TSTP Solution File: GEO603+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO603+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 14.55s 14.81s
% Output : CNFRefutation 14.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 95 ( 31 unt; 0 def)
% Number of atoms : 210 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 189 ( 74 ~; 69 |; 36 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 163 ( 2 sgn 115 !; 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(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(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ) ).
fof(exemplo6GDDFULL618065,conjecture,
! [A,B,C,D,E,F,G] :
( ( circle(D,A,B,C)
& coll(E,A,B)
& para(B,C,F,E)
& coll(F,A,C)
& circle(G,A,E,F) )
=> coll(A,G,D) ) ).
fof(subgoal_0,plain,
! [A,B,C,D,E,F,G] :
( ( circle(D,A,B,C)
& coll(E,A,B)
& para(B,C,F,E)
& coll(F,A,C)
& circle(G,A,E,F) )
=> coll(A,G,D) ),
inference(strip,[],[exemplo6GDDFULL618065]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D,E,F,G] :
( ( circle(D,A,B,C)
& coll(E,A,B)
& para(B,C,F,E)
& coll(F,A,C)
& circle(G,A,E,F) )
=> coll(A,G,D) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[ruleD1]) ).
fof(normalize_0_1,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[ruleD2]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[ruleD3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[ruleD7]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,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_9,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_8]) ).
fof(normalize_0_10,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_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,H] :
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| perp(A,skolemFOFtoCNF_P_3(A,B,C),C,B) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[ruleD8]) ).
fof(normalize_0_13,plain,
! [A,B,C,D] :
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
? [A,B,C,D,E,F,G] :
( ~ coll(A,G,D)
& circle(D,A,B,C)
& circle(G,A,E,F)
& coll(E,A,B)
& coll(F,A,C)
& para(B,C,F,E) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_15,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D)
& circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& circle(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_F)
& coll(skolemFOFtoCNF_E,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1)
& coll(skolemFOFtoCNF_F,skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& para(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1,skolemFOFtoCNF_F,skolemFOFtoCNF_E) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
circle(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_F),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ? [P] : perp(P,A,A,O) ),
inference(canonicalize,[],[ruleX11]) ).
fof(normalize_0_18,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| ? [P] : perp(P,A,A,O) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A,B,C,O] :
( ~ circle(O,A,B,C)
| perp(skolemFOFtoCNF_P_4(A,O),A,A,O) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,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_10]) ).
fof(normalize_0_21,plain,
circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_22,plain,
~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
inference(conjunct,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
( ~ coll(A,B,C)
| coll(A,C,B) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_2,plain,
( ~ coll(A,B,C)
| coll(B,A,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_4,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_5,plain,
( ~ coll(A,B,C)
| ~ coll(A,B,D)
| coll(C,D,A) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_6,plain,
( ~ coll(skolemFOFtoCNF_G,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_G)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G))),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_7,plain,
( ~ coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_G,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G))),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_8,plain,
( ~ perp(A,B,C,D)
| perp(A,B,D,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G))),bind(C,$fot(skolemFOFtoCNF_G)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_10,plain,
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| perp(A,skolemFOFtoCNF_P_3(A,B,C),C,B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_G)),bind(H,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_12,plain,
( ~ perp(A,B,C,D)
| perp(C,D,A,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_13,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G))
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_14,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G)) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_G)),bind(C,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G))),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_15,plain,
( ~ perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G))),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_16,plain,
circle(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_F),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_17,plain,
( ~ circle(O,A,B,C)
| perp(skolemFOFtoCNF_P_4(A,O),A,A,O) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_18,plain,
( ~ circle(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_F)
| perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_F)),bind(O,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_19,plain,
perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_E,skolemFOFtoCNF_F) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_19,refute_0_15]) ).
cnf(refute_0_21,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G)),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A) )],[refute_0_20,refute_0_14]) ).
cnf(refute_0_22,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G)) )],[refute_0_21,refute_0_13]) ).
cnf(refute_0_23,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_22,refute_0_11]) ).
cnf(refute_0_24,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A) )],[refute_0_23,refute_0_9]) ).
cnf(refute_0_25,plain,
( ~ perp(A,H,B,C)
| ~ perp(B,H,A,C)
| coll(skolemFOFtoCNF_P_3(A,B,C),C,B) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_26,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_G)),bind(H,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G)))]]) ).
cnf(refute_0_27,plain,
coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
coll(skolemFOFtoCNF_G,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_G,skolemFOFtoCNF_A) )],[refute_0_27,refute_0_7]) ).
cnf(refute_0_29,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_G,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G),skolemFOFtoCNF_A) )],[refute_0_28,refute_0_6]) ).
cnf(refute_0_30,plain,
( ~ coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_31,plain,
( ~ coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_32,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_33,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_D)),bind(H,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_34,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_35,plain,
( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D))
| perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_36,plain,
( ~ perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D)) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_D)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_37,plain,
( ~ perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A)
| perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_38,plain,
( ~ perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D))),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_A)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_39,plain,
circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_40,plain,
( ~ circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(O,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_41,plain,
perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(resolve,[$cnf( circle(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_41,refute_0_38]) ).
cnf(refute_0_43,plain,
perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_42,refute_0_37]) ).
cnf(refute_0_44,plain,
perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D)),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A) )],[refute_0_43,refute_0_36]) ).
cnf(refute_0_45,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D)) )],[refute_0_44,refute_0_35]) ).
cnf(refute_0_46,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_45,refute_0_34]) ).
cnf(refute_0_47,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_4(skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_46,refute_0_33]) ).
cnf(refute_0_48,plain,
perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_47,refute_0_32]) ).
cnf(refute_0_49,plain,
( ~ perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_D)),bind(H,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_50,plain,
coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A),
inference(resolve,[$cnf( perp(skolemFOFtoCNF_A,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_D,skolemFOFtoCNF_A) )],[refute_0_50,refute_0_31]) ).
cnf(refute_0_52,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_P_3(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D),skolemFOFtoCNF_A) )],[refute_0_51,refute_0_30]) ).
cnf(refute_0_53,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_396)
| ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D)
| coll(skolemFOFtoCNF_D,X_396,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_396))]]) ).
cnf(refute_0_54,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,X_396)
| coll(skolemFOFtoCNF_D,X_396,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_D) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G)
| coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_54:[bind(X_396,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_0_56,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_A),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_29,refute_0_55]) ).
cnf(refute_0_57,plain,
coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_G,skolemFOFtoCNF_A) )],[refute_0_56,refute_0_4]) ).
cnf(refute_0_58,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_G),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_D,skolemFOFtoCNF_A,skolemFOFtoCNF_G) )],[refute_0_57,refute_0_3]) ).
cnf(refute_0_59,plain,
coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_D,skolemFOFtoCNF_G) )],[refute_0_58,refute_0_1]) ).
cnf(refute_0_60,plain,
~ coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_61,plain,
$false,
inference(resolve,[$cnf( coll(skolemFOFtoCNF_A,skolemFOFtoCNF_G,skolemFOFtoCNF_D) )],[refute_0_59,refute_0_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO603+1 : TPTP v8.1.0. Released v7.5.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 18 04:49:43 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 14.55/14.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.55/14.81
% 14.55/14.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.55/14.82
%------------------------------------------------------------------------------