3110,X_3109,X_3109,X_3110) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_3109)),bind(B,$fot(X_3109)),bind(P,$fot(X_3110)),bind(Q,$fot(X_3110))]]) ).
cnf(refute_0_13,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_14,plain,
( ~ cyclic(X_3107,X_3107,X_3107,X_3108)
| cyclic(X_3107,X_3107,X_3108,X_3108) ),
inference(subst,[],[refute_0_13:[bind(A,$fot(X_3107)),bind(B,$fot(X_3107)),bind(C,$fot(X_3107)),bind(D,$fot(X_3108)),bind(E,$fot(X_3108))]]) ).
cnf(refute_0_15,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_16,plain,
( ~ cyclic(X_3105,X_3105,X_3106,X_3105)
| cyclic(X_3105,X_3105,X_3105,X_3106) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_3105)),bind(B,$fot(X_3105)),bind(C,$fot(X_3106)),bind(D,$fot(X_3105))]]) ).
cnf(refute_0_17,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_18,plain,
( ~ cyclic(X_3103,X_3104,X_3103,X_3103)
| cyclic(X_3103,X_3103,X_3104,X_3103) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_3103)),bind(B,$fot(X_3104)),bind(C,$fot(X_3103)),bind(D,$fot(X_3103))]]) ).
cnf(refute_0_19,plain,
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_20,plain,
( ~ cyclic(X_3102,X_3101,X_3101,X_3101)
| cyclic(X_3101,X_3102,X_3101,X_3101) ),
inference(subst,[],[refute_0_19:[bind(A,$fot(X_3102)),bind(B,$fot(X_3101)),bind(C,$fot(X_3101)),bind(D,$fot(X_3101))]]) ).
cnf(refute_0_21,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_22,plain,
( ~ cong(skolemFOFtoCNF_P_1(X_3100,X_3099),X_3100,skolemFOFtoCNF_P_1(X_3100,X_3099),X_3099)
| cyclic(X_3100,X_3099,X_3099,X_3099) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(X_3100)),bind(B,$fot(X_3099)),bind(C,$fot(X_3099)),bind(D,$fot(X_3099)),bind(O,$fot(skolemFOFtoCNF_P_1(X_3100,X_3099)))]]) ).
cnf(refute_0_23,plain,
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_24,plain,
( ~ midp(skolemFOFtoCNF_P_1(X_2516,X_2515),X_2516,X_2515)
| cong(skolemFOFtoCNF_P_1(X_2516,X_2515),X_2516,skolemFOFtoCNF_P_1(X_2516,X_2515),X_2515) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_P_1(X_2516,X_2515))),bind(B,$fot(X_2516)),bind(C,$fot(X_2515))]]) ).
cnf(refute_0_25,plain,
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P_1(A,Q),A,Q) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_26,plain,
( ~ coll(D,D,D)
| ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(D)),bind(B,$fot(D)),bind(C,$fot(D)),bind(M,$fot(N))]]) ).
cnf(refute_0_27,plain,
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_28,plain,
( ~ coll(X_368,X_368,X_367)
| coll(X_368,X_367,X_368) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_368)),bind(B,$fot(X_368)),bind(C,$fot(X_367))]]) ).
cnf(refute_0_29,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_30,plain,
( ~ coll(X_365,X_366,X_366)
| coll(X_366,X_366,X_365) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_365)),bind(B,$fot(X_366)),bind(C,$fot(X_366)),bind(D,$fot(X_366))]]) ).
cnf(refute_0_31,plain,
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_32,plain,
( ~ para(X_360,X_361,X_360,X_361)
| coll(X_360,X_361,X_361) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(X_360)),bind(B,$fot(X_361)),bind(C,$fot(X_361))]]) ).
cnf(refute_0_33,plain,
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_34,plain,
( ~ eqangle(X_358,X_359,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_358,X_359,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(X_358,X_359,X_358,X_359) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(X_358)),bind(B,$fot(X_359)),bind(C,$fot(X_358)),bind(D,$fot(X_359)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_35,plain,
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_36,plain,
( ~ cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_35:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_37,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_13:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(E,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_38,plain,
( ~ cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_39,plain,
midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_40,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_41,plain,
cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_41,refute_0_38]) ).
