TSTP Solution File: GEO637+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO637+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 05:27:59 EDT 2022
% Result : Theorem 52.13s 52.31s
% Output : CNFRefutation 52.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 90
% Number of leaves : 27
% Syntax : Number of formulae : 355 ( 143 unt; 0 def)
% Number of atoms : 700 ( 0 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 611 ( 266 ~; 261 |; 55 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 857 ( 125 sgn 387 !; 16 ?)
% 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(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(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(ruleX10,axiom,
! [A,B,C,H] :
? [P,Q] :
( ( perp(A,H,B,C)
& perp(B,H,A,C) )
=> ( coll(P,C,B)
& perp(A,P,C,B)
& coll(Q,C,A)
& perp(B,Q,C,A) ) ) ).
fof(exemplo6GDDFULL81109101,conjecture,
! [A,B,C,O,H,D,E] :
( ( circle(O,A,B,C)
& midp(H,C,B)
& coll(D,O,H)
& coll(D,A,B)
& perp(C,O,C,E)
& perp(A,O,A,E) )
=> cyclic(A,O,E,D) ) ).
fof(subgoal_0,plain,
! [A,B,C,O,H,D,E] :
( ( circle(O,A,B,C)
& midp(H,C,B)
& coll(D,O,H)
& coll(D,A,B)
& perp(C,O,C,E)
& perp(A,O,A,E) )
=> cyclic(A,O,E,D) ),
inference(strip,[],[exemplo6GDDFULL81109101]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,O,H,D,E] :
( ( circle(O,A,B,C)
& midp(H,C,B)
& coll(D,O,H)
& coll(D,A,B)
& perp(C,O,C,E)
& perp(A,O,A,E) )
=> cyclic(A,O,E,D) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D,E,H,O] :
( ~ cyclic(A,O,E,D)
& circle(O,A,B,C)
& coll(D,A,B)
& coll(D,O,H)
& midp(H,C,B)
& perp(A,O,A,E)
& perp(C,O,C,E) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_E,skolemFOFtoCNF_D)
& circle(skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& coll(skolemFOFtoCNF_D,skolemFOFtoCNF_O_2,skolemFOFtoCNF_H)
& midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
& perp(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_E)
& perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[ruleD15]) ).
fof(normalize_0_4,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[ruleD16]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,B,C,D) ),
inference(canonicalize,[],[ruleD13]) ).
fof(normalize_0_8,plain,
! [A,B,C,D,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,B,C,D) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[ruleD23]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[ruleD24]) ).
fof(normalize_0_12,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C,M] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(canonicalize,[],[ruleD52]) ).
fof(normalize_0_14,plain,
! [A,B,C,M] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,P,Q] :
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(canonicalize,[],[ruleD57]) ).
fof(normalize_0_16,plain,
! [A,B,P,Q] :
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B,C,D,E] :
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[ruleD17]) ).
fof(normalize_0_18,plain,
! [A,B,C,D,E] :
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[ruleD14]) ).
fof(normalize_0_20,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[ruleD68]) ).
fof(normalize_0_22,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B,C,D] :
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ! [M] : ~ midp(M,A,B)
| ! [N] : ~ midp(N,C,D)
| ! [Q] :
? [P] : midp(P,A,Q) ),
inference(canonicalize,[],[ruleX7]) ).
fof(normalize_0_24,plain,
! [A,B,C,D] :
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ! [M] : ~ midp(M,A,B)
| ! [N] : ~ midp(N,C,D)
| ! [Q] :
? [P] : midp(P,A,Q) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A,B,C,D,M,N,Q] :
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P_1(A,Q),A,Q) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[ruleD1]) ).
fof(normalize_0_27,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[ruleD2]) ).
fof(normalize_0_29,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD66]) ).
fof(normalize_0_31,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q] : ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[ruleD39]) ).
fof(normalize_0_33,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q] : ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [A,B,C,D,P,Q] :
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(clausify,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[ruleD41]) ).
fof(normalize_0_36,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(specialize,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_38,plain,
! [A,B,C,D] :
( ~ para(A,B,C,D)
| ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[ruleD40]) ).
fof(normalize_0_39,plain,
! [A,B,C,D] :
( ~ para(A,B,C,D)
| ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q) ),
inference(specialize,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [A,B,C,D,P,Q] :
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(clausify,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [A,B,C,D,P,Q,U,V] :
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[ruleD19]) ).
fof(normalize_0_42,plain,
! [A,B,C,D,P,Q,U,V] :
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(specialize,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [A,B,C,D,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_44,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_43]) ).
fof(normalize_0_45,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[ruleD67]) ).
fof(normalize_0_46,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(specialize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_48,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_50,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_49]) ).
fof(normalize_0_51,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_52,plain,
! [A,B,C,O] :
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(specialize,[],[normalize_0_51]) ).
fof(normalize_0_53,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_54,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(specialize,[],[normalize_0_53]) ).
fof(normalize_0_55,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_56,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_55]) ).
fof(normalize_0_57,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_58,plain,
! [A,B,C,H] :
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| ? [P,Q] :
( coll(P,C,B)
& coll(Q,C,A)
& perp(A,P,C,B)
& perp(B,Q,C,A) ) ),
inference(canonicalize,[],[ruleX10]) ).
fof(normalize_0_59,plain,
! [A,B,C,H] :
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| ? [P,Q] :
( coll(P,C,B)
& coll(Q,C,A)
& perp(A,P,C,B)
& perp(B,Q,C,A) ) ),
inference(specialize,[],[normalize_0_58]) ).
fof(normalize_0_60,plain,
! [A,B,C,H] :
( ( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_P_3(A,B,C),C,B) )
& ( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_Q_1(A,B,C),C,A) )
& ( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| perp(A,skolemFOFtoCNF_P_3(A,B,C),C,B) )
& ( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| perp(B,skolemFOFtoCNF_Q_1(A,B,C),C,A) ) ),
inference(clausify,[],[normalize_0_59]) ).
fof(normalize_0_61,plain,
! [A,B,C,H] :
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_P_3(A,B,C),C,B) ),
inference(conjunct,[],[normalize_0_60]) ).
fof(normalize_0_62,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
~ cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ cyclic(X_10966,X_10965,X_10966,X_10967)
| cyclic(X_10966,X_10966,X_10965,X_10967) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_10966)),bind(B,$fot(X_10965)),bind(C,$fot(X_10966)),bind(D,$fot(X_10967))]]) ).
cnf(refute_0_3,plain,
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( ~ cyclic(X_10962,X_10963,X_10963,X_10964)
| cyclic(X_10963,X_10962,X_10963,X_10964) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_10962)),bind(B,$fot(X_10963)),bind(C,$fot(X_10963)),bind(D,$fot(X_10964))]]) ).
cnf(refute_0_5,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
( ~ cong(O,A,O,C)
| ~ cong(O,A,O,D)
| cyclic(A,C,C,D) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(C))]]) ).
