%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO600+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 05:27:37 EDT 2022
% Result : Theorem 80.80s 80.97s
% Output : CNFRefutation 80.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 97 ( 27 unt; 0 def)
% Number of atoms : 249 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 223 ( 71 ~; 66 |; 71 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 383 ( 12 sgn 243 !; 35 ?)
% 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(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(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(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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ) ).
fof(exemplo6GDDFULL618062,conjecture,
! [A,B,C,D,E,F,G,H,I,J,K,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
( ( circle(D,A,B,C)
& circle(D,A,E,NWPNT1)
& midp(F,C,E)
& midp(G,A,E)
& circle(F,E,NWPNT2,NWPNT3)
& circle(G,E,NWPNT4,NWPNT5)
& circle(F,E,H,NWPNT6)
& circle(G,E,H,NWPNT7)
& coll(I,A,B)
& circle(G,E,I,NWPNT8)
& midp(J,B,E)
& circle(J,B,NWPNT9,NWPNT01)
& circle(F,E,K,NWPNT11)
& circle(J,B,K,NWPNT21) )
=> coll(I,H,K) ) ).
fof(subgoal_0,plain,
! [A,B,C,D,E,F,G,H,I,J,K,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
( ( circle(D,A,B,C)
& circle(D,A,E,NWPNT1)
& midp(F,C,E)
& midp(G,A,E)
& circle(F,E,NWPNT2,NWPNT3)
& circle(G,E,NWPNT4,NWPNT5)
& circle(F,E,H,NWPNT6)
& circle(G,E,H,NWPNT7)
& coll(I,A,B)
& circle(G,E,I,NWPNT8)
& midp(J,B,E)
& circle(J,B,NWPNT9,NWPNT01)
& circle(F,E,K,NWPNT11)
& circle(J,B,K,NWPNT21) )
=> coll(I,H,K) ),
inference(strip,[],[exemplo6GDDFULL618062]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D,E,F,G,H,I,J,K,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
( ( circle(D,A,B,C)
& circle(D,A,E,NWPNT1)
& midp(F,C,E)
& midp(G,A,E)
& circle(F,E,NWPNT2,NWPNT3)
& circle(G,E,NWPNT4,NWPNT5)
& circle(F,E,H,NWPNT6)
& circle(G,E,H,NWPNT7)
& coll(I,A,B)
& circle(G,E,I,NWPNT8)
& midp(J,B,E)
& circle(J,B,NWPNT9,NWPNT01)
& circle(F,E,K,NWPNT11)
& circle(J,B,K,NWPNT21) )
=> coll(I,H,K) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D,E,F,G,H,I,J,K] :
( ~ coll(I,H,K)
& circle(D,A,B,C)
& coll(I,A,B)
& midp(F,C,E)
& midp(G,A,E)
& midp(J,B,E)
& ? [NWPNT1] : circle(D,A,E,NWPNT1)
& ? [NWPNT11] : circle(F,E,K,NWPNT11)
& ? [NWPNT21] : circle(J,B,K,NWPNT21)
& ? [NWPNT6] : circle(F,E,H,NWPNT6)
& ? [NWPNT7] : circle(G,E,H,NWPNT7)
& ? [NWPNT8] : circle(G,E,I,NWPNT8)
& ? [NWPNT01,NWPNT9] : circle(J,B,NWPNT9,NWPNT01)
& ? [NWPNT2,NWPNT3] : circle(F,E,NWPNT2,NWPNT3)
& ? [NWPNT4,NWPNT5] : circle(G,E,NWPNT4,NWPNT5) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ coll(skolemFOFtoCNF_I,skolemFOFtoCNF_H,skolemFOFtoCNF_K)
& circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_I,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& midp(skolemFOFtoCNF_F,skolemFOFtoCNF_C_1,skolemFOFtoCNF_E)
& midp(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E)
& midp(skolemFOFtoCNF_J,skolemFOFtoCNF_B_1,skolemFOFtoCNF_E)
& ? [NWPNT1] : circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_E,NWPNT1)
& ? [NWPNT11] : circle(skolemFOFtoCNF_F,skolemFOFtoCNF_E,skolemFOFtoCNF_K,NWPNT11)
& ? [NWPNT21] : circle(skolemFOFtoCNF_J,skolemFOFtoCNF_B_1,skolemFOFtoCNF_K,NWPNT21)
& ? [NWPNT6] : circle(skolemFOFtoCNF_F,skolemFOFtoCNF_E,skolemFOFtoCNF_H,NWPNT6)
& ? [NWPNT7] : circle(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_H,NWPNT7)
& ? [NWPNT8] : circle(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_I,NWPNT8)
& ? [NWPNT01,NWPNT9] : circle(skolemFOFtoCNF_J,skolemFOFtoCNF_B_1,NWPNT9,NWPNT01)
& ? [NWPNT2,NWPNT3] : circle(skolemFOFtoCNF_F,skolemFOFtoCNF_E,NWPNT2,NWPNT3)
& ? [NWPNT4,NWPNT5] : circle(skolemFOFtoCNF_G,skolemFOFtoCNF_E,NWPNT4,NWPNT5) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ coll(skolemFOFtoCNF_I,skolemFOFtoCNF_H,skolemFOFtoCNF_K),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_4,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[ruleD66]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,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_8,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_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,plain,
! [A,B,C,D,E] :
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[ruleD17]) ).