cnf(refute_0_43,plain,
cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_42,refute_0_37]) ).
cnf(refute_0_44,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_43,refute_0_36]) ).
cnf(refute_0_45,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_46,plain,
para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_48,plain,
( ~ para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154) ),
inference(subst,[],[refute_0_47:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(P,$fot(X_153)),bind(Q,$fot(X_154))]]) ).
cnf(refute_0_49,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_46,refute_0_48]) ).
cnf(refute_0_50,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_356,X_357,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_356,X_357),
inference(subst,[],[refute_0_49:[bind(X_153,$fot(X_356)),bind(X_154,$fot(X_357))]]) ).
cnf(refute_0_51,plain,
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_52,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_356,X_357,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_356,X_357)
| eqangle(X_356,X_357,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_356,X_357,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_51:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(X_356)),bind(D,$fot(X_357)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A)),bind(U,$fot(X_356)),bind(V,$fot(X_357))]]) ).
cnf(refute_0_53,plain,
eqangle(X_356,X_357,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_356,X_357,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_356,X_357,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_356,X_357) )],[refute_0_50,refute_0_52]) ).
cnf(refute_0_54,plain,
eqangle(X_358,X_359,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_358,X_359,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_53:[bind(X_356,$fot(X_358)),bind(X_357,$fot(X_359))]]) ).
cnf(refute_0_55,plain,
para(X_358,X_359,X_358,X_359),
inference(resolve,[$cnf( eqangle(X_358,X_359,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_358,X_359,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_54,refute_0_34]) ).
cnf(refute_0_56,plain,
para(X_360,X_361,X_360,X_361),
inference(subst,[],[refute_0_55:[bind(X_358,$fot(X_360)),bind(X_359,$fot(X_361))]]) ).
cnf(refute_0_57,plain,
coll(X_360,X_361,X_361),
inference(resolve,[$cnf( para(X_360,X_361,X_360,X_361) )],[refute_0_56,refute_0_32]) ).
cnf(refute_0_58,plain,
coll(X_365,X_366,X_366),
inference(subst,[],[refute_0_57:[bind(X_360,$fot(X_365)),bind(X_361,$fot(X_366))]]) ).
cnf(refute_0_59,plain,
coll(X_366,X_366,X_365),
inference(resolve,[$cnf( coll(X_365,X_366,X_366) )],[refute_0_58,refute_0_30]) ).
cnf(refute_0_60,plain,
coll(X_368,X_368,X_367),
inference(subst,[],[refute_0_59:[bind(X_365,$fot(X_367)),bind(X_366,$fot(X_368))]]) ).
cnf(refute_0_61,plain,
coll(X_368,X_367,X_368),
inference(resolve,[$cnf( coll(X_368,X_368,X_367) )],[refute_0_60,refute_0_28]) ).
cnf(refute_0_62,plain,
coll(D,D,D),
inference(subst,[],[refute_0_61:[bind(X_367,$fot(D)),bind(X_368,$fot(D))]]) ).
cnf(refute_0_63,plain,
( ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(resolve,[$cnf( coll(D,D,D) )],[refute_0_62,refute_0_26]) ).
cnf(refute_0_64,plain,
( ~ midp(skolemFOFtoCNF_B_1,X_2489,X_2489)
| midp(skolemFOFtoCNF_P_1(X_2489,Q),X_2489,Q) ),
inference(subst,[],[refute_0_63:[bind(D,$fot(X_2489)),bind(N,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_65,plain,
para(X_2428,X_2429,X_2428,X_2429),
inference(subst,[],[refute_0_55:[bind(X_358,$fot(X_2428)),bind(X_359,$fot(X_2429))]]) ).
cnf(refute_0_66,plain,
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_67,plain,
( ~ midp(X_2430,X_2428,X_2428)
| ~ para(X_2428,X_2429,X_2428,X_2429)
| midp(X_2430,X_2429,X_2429) ),
inference(subst,[],[refute_0_66:[bind(A,$fot(X_2428)),bind(B,$fot(X_2428)),bind(C,$fot(X_2429)),bind(D,$fot(X_2429)),bind(M,$fot(X_2430))]]) ).