cnf(refute_0_7,plain,
( ~ cong(A,B,C,D)
| cong(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ cong(X_3908,X_3909,X_3910,X_3908)
| cong(X_3908,X_3909,X_3908,X_3910) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_3908)),bind(B,$fot(X_3909)),bind(C,$fot(X_3910)),bind(D,$fot(X_3908))]]) ).
cnf(refute_0_9,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ cong(X_3885,X_3883,X_3883,X_3884)
| cong(X_3883,X_3884,X_3885,X_3883) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_3885)),bind(B,$fot(X_3883)),bind(C,$fot(X_3883)),bind(D,$fot(X_3884))]]) ).
cnf(refute_0_11,plain,
( ~ cong(X_3882,X_3880,X_3881,X_3880)
| cong(X_3882,X_3880,X_3880,X_3881) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_3882)),bind(B,$fot(X_3880)),bind(C,$fot(X_3881)),bind(D,$fot(X_3880))]]) ).
cnf(refute_0_12,plain,
( ~ midp(M,A,C)
| ~ perp(A,B,B,C)
| cong(A,M,B,M) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
( ~ midp(M,X_3863,X_3863)
| ~ perp(X_3863,X_3862,X_3862,X_3863)
| cong(X_3863,M,X_3862,M) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_3863)),bind(B,$fot(X_3862)),bind(C,$fot(X_3863))]]) ).
cnf(refute_0_14,plain,
( ~ cong(A,P,B,P)
| ~ cong(A,Q,B,Q)
| ~ cyclic(A,B,P,Q)
| perp(P,A,A,Q) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_15,plain,
( ~ cong(X_3860,X_3861,X_3860,X_3861)
| ~ cyclic(X_3860,X_3860,X_3861,X_3861)
| perp(X_3861,X_3860,X_3860,X_3861) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_3860)),bind(B,$fot(X_3860)),bind(P,$fot(X_3861)),bind(Q,$fot(X_3861))]]) ).
cnf(refute_0_16,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_17,plain,
( ~ cyclic(X_3858,X_3858,X_3858,X_3859)
| cyclic(X_3858,X_3858,X_3859,X_3859) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_3858)),bind(B,$fot(X_3858)),bind(C,$fot(X_3858)),bind(D,$fot(X_3859)),bind(E,$fot(X_3859))]]) ).
cnf(refute_0_18,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_19,plain,
( ~ cyclic(X_3856,X_3856,X_3857,X_3856)
| cyclic(X_3856,X_3856,X_3856,X_3857) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(X_3856)),bind(B,$fot(X_3856)),bind(C,$fot(X_3857)),bind(D,$fot(X_3856))]]) ).
cnf(refute_0_20,plain,
( ~ cyclic(X_3854,X_3855,X_3854,X_3854)
| cyclic(X_3854,X_3854,X_3855,X_3854) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_3854)),bind(B,$fot(X_3855)),bind(C,$fot(X_3854)),bind(D,$fot(X_3854))]]) ).
cnf(refute_0_21,plain,
( ~ cyclic(X_3853,X_3852,X_3852,X_3852)
| cyclic(X_3852,X_3853,X_3852,X_3852) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_3853)),bind(B,$fot(X_3852)),bind(C,$fot(X_3852)),bind(D,$fot(X_3852))]]) ).
cnf(refute_0_22,plain,
( ~ cong(skolemFOFtoCNF_P_1(X_3851,X_3850),X_3851,skolemFOFtoCNF_P_1(X_3851,X_3850),X_3850)
| cyclic(X_3851,X_3850,X_3850,X_3850) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_3851)),bind(B,$fot(X_3850)),bind(C,$fot(X_3850)),bind(D,$fot(X_3850)),bind(O,$fot(skolemFOFtoCNF_P_1(X_3851,X_3850)))]]) ).
cnf(refute_0_23,plain,
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_24,plain,
( ~ midp(skolemFOFtoCNF_P_1(X_1573,X_1572),X_1573,X_1572)
| cong(skolemFOFtoCNF_P_1(X_1573,X_1572),X_1573,skolemFOFtoCNF_P_1(X_1573,X_1572),X_1572) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_P_1(X_1573,X_1572))),bind(B,$fot(X_1573)),bind(C,$fot(X_1572))]]) ).
cnf(refute_0_25,plain,
( ~ coll(C,A,B)
| ~ coll(D,A,B)
| ~ midp(M,A,B)
| ~ midp(N,C,D)
| midp(skolemFOFtoCNF_P_1(A,Q),A,Q) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_26,plain,
( ~ coll(D,D,D)
| ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(D)),bind(B,$fot(D)),bind(C,$fot(D)),bind(M,$fot(N))]]) ).
cnf(refute_0_27,plain,
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_28,plain,
( ~ coll(X_357,X_356,X_357)
| coll(X_357,X_357,X_356) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_357)),bind(B,$fot(X_356)),bind(C,$fot(X_357))]]) ).
cnf(refute_0_29,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_30,plain,
( ~ coll(X_354,X_355,X_355)
| coll(X_355,X_354,X_355) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_354)),bind(B,$fot(X_355)),bind(C,$fot(X_355))]]) ).
cnf(refute_0_31,plain,
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_32,plain,
( ~ para(X_349,X_350,X_349,X_350)
| coll(X_349,X_350,X_350) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(X_349)),bind(B,$fot(X_350)),bind(C,$fot(X_350))]]) ).
cnf(refute_0_33,plain,
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_34,plain,
( ~ eqangle(X_347,X_348,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_347,X_348,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| para(X_347,X_348,X_347,X_348) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(X_347)),bind(B,$fot(X_348)),bind(C,$fot(X_347)),bind(D,$fot(X_348)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_35,plain,
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_36,plain,
( ~ cyclic(skolemFOFtoCNF_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_35:[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_37,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_16:[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,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_38,plain,
( ~ cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_5:[bind(A,$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_H))]]) ).
cnf(refute_0_39,plain,
midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_40,plain,
( ~ midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_H)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_41,plain,
cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_B_1) )],[refute_0_41,refute_0_38]) ).
cnf(refute_0_43,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_42,refute_0_37]) ).
cnf(refute_0_44,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,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_43,refute_0_36]) ).
cnf(refute_0_45,plain,
( ~ eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_33:[bind(A,$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,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_46,plain,
para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$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_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_48,plain,
( ~ para(skolemFOFtoCNF_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_47:[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_49,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_46,refute_0_48]) ).
cnf(refute_0_50,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346),
inference(subst,[],[refute_0_49:[bind(X_153,$fot(X_345)),bind(X_154,$fot(X_346))]]) ).
cnf(refute_0_51,plain,
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_52,plain,
( ~ eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346)
| eqangle(X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_51:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_345)),bind(D,$fot(X_346)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1)),bind(U,$fot(X_345)),bind(V,$fot(X_346))]]) ).
cnf(refute_0_53,plain,
eqangle(X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_345,X_346) )],[refute_0_50,refute_0_52]) ).
