TSTP Solution File: GEO567+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO567+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 05:27:24 EDT 2022
% Result : Theorem 0.57s 0.75s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 125 ( 43 unt; 0 def)
% Number of atoms : 252 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 213 ( 86 ~; 81 |; 31 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 309 ( 25 sgn 192 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(ruleD9,axiom,
! [A,B,C,D,E,F] :
( ( perp(A,B,C,D)
& perp(C,D,E,F) )
=> para(A,B,E,F) ) ).
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(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ) ).
fof(ruleD42b,axiom,
! [A,B,P,Q] :
( ( eqangle(P,A,P,B,Q,A,Q,B)
& coll(P,Q,B) )
=> cyclic(A,B,P,Q) ) ).
fof(exemplo6GDDFULL214029,conjecture,
! [A,B,C,D,Q,P] :
( ( perp(D,A,B,C)
& coll(D,B,C)
& perp(Q,D,A,B)
& coll(Q,A,B)
& perp(P,D,A,C)
& coll(P,A,C) )
=> cyclic(B,Q,P,C) ) ).
fof(subgoal_0,plain,
! [A,B,C,D,Q,P] :
( ( perp(D,A,B,C)
& coll(D,B,C)
& perp(Q,D,A,B)
& coll(Q,A,B)
& perp(P,D,A,C)
& coll(P,A,C) )
=> cyclic(B,Q,P,C) ),
inference(strip,[],[exemplo6GDDFULL214029]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D,Q,P] :
( ( perp(D,A,B,C)
& coll(D,B,C)
& perp(Q,D,A,B)
& coll(Q,A,B)
& perp(P,D,A,C)
& coll(P,A,C) )
=> cyclic(B,Q,P,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D,P,Q] :
( ~ cyclic(B,Q,P,C)
& coll(D,B,C)
& coll(P,A,C)
& coll(Q,A,B)
& perp(D,A,B,C)
& perp(P,D,A,C)
& perp(Q,D,A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_P_8,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_P_8,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& coll(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& perp(skolemFOFtoCNF_P_8,skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& perp(skolemFOFtoCNF_Q_3,skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_P_8,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,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_4,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_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[ruleD15]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[ruleD14]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[ruleD16]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,P,Q] :
( ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B)
| cyclic(A,B,P,Q) ),
inference(canonicalize,[],[ruleD42b]) ).
fof(normalize_0_12,plain,
! [A,B,P,Q] :
( ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B)
| cyclic(A,B,P,Q) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,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_14,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_13]) ).
fof(normalize_0_15,plain,
! [A,B,C,D] :
( ~ para(A,B,C,D)
| ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[ruleD40]) ).
fof(normalize_0_16,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_15]) ).
fof(normalize_0_17,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_16]) ).
fof(normalize_0_18,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_19,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_21,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_23,plain,
! [A,B,C,D,E,F] :
( ~ perp(A,B,C,D)
| ~ perp(C,D,E,F)
| para(A,B,E,F) ),
inference(canonicalize,[],[ruleD9]) ).
fof(normalize_0_24,plain,
! [A,B,C,D,E,F] :
( ~ perp(A,B,C,D)
| ~ perp(C,D,E,F)
| para(A,B,E,F) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_26,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
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,
~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_P_8,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ cyclic(A,B,C,D)
| ~ cyclic(A,B,C,E)
| cyclic(B,C,D,E) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_847,D)
| ~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_847,skolemFOFtoCNF_C_1)
| cyclic(skolemFOFtoCNF_B_1,X_847,D,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_847)),bind(E,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_3,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,C,B,D) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,X_840,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_840,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_840)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_5,plain,
( ~ cyclic(A,B,C,D)
| cyclic(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,X_836,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_B_1,X_836,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(X_836)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_7,plain,
( ~ cyclic(A,B,C,D)
| cyclic(B,A,C,D) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ cyclic(X_833,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_B_1,X_833,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_833)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_9,plain,
( ~ cyclic(X_831,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| cyclic(X_831,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_831)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_10,plain,
( ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B)
| cyclic(A,B,P,Q) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| ~ eqangle(skolemFOFtoCNF_B_1,X_830,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,X_830,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| cyclic(X_830,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_830)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_12,plain,
( ~ eqangle(A,B,C,D,P,Q,U,V)
| eqangle(C,D,A,B,U,V,P,Q) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
( ~ eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,X_823,X_824,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,X_823,X_824)
| eqangle(X_823,X_824,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,X_823,X_824,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(X_823)),bind(D,$fot(X_824)),bind(P,$fot(skolemFOFtoCNF_B_1)),bind(Q,$fot(skolemFOFtoCNF_C_1)),bind(U,$fot(X_823)),bind(V,$fot(X_824))]]) ).
cnf(refute_0_14,plain,
( ~ para(A,B,C,D)
| eqangle(A,B,P,Q,C,D,P,Q) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_15,plain,
( ~ para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,P,Q,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,P,Q) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_16,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_17,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_18,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_19,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_20,plain,
( ~ perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_21,plain,
perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_22,plain,
( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_23,plain,
perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_25,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_25,refute_0_20]) ).
cnf(refute_0_27,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_26,refute_0_19]) ).
cnf(refute_0_28,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_27,refute_0_17]) ).
cnf(refute_0_29,plain,
( ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_30,plain,
( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_31,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_21,refute_0_30]) ).
cnf(refute_0_32,plain,
perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_31,refute_0_29]) ).
cnf(refute_0_33,plain,
( ~ perp(A,B,C,D)
| ~ perp(C,D,E,F)
| para(A,B,E,F) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_34,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,X_819,X_820)
| ~ perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,X_819,X_820) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_D)),bind(E,$fot(X_819)),bind(F,$fot(X_820))]]) ).