cnf(refute_0_68,plain,
( ~ midp(X_2430,X_2428,X_2428)
| midp(X_2430,X_2429,X_2429) ),
inference(resolve,[$cnf( para(X_2428,X_2429,X_2428,X_2429) )],[refute_0_65,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| midp(skolemFOFtoCNF_B_1,X_2429,X_2429) ),
inference(subst,[],[refute_0_68:[bind(X_2428,$fot(skolemFOFtoCNF_D)),bind(X_2430,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_70,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| ~ cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D)
| midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_71,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_72,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_71:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_73,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_74,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_73:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_75,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_76,plain,
( ~ cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1)
| circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_75:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(O,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_77,plain,
( ~ midp(M,B,A)
| midp(M,A,B) ),
inference(canonicalize,[],[normalize_0_56]) ).
cnf(refute_0_78,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_77:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(M,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_79,plain,
midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_39,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_81,plain,
cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1) )],[refute_0_81,refute_0_76]) ).
cnf(refute_0_83,plain,
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_84,plain,
( ~ coll(X_1762,skolemFOFtoCNF_A,C)
| ~ coll(X_1762,skolemFOFtoCNF_A,X_1763)
| coll(C,X_1763,X_1762) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_1762)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_1763))]]) ).
cnf(refute_0_85,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_60]) ).
cnf(refute_0_86,plain,
( ~ coll(skolemFOFtoCNF_A,X_1760,X_1761)
| coll(X_1760,skolemFOFtoCNF_A,X_1761) ),
inference(subst,[],[refute_0_85:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_1760)),bind(C,$fot(X_1761))]]) ).
cnf(refute_0_87,plain,
( ~ coll(X_1746,skolemFOFtoCNF_B_1,D)
| ~ coll(X_1746,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,D,X_1746) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_1746)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_88,plain,
( ~ coll(skolemFOFtoCNF_A,X_1733,C)
| ~ coll(skolemFOFtoCNF_A,X_1733,skolemFOFtoCNF_B_1)
| coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(X_1733)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_89,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_90,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_85:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_91,plain,
( ~ midp(A,B,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_62]) ).
cnf(refute_0_92,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_91:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_93,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_79,refute_0_92]) ).
cnf(refute_0_94,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_93,refute_0_90]) ).
cnf(refute_0_95,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1) )],[refute_0_94,refute_0_89]) ).
cnf(refute_0_96,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1727)
| ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,X_1727,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(X_1727))]]) ).
cnf(refute_0_97,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1727)
| coll(skolemFOFtoCNF_A,X_1727,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1727),
inference(subst,[],[refute_0_59:[bind(X_365,$fot(X_1727)),bind(X_366,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_99,plain,
coll(skolemFOFtoCNF_A,X_1727,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_1727) )],[refute_0_98,refute_0_97]) ).
cnf(refute_0_100,plain,
coll(skolemFOFtoCNF_A,X_1733,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_99:[bind(X_1727,$fot(X_1733))]]) ).
cnf(refute_0_101,plain,
( ~ coll(skolemFOFtoCNF_A,X_1733,C)
| coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_1733,skolemFOFtoCNF_B_1) )],[refute_0_100,refute_0_88]) ).
cnf(refute_0_102,plain,
coll(X_1725,X_1725,X_1726),
inference(subst,[],[refute_0_59:[bind(X_365,$fot(X_1726)),bind(X_366,$fot(X_1725))]]) ).
cnf(refute_0_103,plain,
( ~ coll(X_1725,X_1725,X_1726)
| ~ coll(X_1725,X_1725,X_1727)
| coll(X_1726,X_1727,X_1725) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_1725)),bind(B,$fot(X_1725)),bind(C,$fot(X_1726)),bind(D,$fot(X_1727))]]) ).
cnf(refute_0_104,plain,
( ~ coll(X_1725,X_1725,X_1727)
| coll(X_1726,X_1727,X_1725) ),
inference(resolve,[$cnf( coll(X_1725,X_1725,X_1726) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
coll(X_1725,X_1725,X_1727),
inference(subst,[],[refute_0_59:[bind(X_365,$fot(X_1727)),bind(X_366,$fot(X_1725))]]) ).