cnf(refute_0_54,plain,
eqangle(X_347,X_348,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_347,X_348,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_53:[bind(X_345,$fot(X_347)),bind(X_346,$fot(X_348))]]) ).
cnf(refute_0_55,plain,
para(X_347,X_348,X_347,X_348),
inference(resolve,[$cnf( eqangle(X_347,X_348,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_347,X_348,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_54,refute_0_34]) ).
cnf(refute_0_56,plain,
para(X_349,X_350,X_349,X_350),
inference(subst,[],[refute_0_55:[bind(X_347,$fot(X_349)),bind(X_348,$fot(X_350))]]) ).
cnf(refute_0_57,plain,
coll(X_349,X_350,X_350),
inference(resolve,[$cnf( para(X_349,X_350,X_349,X_350) )],[refute_0_56,refute_0_32]) ).
cnf(refute_0_58,plain,
coll(X_354,X_355,X_355),
inference(subst,[],[refute_0_57:[bind(X_349,$fot(X_354)),bind(X_350,$fot(X_355))]]) ).
cnf(refute_0_59,plain,
coll(X_355,X_354,X_355),
inference(resolve,[$cnf( coll(X_354,X_355,X_355) )],[refute_0_58,refute_0_30]) ).
cnf(refute_0_60,plain,
coll(X_357,X_356,X_357),
inference(subst,[],[refute_0_59:[bind(X_354,$fot(X_356)),bind(X_355,$fot(X_357))]]) ).
cnf(refute_0_61,plain,
coll(X_357,X_357,X_356),
inference(resolve,[$cnf( coll(X_357,X_356,X_357) )],[refute_0_60,refute_0_28]) ).
cnf(refute_0_62,plain,
coll(D,D,D),
inference(subst,[],[refute_0_61:[bind(X_356,$fot(D)),bind(X_357,$fot(D))]]) ).
cnf(refute_0_63,plain,
( ~ midp(N,D,D)
| midp(skolemFOFtoCNF_P_1(D,Q),D,Q) ),
inference(resolve,[$cnf( coll(D,D,D) )],[refute_0_62,refute_0_26]) ).
cnf(refute_0_64,plain,
( ~ midp(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,skolemFOFtoCNF_H),X_1560,X_1560)
| midp(skolemFOFtoCNF_P_1(X_1560,Q),X_1560,Q) ),
inference(subst,[],[refute_0_63:[bind(D,$fot(X_1560)),bind(N,$fot(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,skolemFOFtoCNF_H)))]]) ).
cnf(refute_0_65,plain,
para(X_1501,X_1502,X_1501,X_1502),
inference(subst,[],[refute_0_55:[bind(X_347,$fot(X_1501)),bind(X_348,$fot(X_1502))]]) ).
cnf(refute_0_66,plain,
( ~ midp(M,A,B)
| ~ para(A,C,B,D)
| ~ para(A,D,B,C)
| midp(M,C,D) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_67,plain,
( ~ midp(X_1503,X_1501,X_1501)
| ~ para(X_1501,X_1502,X_1501,X_1502)
| midp(X_1503,X_1502,X_1502) ),
inference(subst,[],[refute_0_66:[bind(A,$fot(X_1501)),bind(B,$fot(X_1501)),bind(C,$fot(X_1502)),bind(D,$fot(X_1502)),bind(M,$fot(X_1503))]]) ).
cnf(refute_0_68,plain,
( ~ midp(X_1503,X_1501,X_1501)
| midp(X_1503,X_1502,X_1502) ),
inference(resolve,[$cnf( para(X_1501,X_1502,X_1501,X_1502) )],[refute_0_65,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ midp(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,skolemFOFtoCNF_H),skolemFOFtoCNF_H,skolemFOFtoCNF_H)
| midp(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,skolemFOFtoCNF_H),X_1502,X_1502) ),
inference(subst,[],[refute_0_68:[bind(X_1501,$fot(skolemFOFtoCNF_H)),bind(X_1503,$fot(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,skolemFOFtoCNF_H)))]]) ).
cnf(refute_0_70,plain,
( ~ midp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H)
| midp(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,Q),skolemFOFtoCNF_H,Q) ),
inference(subst,[],[refute_0_63:[bind(D,$fot(skolemFOFtoCNF_H)),bind(N,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_71,plain,
( ~ coll(A,B,C)
| ~ cong(A,B,A,C)
| midp(A,B,C) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_72,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H)
| ~ cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H)
| midp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H) ),
inference(subst,[],[refute_0_71:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_H)),bind(C,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_73,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_74,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_73:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_75,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_76,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_75:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_77,plain,
( ~ cong(O,A,O,B)
| ~ cong(O,A,O,C)
| circle(O,A,B,C) ),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_78,plain,
( ~ cong(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1)
| circle(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_77:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(O,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_79,plain,
( ~ cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_H)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_H)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_80,plain,
cong(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_B_1) )],[refute_0_41,refute_0_79]) ).
cnf(refute_0_81,plain,
circle(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1) )],[refute_0_80,refute_0_78]) ).
cnf(refute_0_82,plain,
( ~ circle(O,A,B,C)
| ~ coll(O,A,C)
| perp(A,B,B,C) ),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_83,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_56]) ).
cnf(refute_0_84,plain,
( ~ coll(X_1488,skolemFOFtoCNF_O_2,C)
| ~ coll(X_1488,skolemFOFtoCNF_O_2,X_1489)
| coll(C,X_1489,X_1488) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(X_1488)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(X_1489))]]) ).
cnf(refute_0_85,plain,
( ~ coll(X_1459,skolemFOFtoCNF_A,C)
| ~ coll(X_1459,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)
| coll(C,skolemFOFtoCNF_O_2,X_1459) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(X_1459)),bind(B,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_86,plain,
( ~ coll(skolemFOFtoCNF_O_2,X_1434,C)
| ~ coll(skolemFOFtoCNF_O_2,X_1434,skolemFOFtoCNF_A)
| coll(C,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(X_1434)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_87,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2))),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_88,plain,
( ~ coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2))),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_89,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_90,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_E)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_75:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_91,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_A,skolemFOFtoCNF_E) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_P_3(A,B,C),C,B) ),
inference(canonicalize,[],[normalize_0_61]) ).
cnf(refute_0_93,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)
| coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_92:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(H,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_94,plain,
coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) )],[refute_0_91,refute_0_93]) ).
cnf(refute_0_95,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_A) )],[refute_0_94,refute_0_88]) ).
cnf(refute_0_96,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),skolemFOFtoCNF_A) )],[refute_0_95,refute_0_87]) ).
cnf(refute_0_97,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_1396)
| ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2)
| coll(skolemFOFtoCNF_O_2,X_1396,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_98,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_1396)
| coll(skolemFOFtoCNF_O_2,X_1396,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_1396),
inference(subst,[],[refute_0_61:[bind(X_356,$fot(X_1396)),bind(X_357,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_100,plain,
coll(skolemFOFtoCNF_O_2,X_1396,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_1396) )],[refute_0_99,refute_0_98]) ).