fof(normalize_0_11,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_10]) ).
fof(normalize_0_12,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_13,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_12]) ).
fof(normalize_0_14,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[ruleD24]) ).
fof(normalize_0_15,plain,
! [A,B,C,D] :
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
midp(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_17,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[ruleD68]) ).
fof(normalize_0_18,plain,
! [A,B,C] :
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,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_20,plain,
! [A,B,P,Q] :
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,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_22,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_21]) ).
fof(normalize_0_23,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_22]) ).
fof(normalize_0_24,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_25,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_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]) ).
cnf(refute_0_0,plain,
~ coll(skolemFOFtoCNF_I,skolemFOFtoCNF_H,skolemFOFtoCNF_K),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ coll(X_603,X_604,X_604)
| coll(X_604,X_604,X_603) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_603)),bind(B,$fot(X_604)),bind(C,$fot(X_604)),bind(D,$fot(X_604))]]) ).
cnf(refute_0_3,plain,
( ~ para(A,B,A,C)
| coll(A,B,C) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( ~ para(X_598,X_599,X_598,X_599)
| coll(X_598,X_599,X_599) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_598)),bind(B,$fot(X_599)),bind(C,$fot(X_599))]]) ).
cnf(refute_0_5,plain,
( ~ eqangle(A,B,P,Q,C,D,P,Q)
| para(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ eqangle(X_596,X_597,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_596,X_597,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(X_596,X_597,X_596,X_597) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_596)),bind(B,$fot(X_597)),bind(C,$fot(X_596)),bind(D,$fot(X_597)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_7,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ cyclic(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(E,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_9,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_13]) ).
cnf(refute_0_10,plain,
( ~ cong(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_A)
| cyclic(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_E)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A)),bind(O,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_11,plain,
( ~ cong(A,B,C,D)
| cong(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ cong(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_E)
| cong(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_13,plain,
midp(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_14,plain,
( ~ midp(A,B,C)
| cong(A,B,A,C) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_15,plain,
( ~ midp(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E)
| cong(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_16,plain,
cong(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_E),
inference(resolve,[$cnf( midp(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
cong(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_E) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
cyclic(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cong(skolemFOFtoCNF_G,skolemFOFtoCNF_E,skolemFOFtoCNF_G,skolemFOFtoCNF_A) )],[refute_0_17,refute_0_10]) ).
cnf(refute_0_19,plain,
cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_18,refute_0_8]) ).
cnf(refute_0_20,plain,
( ~ cyclic(A,B,P,Q)
| eqangle(P,A,P,B,Q,A,Q,B) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_21,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_20:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_22,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_5:[bind(A,$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,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_24,plain,
para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_26,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_25:[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_27,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_153,X_154),
inference(resolve,[$cnf( para(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_594,X_595,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_594,X_595),
inference(subst,[],[refute_0_27:[bind(X_153,$fot(X_594)),bind(X_154,$fot(X_595))]]) ).
cnf(refute_0_29,plain,
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_30,plain,
( ~ eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_594,X_595,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_594,X_595)
| eqangle(X_594,X_595,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_594,X_595,skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(X_594)),bind(D,$fot(X_595)),bind(P,$fot(skolemFOFtoCNF_A)),bind(Q,$fot(skolemFOFtoCNF_A)),bind(U,$fot(X_594)),bind(V,$fot(X_595))]]) ).
cnf(refute_0_31,plain,
eqangle(X_594,X_595,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_594,X_595,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_594,X_595,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_594,X_595) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
eqangle(X_596,X_597,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_596,X_597,skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_31:[bind(X_594,$fot(X_596)),bind(X_595,$fot(X_597))]]) ).