cnf(refute_0_106,plain,
coll(X_1726,X_1727,X_1725),
inference(resolve,[$cnf( coll(X_1725,X_1725,X_1727) )],[refute_0_105,refute_0_104]) ).
cnf(refute_0_107,plain,
coll(skolemFOFtoCNF_A,X_1733,C),
inference(subst,[],[refute_0_106:[bind(X_1725,$fot(C)),bind(X_1726,$fot(skolemFOFtoCNF_A)),bind(X_1727,$fot(X_1733))]]) ).
cnf(refute_0_108,plain,
coll(C,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_1733,C) )],[refute_0_107,refute_0_101]) ).
cnf(refute_0_109,plain,
coll(X_1746,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_108:[bind(C,$fot(X_1746))]]) ).
cnf(refute_0_110,plain,
( ~ coll(X_1746,skolemFOFtoCNF_B_1,D)
| coll(skolemFOFtoCNF_A,D,X_1746) ),
inference(resolve,[$cnf( coll(X_1746,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_109,refute_0_87]) ).
cnf(refute_0_111,plain,
coll(X_1746,skolemFOFtoCNF_B_1,D),
inference(subst,[],[refute_0_106:[bind(X_1725,$fot(D)),bind(X_1726,$fot(X_1746)),bind(X_1727,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_112,plain,
coll(skolemFOFtoCNF_A,D,X_1746),
inference(resolve,[$cnf( coll(X_1746,skolemFOFtoCNF_B_1,D) )],[refute_0_111,refute_0_110]) ).
cnf(refute_0_113,plain,
coll(skolemFOFtoCNF_A,X_1760,X_1761),
inference(subst,[],[refute_0_112:[bind(D,$fot(X_1760)),bind(X_1746,$fot(X_1761))]]) ).
cnf(refute_0_114,plain,
coll(X_1760,skolemFOFtoCNF_A,X_1761),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,X_1760,X_1761) )],[refute_0_113,refute_0_86]) ).
cnf(refute_0_115,plain,
coll(X_1762,skolemFOFtoCNF_A,X_1763),
inference(subst,[],[refute_0_114:[bind(X_1760,$fot(X_1762)),bind(X_1761,$fot(X_1763))]]) ).
cnf(refute_0_116,plain,
( ~ coll(X_1762,skolemFOFtoCNF_A,C)
| coll(C,X_1763,X_1762) ),
inference(resolve,[$cnf( coll(X_1762,skolemFOFtoCNF_A,X_1763) )],[refute_0_115,refute_0_84]) ).
cnf(refute_0_117,plain,
coll(X_1762,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_106:[bind(X_1725,$fot(C)),bind(X_1726,$fot(X_1762)),bind(X_1727,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_118,plain,
coll(C,X_1763,X_1762),
inference(resolve,[$cnf( coll(X_1762,skolemFOFtoCNF_A,C) )],[refute_0_117,refute_0_116]) ).
cnf(refute_0_119,plain,
coll(O,A,C),
inference(subst,[],[refute_0_118:[bind(C,$fot(O)),bind(X_1762,$fot(C)),bind(X_1763,$fot(A))]]) ).
cnf(refute_0_120,plain,
( ~ circle(O,A,B,C)
| perp(A,B,B,C) ),
inference(resolve,[$cnf( coll(O,A,C) )],[refute_0_119,refute_0_83]) ).
cnf(refute_0_121,plain,
( ~ circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_120:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(O,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_122,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_82,refute_0_121]) ).
cnf(refute_0_123,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_122,refute_0_74]) ).
cnf(refute_0_124,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_123,refute_0_72]) ).
cnf(refute_0_125,plain,
( ~ midp(X_2486,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_B_1,X_2486,skolemFOFtoCNF_B_1,X_2486) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A)),bind(M,$fot(X_2486))]]) ).
cnf(refute_0_126,plain,
( ~ midp(X_2486,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_B_1,X_2486,skolemFOFtoCNF_B_1,X_2486) ),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_126:[bind(X_2486,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_128,plain,
cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A) )],[refute_0_39,refute_0_127]) ).