cnf(refute_0_101,plain,
coll(skolemFOFtoCNF_O_2,X_1434,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_100:[bind(X_1396,$fot(X_1434))]]) ).
cnf(refute_0_102,plain,
( ~ coll(skolemFOFtoCNF_O_2,X_1434,C)
| coll(C,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,X_1434,skolemFOFtoCNF_A) )],[refute_0_101,refute_0_86]) ).
cnf(refute_0_103,plain,
coll(X_1394,X_1394,X_1395),
inference(subst,[],[refute_0_61:[bind(X_356,$fot(X_1395)),bind(X_357,$fot(X_1394))]]) ).
cnf(refute_0_104,plain,
( ~ coll(X_1394,X_1394,X_1395)
| ~ coll(X_1394,X_1394,X_1396)
| coll(X_1395,X_1396,X_1394) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(X_1394)),bind(B,$fot(X_1394)),bind(C,$fot(X_1395)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_105,plain,
( ~ coll(X_1394,X_1394,X_1396)
| coll(X_1395,X_1396,X_1394) ),
inference(resolve,[$cnf( coll(X_1394,X_1394,X_1395) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
coll(X_1394,X_1394,X_1396),
inference(subst,[],[refute_0_61:[bind(X_356,$fot(X_1396)),bind(X_357,$fot(X_1394))]]) ).
cnf(refute_0_107,plain,
coll(X_1395,X_1396,X_1394),
inference(resolve,[$cnf( coll(X_1394,X_1394,X_1396) )],[refute_0_106,refute_0_105]) ).
cnf(refute_0_108,plain,
coll(skolemFOFtoCNF_O_2,X_1434,C),
inference(subst,[],[refute_0_107:[bind(X_1394,$fot(C)),bind(X_1395,$fot(skolemFOFtoCNF_O_2)),bind(X_1396,$fot(X_1434))]]) ).
cnf(refute_0_109,plain,
coll(C,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,X_1434,C) )],[refute_0_108,refute_0_102]) ).
cnf(refute_0_110,plain,
coll(X_1459,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2),
inference(subst,[],[refute_0_109:[bind(C,$fot(X_1459))]]) ).
cnf(refute_0_111,plain,
( ~ coll(X_1459,skolemFOFtoCNF_A,C)
| coll(C,skolemFOFtoCNF_O_2,X_1459) ),
inference(resolve,[$cnf( coll(X_1459,skolemFOFtoCNF_A,skolemFOFtoCNF_O_2) )],[refute_0_110,refute_0_85]) ).
cnf(refute_0_112,plain,
( ~ coll(X_1455,skolemFOFtoCNF_E,C)
| ~ coll(X_1455,skolemFOFtoCNF_E,X_1456)
| coll(C,X_1456,X_1455) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(X_1455)),bind(B,$fot(skolemFOFtoCNF_E)),bind(D,$fot(X_1456))]]) ).
cnf(refute_0_113,plain,
( ~ coll(X_1428,skolemFOFtoCNF_C_1,C)
| ~ coll(X_1428,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E)
| coll(C,skolemFOFtoCNF_E,X_1428) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(X_1428)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_114,plain,
( ~ coll(skolemFOFtoCNF_C_1,X_1418,skolemFOFtoCNF_E)
| coll(X_1418,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(X_1418)),bind(C,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_115,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E)
| coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_116,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E))),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_117,plain,
( ~ coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),skolemFOFtoCNF_E,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E))),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_118,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_62]) ).
cnf(refute_0_119,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E)
| coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),skolemFOFtoCNF_E,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_92:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_E)),bind(H,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_120,plain,
coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),skolemFOFtoCNF_E,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),skolemFOFtoCNF_E,skolemFOFtoCNF_C_1) )],[refute_0_120,refute_0_117]) ).
cnf(refute_0_122,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),skolemFOFtoCNF_C_1) )],[refute_0_121,refute_0_116]) ).
cnf(refute_0_123,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E) )],[refute_0_122,refute_0_115]) ).
cnf(refute_0_124,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_1396)
| ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_125,plain,
( ~ coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_1396)
| coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_1396),
inference(subst,[],[refute_0_61:[bind(X_356,$fot(X_1396)),bind(X_357,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_127,plain,
coll(skolemFOFtoCNF_C_1,X_1396,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_E,skolemFOFtoCNF_E,X_1396) )],[refute_0_126,refute_0_125]) ).
cnf(refute_0_128,plain,
coll(skolemFOFtoCNF_C_1,X_1418,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_127:[bind(X_1396,$fot(X_1418))]]) ).
cnf(refute_0_129,plain,
coll(X_1418,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,X_1418,skolemFOFtoCNF_E) )],[refute_0_128,refute_0_114]) ).
cnf(refute_0_130,plain,
coll(X_1428,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E),
inference(subst,[],[refute_0_129:[bind(X_1418,$fot(X_1428))]]) ).
cnf(refute_0_131,plain,
( ~ coll(X_1428,skolemFOFtoCNF_C_1,C)
| coll(C,skolemFOFtoCNF_E,X_1428) ),
inference(resolve,[$cnf( coll(X_1428,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E) )],[refute_0_130,refute_0_113]) ).
cnf(refute_0_132,plain,
coll(X_1428,skolemFOFtoCNF_C_1,C),
inference(subst,[],[refute_0_107:[bind(X_1394,$fot(C)),bind(X_1395,$fot(X_1428)),bind(X_1396,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_133,plain,
coll(C,skolemFOFtoCNF_E,X_1428),
inference(resolve,[$cnf( coll(X_1428,skolemFOFtoCNF_C_1,C) )],[refute_0_132,refute_0_131]) ).
cnf(refute_0_134,plain,
coll(X_1455,skolemFOFtoCNF_E,X_1456),
inference(subst,[],[refute_0_133:[bind(C,$fot(X_1455)),bind(X_1428,$fot(X_1456))]]) ).
cnf(refute_0_135,plain,
( ~ coll(X_1455,skolemFOFtoCNF_E,C)
| coll(C,X_1456,X_1455) ),
inference(resolve,[$cnf( coll(X_1455,skolemFOFtoCNF_E,X_1456) )],[refute_0_134,refute_0_112]) ).
cnf(refute_0_136,plain,
coll(X_1455,skolemFOFtoCNF_E,C),
inference(subst,[],[refute_0_107:[bind(X_1394,$fot(C)),bind(X_1395,$fot(X_1455)),bind(X_1396,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_137,plain,
coll(C,X_1456,X_1455),
inference(resolve,[$cnf( coll(X_1455,skolemFOFtoCNF_E,C) )],[refute_0_136,refute_0_135]) ).