cnf(refute_0_35,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,X_819,X_820)
| para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,X_819,X_820) ),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_32,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_35:[bind(X_819,$fot(skolemFOFtoCNF_B_1)),bind(X_820,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_37,plain,
para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,P,Q,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,P,Q),
inference(resolve,[$cnf( para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_37,refute_0_15]) ).
cnf(refute_0_39,plain,
eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,X_823,X_824,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,X_823,X_824),
inference(subst,[],[refute_0_38:[bind(P,$fot(X_823)),bind(Q,$fot(X_824))]]) ).
cnf(refute_0_40,plain,
eqangle(X_823,X_824,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,X_823,X_824,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,X_823,X_824,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,X_823,X_824) )],[refute_0_39,refute_0_13]) ).
cnf(refute_0_41,plain,
eqangle(skolemFOFtoCNF_B_1,X_830,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,X_830,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_40:[bind(X_823,$fot(skolemFOFtoCNF_B_1)),bind(X_824,$fot(X_830))]]) ).
cnf(refute_0_42,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| cyclic(X_830,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( eqangle(skolemFOFtoCNF_B_1,X_830,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,X_830,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_41,refute_0_11]) ).
cnf(refute_0_43,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_44,plain,
( ~ coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_43:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_45,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_46,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_47,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_46:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_48,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1)
| coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_43:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_50,plain,
coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D,skolemFOFtoCNF_C_1) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_C_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_50,refute_0_44]) ).
cnf(refute_0_52,plain,
cyclic(X_830,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_51,refute_0_42]) ).
cnf(refute_0_53,plain,
cyclic(X_831,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_52:[bind(X_830,$fot(X_831))]]) ).
cnf(refute_0_54,plain,
cyclic(X_831,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cyclic(X_831,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_53,refute_0_9]) ).
cnf(refute_0_55,plain,
cyclic(X_833,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_54:[bind(X_831,$fot(X_833))]]) ).
cnf(refute_0_56,plain,
cyclic(skolemFOFtoCNF_B_1,X_833,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cyclic(X_833,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_55,refute_0_8]) ).
cnf(refute_0_57,plain,
cyclic(skolemFOFtoCNF_B_1,X_836,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_56:[bind(X_833,$fot(X_836))]]) ).
cnf(refute_0_58,plain,
cyclic(skolemFOFtoCNF_B_1,X_836,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,X_836,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_57,refute_0_6]) ).
cnf(refute_0_59,plain,
cyclic(skolemFOFtoCNF_B_1,X_840,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_58:[bind(X_836,$fot(X_840))]]) ).
cnf(refute_0_60,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_840,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,X_840,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_59,refute_0_4]) ).
cnf(refute_0_61,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_847,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_60:[bind(X_840,$fot(X_847))]]) ).
cnf(refute_0_62,plain,
( ~ cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_847,D)
| cyclic(skolemFOFtoCNF_B_1,X_847,D,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_847,skolemFOFtoCNF_C_1) )],[refute_0_61,refute_0_2]) ).
cnf(refute_0_63,plain,
( ~ cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,D)
| ~ cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_841)
| cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,D,X_841) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(E,$fot(X_841))]]) ).
cnf(refute_0_64,plain,
( ~ cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,X_835,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_835) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_835)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_65,plain,
( ~ cyclic(skolemFOFtoCNF_C_1,X_832,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,X_832,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(X_832)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_66,plain,
( ~ cyclic(X_831,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| cyclic(skolemFOFtoCNF_C_1,X_831,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_831)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_67,plain,
cyclic(skolemFOFtoCNF_C_1,X_831,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cyclic(X_831,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_53,refute_0_66]) ).
cnf(refute_0_68,plain,
cyclic(skolemFOFtoCNF_C_1,X_832,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_67:[bind(X_831,$fot(X_832))]]) ).
cnf(refute_0_69,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,X_832,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_C_1,X_832,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_68,refute_0_65]) ).
cnf(refute_0_70,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,X_835,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_69:[bind(X_832,$fot(X_835))]]) ).
cnf(refute_0_71,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_835),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,X_835,skolemFOFtoCNF_B_1) )],[refute_0_70,refute_0_64]) ).
cnf(refute_0_72,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_841),
inference(subst,[],[refute_0_71:[bind(X_835,$fot(X_841))]]) ).
cnf(refute_0_73,plain,
( ~ cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,D)
| cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,D,X_841) ),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_841) )],[refute_0_72,refute_0_63]) ).
cnf(refute_0_74,plain,
cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,D),
inference(subst,[],[refute_0_71:[bind(X_835,$fot(D))]]) ).
cnf(refute_0_75,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,D,X_841),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,D) )],[refute_0_74,refute_0_73]) ).
cnf(refute_0_76,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_847,D),
inference(subst,[],[refute_0_75:[bind(D,$fot(X_847)),bind(X_841,$fot(D))]]) ).
cnf(refute_0_77,plain,
cyclic(skolemFOFtoCNF_B_1,X_847,D,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1,X_847,D) )],[refute_0_76,refute_0_62]) ).
cnf(refute_0_78,plain,
cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_P_8,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_77:[bind(D,$fot(skolemFOFtoCNF_P_8)),bind(X_847,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_79,plain,
$false,
inference(resolve,[$cnf( cyclic(skolemFOFtoCNF_B_1,skolemFOFtoCNF_Q_3,skolemFOFtoCNF_P_8,skolemFOFtoCNF_C_1) )],[refute_0_78,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO567+1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 02:33:32 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.57/0.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.75
% 0.57/0.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.57/0.76
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