cnf(refute_0_129,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D) )],[refute_0_128,refute_0_70]) ).
cnf(refute_0_130,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_118:[bind(C,$fot(skolemFOFtoCNF_B_1)),bind(X_1762,$fot(skolemFOFtoCNF_D)),bind(X_1763,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_131,plain,
midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_130,refute_0_129]) ).
cnf(refute_0_132,plain,
midp(skolemFOFtoCNF_B_1,X_2429,X_2429),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_131,refute_0_69]) ).
cnf(refute_0_133,plain,
midp(skolemFOFtoCNF_B_1,X_2489,X_2489),
inference(subst,[],[refute_0_132:[bind(X_2429,$fot(X_2489))]]) ).
cnf(refute_0_134,plain,
midp(skolemFOFtoCNF_P_1(X_2489,Q),X_2489,Q),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_B_1,X_2489,X_2489) )],[refute_0_133,refute_0_64]) ).
cnf(refute_0_135,plain,
midp(skolemFOFtoCNF_P_1(X_2516,X_2515),X_2516,X_2515),
inference(subst,[],[refute_0_134:[bind(Q,$fot(X_2515)),bind(X_2489,$fot(X_2516))]]) ).
cnf(refute_0_136,plain,
cong(skolemFOFtoCNF_P_1(X_2516,X_2515),X_2516,skolemFOFtoCNF_P_1(X_2516,X_2515),X_2515),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(X_2516,X_2515),X_2516,X_2515) )],[refute_0_135,refute_0_24]) ).
cnf(refute_0_137,plain,
cong(skolemFOFtoCNF_P_1(X_3100,X_3099),X_3100,skolemFOFtoCNF_P_1(X_3100,X_3099),X_3099),
inference(subst,[],[refute_0_136:[bind(X_2515,$fot(X_3099)),bind(X_2516,$fot(X_3100))]]) ).
cnf(refute_0_138,plain,
cyclic(X_3100,X_3099,X_3099,X_3099),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_P_1(X_3100,X_3099),X_3100,skolemFOFtoCNF_P_1(X_3100,X_3099),X_3099) )],[refute_0_137,refute_0_22]) ).
cnf(refute_0_139,plain,
cyclic(X_3102,X_3101,X_3101,X_3101),
inference(subst,[],[refute_0_138:[bind(X_3099,$fot(X_3101)),bind(X_3100,$fot(X_3102))]]) ).
cnf(refute_0_140,plain,
cyclic(X_3101,X_3102,X_3101,X_3101),
inference(resolve,[$cnf( cyclic(X_3102,X_3101,X_3101,X_3101) )],[refute_0_139,refute_0_20]) ).
cnf(refute_0_141,plain,
cyclic(X_3103,X_3104,X_3103,X_3103),
inference(subst,[],[refute_0_140:[bind(X_3101,$fot(X_3103)),bind(X_3102,$fot(X_3104))]]) ).
cnf(refute_0_142,plain,
cyclic(X_3103,X_3103,X_3104,X_3103),
inference(resolve,[$cnf( cyclic(X_3103,X_3104,X_3103,X_3103) )],[refute_0_141,refute_0_18]) ).
cnf(refute_0_143,plain,
cyclic(X_3105,X_3105,X_3106,X_3105),
inference(subst,[],[refute_0_142:[bind(X_3103,$fot(X_3105)),bind(X_3104,$fot(X_3106))]]) ).
cnf(refute_0_144,plain,
cyclic(X_3105,X_3105,X_3105,X_3106),
inference(resolve,[$cnf( cyclic(X_3105,X_3105,X_3106,X_3105) )],[refute_0_143,refute_0_16]) ).
cnf(refute_0_145,plain,
cyclic(X_3107,X_3107,X_3107,X_3108),
inference(subst,[],[refute_0_144:[bind(X_3105,$fot(X_3107)),bind(X_3106,$fot(X_3108))]]) ).
cnf(refute_0_146,plain,
cyclic(X_3107,X_3107,X_3108,X_3108),
inference(resolve,[$cnf( cyclic(X_3107,X_3107,X_3107,X_3108) )],[refute_0_145,refute_0_14]) ).