cnf(refute_0_138,plain,
coll(X_1459,skolemFOFtoCNF_A,C),
inference(subst,[],[refute_0_137:[bind(C,$fot(X_1459)),bind(X_1455,$fot(C)),bind(X_1456,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_139,plain,
coll(C,skolemFOFtoCNF_O_2,X_1459),
inference(resolve,[$cnf( coll(X_1459,skolemFOFtoCNF_A,C) )],[refute_0_138,refute_0_111]) ).
cnf(refute_0_140,plain,
coll(X_1488,skolemFOFtoCNF_O_2,X_1489),
inference(subst,[],[refute_0_139:[bind(C,$fot(X_1488)),bind(X_1459,$fot(X_1489))]]) ).
cnf(refute_0_141,plain,
( ~ coll(X_1488,skolemFOFtoCNF_O_2,C)
| coll(C,X_1489,X_1488) ),
inference(resolve,[$cnf( coll(X_1488,skolemFOFtoCNF_O_2,X_1489) )],[refute_0_140,refute_0_84]) ).
cnf(refute_0_142,plain,
( ~ coll(X_1464,skolemFOFtoCNF_C_1,C)
| ~ coll(X_1464,skolemFOFtoCNF_C_1,X_1465)
| coll(C,X_1465,X_1464) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(X_1464)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_1465))]]) ).
cnf(refute_0_143,plain,
( ~ coll(X_1412,skolemFOFtoCNF_O_2,C)
| ~ coll(X_1412,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1)
| coll(C,skolemFOFtoCNF_C_1,X_1412) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(X_1412)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_144,plain,
( ~ coll(skolemFOFtoCNF_O_2,X_1409,skolemFOFtoCNF_C_1)
| coll(X_1409,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(X_1409)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_145,plain,
( ~ coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2),skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(skolemFOFtoCNF_O_2)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2))),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_146,plain,
( ~ coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2))),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_147,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E)
| perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2) ),
inference(subst,[],[refute_0_75:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_O_2)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_148,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E) )],[refute_0_118,refute_0_147]) ).
cnf(refute_0_149,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2)
| coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_92:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(H,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_150,plain,
coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_E,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2),skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1) )],[refute_0_150,refute_0_146]) ).
cnf(refute_0_152,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,skolemFOFtoCNF_P_3(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2),skolemFOFtoCNF_C_1) )],[refute_0_151,refute_0_145]) ).
cnf(refute_0_153,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_1396)
| ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2)
| coll(skolemFOFtoCNF_O_2,X_1396,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_83:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_O_2)),bind(D,$fot(X_1396))]]) ).
cnf(refute_0_154,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_1396)
| coll(skolemFOFtoCNF_O_2,X_1396,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_O_2) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_1396),
inference(subst,[],[refute_0_61:[bind(X_356,$fot(X_1396)),bind(X_357,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_156,plain,
coll(skolemFOFtoCNF_O_2,X_1396,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,X_1396) )],[refute_0_155,refute_0_154]) ).
cnf(refute_0_157,plain,
coll(skolemFOFtoCNF_O_2,X_1409,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_156:[bind(X_1396,$fot(X_1409))]]) ).
cnf(refute_0_158,plain,
coll(X_1409,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_O_2,X_1409,skolemFOFtoCNF_C_1) )],[refute_0_157,refute_0_144]) ).
cnf(refute_0_159,plain,
coll(X_1412,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_158:[bind(X_1409,$fot(X_1412))]]) ).
cnf(refute_0_160,plain,
( ~ coll(X_1412,skolemFOFtoCNF_O_2,C)
| coll(C,skolemFOFtoCNF_C_1,X_1412) ),
inference(resolve,[$cnf( coll(X_1412,skolemFOFtoCNF_O_2,skolemFOFtoCNF_C_1) )],[refute_0_159,refute_0_143]) ).
cnf(refute_0_161,plain,
coll(X_1412,skolemFOFtoCNF_O_2,C),
inference(subst,[],[refute_0_107:[bind(X_1394,$fot(C)),bind(X_1395,$fot(X_1412)),bind(X_1396,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_162,plain,
coll(C,skolemFOFtoCNF_C_1,X_1412),
inference(resolve,[$cnf( coll(X_1412,skolemFOFtoCNF_O_2,C) )],[refute_0_161,refute_0_160]) ).
cnf(refute_0_163,plain,
coll(X_1464,skolemFOFtoCNF_C_1,X_1465),
inference(subst,[],[refute_0_162:[bind(C,$fot(X_1464)),bind(X_1412,$fot(X_1465))]]) ).
cnf(refute_0_164,plain,
( ~ coll(X_1464,skolemFOFtoCNF_C_1,C)
| coll(C,X_1465,X_1464) ),
inference(resolve,[$cnf( coll(X_1464,skolemFOFtoCNF_C_1,X_1465) )],[refute_0_163,refute_0_142]) ).
cnf(refute_0_165,plain,
coll(X_1464,skolemFOFtoCNF_C_1,C),
inference(subst,[],[refute_0_137:[bind(C,$fot(X_1464)),bind(X_1455,$fot(C)),bind(X_1456,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_166,plain,
coll(C,X_1465,X_1464),
inference(resolve,[$cnf( coll(X_1464,skolemFOFtoCNF_C_1,C) )],[refute_0_165,refute_0_164]) ).
cnf(refute_0_167,plain,
coll(X_1488,skolemFOFtoCNF_O_2,C),
inference(subst,[],[refute_0_166:[bind(C,$fot(X_1488)),bind(X_1464,$fot(C)),bind(X_1465,$fot(skolemFOFtoCNF_O_2))]]) ).
cnf(refute_0_168,plain,
coll(C,X_1489,X_1488),
inference(resolve,[$cnf( coll(X_1488,skolemFOFtoCNF_O_2,C) )],[refute_0_167,refute_0_141]) ).
cnf(refute_0_169,plain,
coll(O,A,C),
inference(subst,[],[refute_0_168:[bind(C,$fot(O)),bind(X_1488,$fot(C)),bind(X_1489,$fot(A))]]) ).
cnf(refute_0_170,plain,
( ~ circle(O,A,B,C)
| perp(A,B,B,C) ),
inference(resolve,[$cnf( coll(O,A,C) )],[refute_0_169,refute_0_82]) ).
cnf(refute_0_171,plain,
( ~ circle(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_170:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(O,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_172,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_H,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) )],[refute_0_81,refute_0_171]) ).
cnf(refute_0_173,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) )],[refute_0_172,refute_0_76]) ).
cnf(refute_0_174,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_173,refute_0_74]) ).
cnf(refute_0_175,plain,
( ~ midp(X_1535,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_C_1,X_1535,skolemFOFtoCNF_C_1,X_1535) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(M,$fot(X_1535))]]) ).
cnf(refute_0_176,plain,
( ~ midp(X_1535,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_C_1,X_1535,skolemFOFtoCNF_C_1,X_1535) ),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
( ~ midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H) ),
inference(subst,[],[refute_0_176:[bind(X_1535,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_178,plain,
cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_39,refute_0_177]) ).