cnf(refute_0_33,plain,
para(X_596,X_597,X_596,X_597),
inference(resolve,[$cnf( eqangle(X_596,X_597,skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_596,X_597,skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_32,refute_0_6]) ).
cnf(refute_0_34,plain,
para(X_598,X_599,X_598,X_599),
inference(subst,[],[refute_0_33:[bind(X_596,$fot(X_598)),bind(X_597,$fot(X_599))]]) ).
cnf(refute_0_35,plain,
coll(X_598,X_599,X_599),
inference(resolve,[$cnf( para(X_598,X_599,X_598,X_599) )],[refute_0_34,refute_0_4]) ).
cnf(refute_0_36,plain,
coll(X_603,X_604,X_604),
inference(subst,[],[refute_0_35:[bind(X_598,$fot(X_603)),bind(X_599,$fot(X_604))]]) ).
cnf(refute_0_37,plain,
coll(X_604,X_604,X_603),
inference(resolve,[$cnf( coll(X_603,X_604,X_604) )],[refute_0_36,refute_0_2]) ).
cnf(refute_0_38,plain,
coll(X_3667,X_3667,X_3668),
inference(subst,[],[refute_0_37:[bind(X_603,$fot(X_3668)),bind(X_604,$fot(X_3667))]]) ).
cnf(refute_0_39,plain,
( ~ coll(X_3667,X_3667,X_3668)
| ~ coll(X_3667,X_3667,X_3669)
| coll(X_3668,X_3669,X_3667) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_3667)),bind(B,$fot(X_3667)),bind(C,$fot(X_3668)),bind(D,$fot(X_3669))]]) ).
cnf(refute_0_40,plain,
( ~ coll(X_3667,X_3667,X_3669)
| coll(X_3668,X_3669,X_3667) ),
inference(resolve,[$cnf( coll(X_3667,X_3667,X_3668) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_42,plain,
( ~ coll(X_606,X_605,X_606)
| coll(X_606,X_606,X_605) ),
inference(subst,[],[refute_0_41:[bind(A,$fot(X_606)),bind(B,$fot(X_605)),bind(C,$fot(X_606))]]) ).
cnf(refute_0_43,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_44,plain,
( ~ coll(X_603,X_604,X_604)
| coll(X_604,X_603,X_604) ),
inference(subst,[],[refute_0_43:[bind(A,$fot(X_603)),bind(B,$fot(X_604)),bind(C,$fot(X_604))]]) ).
cnf(refute_0_45,plain,
coll(X_604,X_603,X_604),
inference(resolve,[$cnf( coll(X_603,X_604,X_604) )],[refute_0_36,refute_0_44]) ).
cnf(refute_0_46,plain,
coll(X_606,X_605,X_606),
inference(subst,[],[refute_0_45:[bind(X_603,$fot(X_605)),bind(X_604,$fot(X_606))]]) ).
cnf(refute_0_47,plain,
coll(X_606,X_606,X_605),
inference(resolve,[$cnf( coll(X_606,X_605,X_606) )],[refute_0_46,refute_0_42]) ).
cnf(refute_0_48,plain,
coll(X_3667,X_3667,X_3669),
inference(subst,[],[refute_0_47:[bind(X_605,$fot(X_3669)),bind(X_606,$fot(X_3667))]]) ).
cnf(refute_0_49,plain,
coll(X_3668,X_3669,X_3667),
inference(resolve,[$cnf( coll(X_3667,X_3667,X_3669) )],[refute_0_48,refute_0_40]) ).
cnf(refute_0_50,plain,
coll(skolemFOFtoCNF_I,skolemFOFtoCNF_H,skolemFOFtoCNF_K),
inference(subst,[],[refute_0_49:[bind(X_3667,$fot(skolemFOFtoCNF_K)),bind(X_3668,$fot(skolemFOFtoCNF_I)),bind(X_3669,$fot(skolemFOFtoCNF_H))]]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( coll(skolemFOFtoCNF_I,skolemFOFtoCNF_H,skolemFOFtoCNF_K) )],[refute_0_50,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO600+1 : TPTP v8.1.0. Released v7.5.0.
% 0.14/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Fri Jun 17 19:29:34 EDT 2022
% 0.22/0.36 % CPUTime :
% 0.22/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 80.80/80.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 80.80/80.97
% 80.80/80.97 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 80.80/80.98
%------------------------------------------------------------------------------