cnf(refute_0_147,plain,
cyclic(X_3109,X_3109,X_3110,X_3110),
inference(subst,[],[refute_0_146:[bind(X_3107,$fot(X_3109)),bind(X_3108,$fot(X_3110))]]) ).
cnf(refute_0_148,plain,
( ~ cong(X_3109,X_3110,X_3109,X_3110)
| perp(X_3110,X_3109,X_3109,X_3110) ),
inference(resolve,[$cnf( cyclic(X_3109,X_3109,X_3110,X_3110) )],[refute_0_147,refute_0_12]) ).
cnf(refute_0_149,plain,
( ~ midp(X_2527,X_2526,X_2526)
| cong(X_2527,X_2526,X_2527,X_2526) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_2527)),bind(B,$fot(X_2526)),bind(C,$fot(X_2526))]]) ).
cnf(refute_0_150,plain,
( ~ midp(X_2513,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| midp(X_2513,X_2429,X_2429) ),
inference(subst,[],[refute_0_68:[bind(X_2428,$fot(skolemFOFtoCNF_D)),bind(X_2430,$fot(X_2513))]]) ).
cnf(refute_0_151,plain,
( ~ coll(X_2512,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| ~ cong(X_2512,skolemFOFtoCNF_D,X_2512,skolemFOFtoCNF_D)
| midp(X_2512,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_2512)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_152,plain,
( ~ cong(X_2510,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_2510)
| cong(X_2510,skolemFOFtoCNF_D,X_2510,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_2510)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_2510))]]) ).
cnf(refute_0_153,plain,
( ~ cong(skolemFOFtoCNF_D,X_2507,X_2507,skolemFOFtoCNF_D)
| cong(X_2507,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_2507) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_2507)),bind(C,$fot(X_2507)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_154,plain,
( ~ cong(skolemFOFtoCNF_D,X_2494,skolemFOFtoCNF_D,X_2494)
| cong(skolemFOFtoCNF_D,X_2494,X_2494,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_2494)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_2494))]]) ).
cnf(refute_0_155,plain,
( ~ midp(skolemFOFtoCNF_D,X_2490,X_2490)
| cong(skolemFOFtoCNF_D,X_2490,skolemFOFtoCNF_D,X_2490) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(X_2490)),bind(C,$fot(X_2490))]]) ).
cnf(refute_0_156,plain,
( ~ midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| midp(skolemFOFtoCNF_D,X_2429,X_2429) ),
inference(subst,[],[refute_0_68:[bind(X_2428,$fot(skolemFOFtoCNF_B_1)),bind(X_2430,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_157,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| ~ cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1)
| midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_158,plain,
( ~ cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_159,plain,
( ~ cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_160,plain,
( ~ cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D)
| cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_161,plain,
cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D) )],[refute_0_128,refute_0_160]) ).
cnf(refute_0_162,plain,
cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1) )],[refute_0_161,refute_0_159]) ).
cnf(refute_0_163,plain,
cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D) )],[refute_0_162,refute_0_158]) ).
cnf(refute_0_164,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1) )],[refute_0_163,refute_0_157]) ).
cnf(refute_0_165,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_118:[bind(C,$fot(skolemFOFtoCNF_D)),bind(X_1762,$fot(skolemFOFtoCNF_B_1)),bind(X_1763,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_166,plain,
midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_165,refute_0_164]) ).
cnf(refute_0_167,plain,
midp(skolemFOFtoCNF_D,X_2429,X_2429),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_166,refute_0_156]) ).
cnf(refute_0_168,plain,
midp(skolemFOFtoCNF_D,X_2490,X_2490),
inference(subst,[],[refute_0_167:[bind(X_2429,$fot(X_2490))]]) ).
cnf(refute_0_169,plain,
cong(skolemFOFtoCNF_D,X_2490,skolemFOFtoCNF_D,X_2490),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_D,X_2490,X_2490) )],[refute_0_168,refute_0_155]) ).
cnf(refute_0_170,plain,
cong(skolemFOFtoCNF_D,X_2494,skolemFOFtoCNF_D,X_2494),
inference(subst,[],[refute_0_169:[bind(X_2490,$fot(X_2494))]]) ).