cnf(refute_0_179,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H)
| midp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H) )],[refute_0_178,refute_0_72]) ).
cnf(refute_0_180,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H),
inference(subst,[],[refute_0_168:[bind(C,$fot(skolemFOFtoCNF_C_1)),bind(X_1488,$fot(skolemFOFtoCNF_H)),bind(X_1489,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_181,plain,
midp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H) )],[refute_0_180,refute_0_179]) ).
cnf(refute_0_182,plain,
midp(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,Q),skolemFOFtoCNF_H,Q),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H) )],[refute_0_181,refute_0_70]) ).
cnf(refute_0_183,plain,
midp(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,skolemFOFtoCNF_H),skolemFOFtoCNF_H,skolemFOFtoCNF_H),
inference(subst,[],[refute_0_182:[bind(Q,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_184,plain,
midp(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,skolemFOFtoCNF_H),X_1502,X_1502),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,skolemFOFtoCNF_H),skolemFOFtoCNF_H,skolemFOFtoCNF_H) )],[refute_0_183,refute_0_69]) ).
cnf(refute_0_185,plain,
midp(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,skolemFOFtoCNF_H),X_1560,X_1560),
inference(subst,[],[refute_0_184:[bind(X_1502,$fot(X_1560))]]) ).
cnf(refute_0_186,plain,
midp(skolemFOFtoCNF_P_1(X_1560,Q),X_1560,Q),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(skolemFOFtoCNF_H,skolemFOFtoCNF_H),X_1560,X_1560) )],[refute_0_185,refute_0_64]) ).
cnf(refute_0_187,plain,
midp(skolemFOFtoCNF_P_1(X_1573,X_1572),X_1573,X_1572),
inference(subst,[],[refute_0_186:[bind(Q,$fot(X_1572)),bind(X_1560,$fot(X_1573))]]) ).
cnf(refute_0_188,plain,
cong(skolemFOFtoCNF_P_1(X_1573,X_1572),X_1573,skolemFOFtoCNF_P_1(X_1573,X_1572),X_1572),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_P_1(X_1573,X_1572),X_1573,X_1572) )],[refute_0_187,refute_0_24]) ).
cnf(refute_0_189,plain,
cong(skolemFOFtoCNF_P_1(X_3851,X_3850),X_3851,skolemFOFtoCNF_P_1(X_3851,X_3850),X_3850),
inference(subst,[],[refute_0_188:[bind(X_1572,$fot(X_3850)),bind(X_1573,$fot(X_3851))]]) ).
cnf(refute_0_190,plain,
cyclic(X_3851,X_3850,X_3850,X_3850),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_P_1(X_3851,X_3850),X_3851,skolemFOFtoCNF_P_1(X_3851,X_3850),X_3850) )],[refute_0_189,refute_0_22]) ).
cnf(refute_0_191,plain,
cyclic(X_3853,X_3852,X_3852,X_3852),
inference(subst,[],[refute_0_190:[bind(X_3850,$fot(X_3852)),bind(X_3851,$fot(X_3853))]]) ).
cnf(refute_0_192,plain,
cyclic(X_3852,X_3853,X_3852,X_3852),
inference(resolve,[$cnf( cyclic(X_3853,X_3852,X_3852,X_3852) )],[refute_0_191,refute_0_21]) ).
cnf(refute_0_193,plain,
cyclic(X_3854,X_3855,X_3854,X_3854),
inference(subst,[],[refute_0_192:[bind(X_3852,$fot(X_3854)),bind(X_3853,$fot(X_3855))]]) ).
cnf(refute_0_194,plain,
cyclic(X_3854,X_3854,X_3855,X_3854),
inference(resolve,[$cnf( cyclic(X_3854,X_3855,X_3854,X_3854) )],[refute_0_193,refute_0_20]) ).
cnf(refute_0_195,plain,
cyclic(X_3856,X_3856,X_3857,X_3856),
inference(subst,[],[refute_0_194:[bind(X_3854,$fot(X_3856)),bind(X_3855,$fot(X_3857))]]) ).
cnf(refute_0_196,plain,
cyclic(X_3856,X_3856,X_3856,X_3857),
inference(resolve,[$cnf( cyclic(X_3856,X_3856,X_3857,X_3856) )],[refute_0_195,refute_0_19]) ).
cnf(refute_0_197,plain,
cyclic(X_3858,X_3858,X_3858,X_3859),
inference(subst,[],[refute_0_196:[bind(X_3856,$fot(X_3858)),bind(X_3857,$fot(X_3859))]]) ).
cnf(refute_0_198,plain,
cyclic(X_3858,X_3858,X_3859,X_3859),
inference(resolve,[$cnf( cyclic(X_3858,X_3858,X_3858,X_3859) )],[refute_0_197,refute_0_17]) ).
cnf(refute_0_199,plain,
cyclic(X_3860,X_3860,X_3861,X_3861),
inference(subst,[],[refute_0_198:[bind(X_3858,$fot(X_3860)),bind(X_3859,$fot(X_3861))]]) ).
cnf(refute_0_200,plain,
( ~ cong(X_3860,X_3861,X_3860,X_3861)
| perp(X_3861,X_3860,X_3860,X_3861) ),
inference(resolve,[$cnf( cyclic(X_3860,X_3860,X_3861,X_3861) )],[refute_0_199,refute_0_15]) ).
cnf(refute_0_201,plain,
( ~ midp(X_1566,X_1565,X_1565)
| cong(X_1566,X_1565,X_1566,X_1565) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_1566)),bind(B,$fot(X_1565)),bind(C,$fot(X_1565))]]) ).
cnf(refute_0_202,plain,
( ~ midp(X_1564,skolemFOFtoCNF_H,skolemFOFtoCNF_H)
| midp(X_1564,X_1502,X_1502) ),
inference(subst,[],[refute_0_68:[bind(X_1501,$fot(skolemFOFtoCNF_H)),bind(X_1503,$fot(X_1564))]]) ).
cnf(refute_0_203,plain,
( ~ coll(X_1563,skolemFOFtoCNF_H,skolemFOFtoCNF_H)
| ~ cong(X_1563,skolemFOFtoCNF_H,X_1563,skolemFOFtoCNF_H)
| midp(X_1563,skolemFOFtoCNF_H,skolemFOFtoCNF_H) ),
inference(subst,[],[refute_0_71:[bind(A,$fot(X_1563)),bind(B,$fot(skolemFOFtoCNF_H)),bind(C,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_204,plain,
( ~ cong(X_1561,skolemFOFtoCNF_H,skolemFOFtoCNF_H,X_1561)
| cong(X_1561,skolemFOFtoCNF_H,X_1561,skolemFOFtoCNF_H) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_1561)),bind(B,$fot(skolemFOFtoCNF_H)),bind(C,$fot(skolemFOFtoCNF_H)),bind(D,$fot(X_1561))]]) ).