cnf(refute_0_171,plain,
cong(skolemFOFtoCNF_D,X_2494,X_2494,skolemFOFtoCNF_D),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,X_2494,skolemFOFtoCNF_D,X_2494) )],[refute_0_170,refute_0_154]) ).
cnf(refute_0_172,plain,
cong(skolemFOFtoCNF_D,X_2507,X_2507,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_171:[bind(X_2494,$fot(X_2507))]]) ).
cnf(refute_0_173,plain,
cong(X_2507,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_2507),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_D,X_2507,X_2507,skolemFOFtoCNF_D) )],[refute_0_172,refute_0_153]) ).
cnf(refute_0_174,plain,
cong(X_2510,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_2510),
inference(subst,[],[refute_0_173:[bind(X_2507,$fot(X_2510))]]) ).
cnf(refute_0_175,plain,
cong(X_2510,skolemFOFtoCNF_D,X_2510,skolemFOFtoCNF_D),
inference(resolve,[$cnf( cong(X_2510,skolemFOFtoCNF_D,skolemFOFtoCNF_D,X_2510) )],[refute_0_174,refute_0_152]) ).
cnf(refute_0_176,plain,
cong(X_2512,skolemFOFtoCNF_D,X_2512,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_175:[bind(X_2510,$fot(X_2512))]]) ).
cnf(refute_0_177,plain,
( ~ coll(X_2512,skolemFOFtoCNF_D,skolemFOFtoCNF_D)
| midp(X_2512,skolemFOFtoCNF_D,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( cong(X_2512,skolemFOFtoCNF_D,X_2512,skolemFOFtoCNF_D) )],[refute_0_176,refute_0_151]) ).
cnf(refute_0_178,plain,
coll(X_2512,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_118:[bind(C,$fot(X_2512)),bind(X_1762,$fot(skolemFOFtoCNF_D)),bind(X_1763,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_179,plain,
midp(X_2512,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(X_2512,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_178,refute_0_177]) ).
cnf(refute_0_180,plain,
midp(X_2513,skolemFOFtoCNF_D,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_179:[bind(X_2512,$fot(X_2513))]]) ).
cnf(refute_0_181,plain,
midp(X_2513,X_2429,X_2429),
inference(resolve,[$cnf( midp(X_2513,skolemFOFtoCNF_D,skolemFOFtoCNF_D) )],[refute_0_180,refute_0_150]) ).
cnf(refute_0_182,plain,
midp(X_2527,X_2526,X_2526),
inference(subst,[],[refute_0_181:[bind(X_2429,$fot(X_2526)),bind(X_2513,$fot(X_2527))]]) ).
cnf(refute_0_183,plain,
cong(X_2527,X_2526,X_2527,X_2526),
inference(resolve,[$cnf( midp(X_2527,X_2526,X_2526) )],[refute_0_182,refute_0_149]) ).
cnf(refute_0_184,plain,
cong(X_3109,X_3110,X_3109,X_3110),
inference(subst,[],[refute_0_183:[bind(X_2526,$fot(X_3110)),bind(X_2527,$fot(X_3109))]]) ).
cnf(refute_0_185,plain,
perp(X_3110,X_3109,X_3109,X_3110),
inference(resolve,[$cnf( cong(X_3109,X_3110,X_3109,X_3110) )],[refute_0_184,refute_0_148]) ).
cnf(refute_0_186,plain,
perp(X_3112,X_3111,X_3111,X_3112),
inference(subst,[],[refute_0_185:[bind(X_3109,$fot(X_3111)),bind(X_3110,$fot(X_3112))]]) ).
cnf(refute_0_187,plain,
( ~ midp(M,X_3112,X_3112)
| cong(X_3112,M,X_3111,M) ),
inference(resolve,[$cnf( perp(X_3112,X_3111,X_3111,X_3112) )],[refute_0_186,refute_0_10]) ).
cnf(refute_0_188,plain,
midp(M,X_3112,X_3112),
inference(subst,[],[refute_0_181:[bind(X_2429,$fot(X_3112)),bind(X_2513,$fot(M))]]) ).