cnf(refute_0_205,plain,
( ~ cong(skolemFOFtoCNF_H,X_1557,X_1557,skolemFOFtoCNF_H)
| cong(X_1557,skolemFOFtoCNF_H,skolemFOFtoCNF_H,X_1557) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_H)),bind(B,$fot(X_1557)),bind(C,$fot(X_1557)),bind(D,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_206,plain,
( ~ cong(skolemFOFtoCNF_H,X_1546,skolemFOFtoCNF_H,X_1546)
| cong(skolemFOFtoCNF_H,X_1546,X_1546,skolemFOFtoCNF_H) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_H)),bind(B,$fot(X_1546)),bind(C,$fot(skolemFOFtoCNF_H)),bind(D,$fot(X_1546))]]) ).
cnf(refute_0_207,plain,
( ~ midp(skolemFOFtoCNF_H,X_1540,X_1540)
| cong(skolemFOFtoCNF_H,X_1540,skolemFOFtoCNF_H,X_1540) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_H)),bind(B,$fot(X_1540)),bind(C,$fot(X_1540))]]) ).
cnf(refute_0_208,plain,
( ~ midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| midp(skolemFOFtoCNF_H,X_1502,X_1502) ),
inference(subst,[],[refute_0_68:[bind(X_1501,$fot(skolemFOFtoCNF_C_1)),bind(X_1503,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_209,plain,
( ~ coll(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| ~ cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1)
| midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_71:[bind(A,$fot(skolemFOFtoCNF_H)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_210,plain,
( ~ cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H)
| cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_H)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_211,plain,
( ~ cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1)
| cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_H)),bind(C,$fot(skolemFOFtoCNF_H)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_212,plain,
( ~ cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H)
| cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_H)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_213,plain,
cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H) )],[refute_0_178,refute_0_212]) ).
cnf(refute_0_214,plain,
cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1) )],[refute_0_213,refute_0_211]) ).
cnf(refute_0_215,plain,
cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H) )],[refute_0_214,refute_0_210]) ).
cnf(refute_0_216,plain,
( ~ coll(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1)
| midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_H,skolemFOFtoCNF_C_1) )],[refute_0_215,refute_0_209]) ).
cnf(refute_0_217,plain,
coll(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_168:[bind(C,$fot(skolemFOFtoCNF_H)),bind(X_1488,$fot(skolemFOFtoCNF_C_1)),bind(X_1489,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_218,plain,
midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) )],[refute_0_217,refute_0_216]) ).
cnf(refute_0_219,plain,
midp(skolemFOFtoCNF_H,X_1502,X_1502),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_H,skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1) )],[refute_0_218,refute_0_208]) ).
cnf(refute_0_220,plain,
midp(skolemFOFtoCNF_H,X_1540,X_1540),
inference(subst,[],[refute_0_219:[bind(X_1502,$fot(X_1540))]]) ).
cnf(refute_0_221,plain,
cong(skolemFOFtoCNF_H,X_1540,skolemFOFtoCNF_H,X_1540),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_H,X_1540,X_1540) )],[refute_0_220,refute_0_207]) ).
cnf(refute_0_222,plain,
cong(skolemFOFtoCNF_H,X_1546,skolemFOFtoCNF_H,X_1546),
inference(subst,[],[refute_0_221:[bind(X_1540,$fot(X_1546))]]) ).
cnf(refute_0_223,plain,
cong(skolemFOFtoCNF_H,X_1546,X_1546,skolemFOFtoCNF_H),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_H,X_1546,skolemFOFtoCNF_H,X_1546) )],[refute_0_222,refute_0_206]) ).
cnf(refute_0_224,plain,
cong(skolemFOFtoCNF_H,X_1557,X_1557,skolemFOFtoCNF_H),
inference(subst,[],[refute_0_223:[bind(X_1546,$fot(X_1557))]]) ).
cnf(refute_0_225,plain,
cong(X_1557,skolemFOFtoCNF_H,skolemFOFtoCNF_H,X_1557),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_H,X_1557,X_1557,skolemFOFtoCNF_H) )],[refute_0_224,refute_0_205]) ).
cnf(refute_0_226,plain,
cong(X_1561,skolemFOFtoCNF_H,skolemFOFtoCNF_H,X_1561),
inference(subst,[],[refute_0_225:[bind(X_1557,$fot(X_1561))]]) ).
cnf(refute_0_227,plain,
cong(X_1561,skolemFOFtoCNF_H,X_1561,skolemFOFtoCNF_H),
inference(resolve,[$cnf( cong(X_1561,skolemFOFtoCNF_H,skolemFOFtoCNF_H,X_1561) )],[refute_0_226,refute_0_204]) ).
cnf(refute_0_228,plain,
cong(X_1563,skolemFOFtoCNF_H,X_1563,skolemFOFtoCNF_H),
inference(subst,[],[refute_0_227:[bind(X_1561,$fot(X_1563))]]) ).
cnf(refute_0_229,plain,
( ~ coll(X_1563,skolemFOFtoCNF_H,skolemFOFtoCNF_H)
| midp(X_1563,skolemFOFtoCNF_H,skolemFOFtoCNF_H) ),
inference(resolve,[$cnf( cong(X_1563,skolemFOFtoCNF_H,X_1563,skolemFOFtoCNF_H) )],[refute_0_228,refute_0_203]) ).
cnf(refute_0_230,plain,
coll(X_1563,skolemFOFtoCNF_H,skolemFOFtoCNF_H),
inference(subst,[],[refute_0_168:[bind(C,$fot(X_1563)),bind(X_1488,$fot(skolemFOFtoCNF_H)),bind(X_1489,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_231,plain,
midp(X_1563,skolemFOFtoCNF_H,skolemFOFtoCNF_H),
inference(resolve,[$cnf( coll(X_1563,skolemFOFtoCNF_H,skolemFOFtoCNF_H) )],[refute_0_230,refute_0_229]) ).
cnf(refute_0_232,plain,
midp(X_1564,skolemFOFtoCNF_H,skolemFOFtoCNF_H),
inference(subst,[],[refute_0_231:[bind(X_1563,$fot(X_1564))]]) ).
cnf(refute_0_233,plain,
midp(X_1564,X_1502,X_1502),
inference(resolve,[$cnf( midp(X_1564,skolemFOFtoCNF_H,skolemFOFtoCNF_H) )],[refute_0_232,refute_0_202]) ).
cnf(refute_0_234,plain,
midp(X_1566,X_1565,X_1565),
inference(subst,[],[refute_0_233:[bind(X_1502,$fot(X_1565)),bind(X_1564,$fot(X_1566))]]) ).
cnf(refute_0_235,plain,
cong(X_1566,X_1565,X_1566,X_1565),
inference(resolve,[$cnf( midp(X_1566,X_1565,X_1565) )],[refute_0_234,refute_0_201]) ).
cnf(refute_0_236,plain,
cong(X_3860,X_3861,X_3860,X_3861),
inference(subst,[],[refute_0_235:[bind(X_1565,$fot(X_3861)),bind(X_1566,$fot(X_3860))]]) ).