cnf(refute_0_189,plain,
cong(X_3112,M,X_3111,M),
inference(resolve,[$cnf( midp(M,X_3112,X_3112) )],[refute_0_188,refute_0_187]) ).
cnf(refute_0_190,plain,
cong(X_3131,X_3129,X_3130,X_3129),
inference(subst,[],[refute_0_189:[bind(M,$fot(X_3129)),bind(X_3111,$fot(X_3130)),bind(X_3112,$fot(X_3131))]]) ).
cnf(refute_0_191,plain,
cong(X_3131,X_3129,X_3129,X_3130),
inference(resolve,[$cnf( cong(X_3131,X_3129,X_3130,X_3129) )],[refute_0_190,refute_0_8]) ).
cnf(refute_0_192,plain,
cong(X_3134,X_3132,X_3132,X_3133),
inference(subst,[],[refute_0_191:[bind(X_3129,$fot(X_3132)),bind(X_3130,$fot(X_3133)),bind(X_3131,$fot(X_3134))]]) ).
cnf(refute_0_193,plain,
cong(X_3132,X_3133,X_3134,X_3132),
inference(resolve,[$cnf( cong(X_3134,X_3132,X_3132,X_3133) )],[refute_0_192,refute_0_7]) ).
cnf(refute_0_194,plain,
cong(X_3157,X_3158,X_3159,X_3157),
inference(subst,[],[refute_0_193:[bind(X_3132,$fot(X_3157)),bind(X_3133,$fot(X_3158)),bind(X_3134,$fot(X_3159))]]) ).
cnf(refute_0_195,plain,
cong(X_3157,X_3158,X_3157,X_3159),
inference(resolve,[$cnf( cong(X_3157,X_3158,X_3159,X_3157) )],[refute_0_194,refute_0_5]) ).
cnf(refute_0_196,plain,
cong(X_3162,X_3163,X_3162,X_3164),
inference(subst,[],[refute_0_195:[bind(X_3157,$fot(X_3162)),bind(X_3158,$fot(X_3163)),bind(X_3159,$fot(X_3164))]]) ).
cnf(refute_0_197,plain,
( ~ coll(X_3162,X_3163,X_3164)
| midp(X_3162,X_3163,X_3164) ),
inference(resolve,[$cnf( cong(X_3162,X_3163,X_3162,X_3164) )],[refute_0_196,refute_0_3]) ).
cnf(refute_0_198,plain,
coll(X_3162,X_3163,X_3164),
inference(subst,[],[refute_0_118:[bind(C,$fot(X_3162)),bind(X_1762,$fot(X_3164)),bind(X_1763,$fot(X_3163))]]) ).
cnf(refute_0_199,plain,
midp(X_3162,X_3163,X_3164),
inference(resolve,[$cnf( coll(X_3162,X_3163,X_3164) )],[refute_0_198,refute_0_197]) ).
cnf(refute_0_200,plain,
midp(E,A,B),
inference(subst,[],[refute_0_199:[bind(X_3162,$fot(E)),bind(X_3163,$fot(A)),bind(X_3164,$fot(B))]]) ).
cnf(refute_0_201,plain,
( ~ midp(F,A,C)
| para(E,F,B,C) ),
inference(resolve,[$cnf( midp(E,A,B) )],[refute_0_200,refute_0_1]) ).
cnf(refute_0_202,plain,
midp(F,A,C),
inference(subst,[],[refute_0_199:[bind(X_3162,$fot(F)),bind(X_3163,$fot(A)),bind(X_3164,$fot(C))]]) ).
cnf(refute_0_203,plain,
para(E,F,B,C),
inference(resolve,[$cnf( midp(F,A,C) )],[refute_0_202,refute_0_201]) ).
cnf(refute_0_204,plain,
para(skolemFOFtoCNF_E,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_203:[bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(E,$fot(skolemFOFtoCNF_E)),bind(F,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_205,plain,
$false,
inference(resolve,[$cnf( para(skolemFOFtoCNF_E,skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) )],[refute_0_204,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GEO656+1 : TPTP v8.1.0. Released v7.5.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n010.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 : Sat Jun 18 00:08:08 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 32.98/33.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.98/33.20
% 32.98/33.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 33.06/33.22
%------------------------------------------------------------------------------