cnf(refute_0_237,plain,
perp(X_3861,X_3860,X_3860,X_3861),
inference(resolve,[$cnf( cong(X_3860,X_3861,X_3860,X_3861) )],[refute_0_236,refute_0_200]) ).
cnf(refute_0_238,plain,
perp(X_3863,X_3862,X_3862,X_3863),
inference(subst,[],[refute_0_237:[bind(X_3860,$fot(X_3862)),bind(X_3861,$fot(X_3863))]]) ).
cnf(refute_0_239,plain,
( ~ midp(M,X_3863,X_3863)
| cong(X_3863,M,X_3862,M) ),
inference(resolve,[$cnf( perp(X_3863,X_3862,X_3862,X_3863) )],[refute_0_238,refute_0_13]) ).
cnf(refute_0_240,plain,
midp(M,X_3863,X_3863),
inference(subst,[],[refute_0_233:[bind(X_1502,$fot(X_3863)),bind(X_1564,$fot(M))]]) ).
cnf(refute_0_241,plain,
cong(X_3863,M,X_3862,M),
inference(resolve,[$cnf( midp(M,X_3863,X_3863) )],[refute_0_240,refute_0_239]) ).
cnf(refute_0_242,plain,
cong(X_3882,X_3880,X_3881,X_3880),
inference(subst,[],[refute_0_241:[bind(M,$fot(X_3880)),bind(X_3862,$fot(X_3881)),bind(X_3863,$fot(X_3882))]]) ).
cnf(refute_0_243,plain,
cong(X_3882,X_3880,X_3880,X_3881),
inference(resolve,[$cnf( cong(X_3882,X_3880,X_3881,X_3880) )],[refute_0_242,refute_0_11]) ).
cnf(refute_0_244,plain,
cong(X_3885,X_3883,X_3883,X_3884),
inference(subst,[],[refute_0_243:[bind(X_3880,$fot(X_3883)),bind(X_3881,$fot(X_3884)),bind(X_3882,$fot(X_3885))]]) ).
cnf(refute_0_245,plain,
cong(X_3883,X_3884,X_3885,X_3883),
inference(resolve,[$cnf( cong(X_3885,X_3883,X_3883,X_3884) )],[refute_0_244,refute_0_10]) ).
cnf(refute_0_246,plain,
cong(X_3908,X_3909,X_3910,X_3908),
inference(subst,[],[refute_0_245:[bind(X_3883,$fot(X_3908)),bind(X_3884,$fot(X_3909)),bind(X_3885,$fot(X_3910))]]) ).
cnf(refute_0_247,plain,
cong(X_3908,X_3909,X_3908,X_3910),
inference(resolve,[$cnf( cong(X_3908,X_3909,X_3910,X_3908) )],[refute_0_246,refute_0_8]) ).
cnf(refute_0_248,plain,
cong(O,A,O,C),
inference(subst,[],[refute_0_247:[bind(X_3908,$fot(O)),bind(X_3909,$fot(A)),bind(X_3910,$fot(C))]]) ).
cnf(refute_0_249,plain,
( ~ cong(O,A,O,D)
| cyclic(A,C,C,D) ),
inference(resolve,[$cnf( cong(O,A,O,C) )],[refute_0_248,refute_0_6]) ).
cnf(refute_0_250,plain,
cong(O,A,O,D),
inference(subst,[],[refute_0_247:[bind(X_3908,$fot(O)),bind(X_3909,$fot(A)),bind(X_3910,$fot(D))]]) ).
cnf(refute_0_251,plain,
cyclic(A,C,C,D),
inference(resolve,[$cnf( cong(O,A,O,D) )],[refute_0_250,refute_0_249]) ).
cnf(refute_0_252,plain,
cyclic(X_10962,X_10963,X_10963,X_10964),
inference(subst,[],[refute_0_251:[bind(A,$fot(X_10962)),bind(C,$fot(X_10963)),bind(D,$fot(X_10964))]]) ).
cnf(refute_0_253,plain,
cyclic(X_10963,X_10962,X_10963,X_10964),
inference(resolve,[$cnf( cyclic(X_10962,X_10963,X_10963,X_10964) )],[refute_0_252,refute_0_4]) ).
cnf(refute_0_254,plain,
cyclic(X_10966,X_10965,X_10966,X_10967),
inference(subst,[],[refute_0_253:[bind(X_10962,$fot(X_10965)),bind(X_10963,$fot(X_10966)),bind(X_10964,$fot(X_10967))]]) ).
cnf(refute_0_255,plain,
cyclic(X_10966,X_10966,X_10965,X_10967),
inference(resolve,[$cnf( cyclic(X_10966,X_10965,X_10966,X_10967) )],[refute_0_254,refute_0_2]) ).
cnf(refute_0_256,plain,
cyclic(X_11721,X_11721,X_11722,X_11723),
inference(subst,[],[refute_0_255:[bind(X_10965,$fot(X_11722)),bind(X_10966,$fot(X_11721)),bind(X_10967,$fot(X_11723))]]) ).
cnf(refute_0_257,plain,
( ~ cyclic(X_11721,X_11721,X_11722,X_11723)
| ~ cyclic(X_11721,X_11721,X_11722,X_11724)
| cyclic(X_11721,X_11722,X_11723,X_11724) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_11721)),bind(B,$fot(X_11721)),bind(C,$fot(X_11722)),bind(D,$fot(X_11723)),bind(E,$fot(X_11724))]]) ).
cnf(refute_0_258,plain,
( ~ cyclic(X_11721,X_11721,X_11722,X_11724)
| cyclic(X_11721,X_11722,X_11723,X_11724) ),
inference(resolve,[$cnf( cyclic(X_11721,X_11721,X_11722,X_11723) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
cyclic(X_11721,X_11721,X_11722,X_11724),
inference(subst,[],[refute_0_255:[bind(X_10965,$fot(X_11722)),bind(X_10966,$fot(X_11721)),bind(X_10967,$fot(X_11724))]]) ).
cnf(refute_0_260,plain,
cyclic(X_11721,X_11722,X_11723,X_11724),
inference(resolve,[$cnf( cyclic(X_11721,X_11721,X_11722,X_11724) )],[refute_0_259,refute_0_258]) ).
cnf(refute_0_261,plain,
cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_E,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_260:[bind(X_11721,$fot(skolemFOFtoCNF_A)),bind(X_11722,$fot(skolemFOFtoCNF_O_2)),bind(X_11723,$fot(skolemFOFtoCNF_E)),bind(X_11724,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_262,plain,
$false,
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_O_2,skolemFOFtoCNF_E,skolemFOFtoCNF_D) )],[refute_0_261,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO637+1 : TPTP v8.1.0. Released v7.5.0.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 16:36:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 52.13/52.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.13/52.31
% 52.13/52.31 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 52.16/52.33
%------------------------------------------------------------------------------