%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO584+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:18:09 AM UTC 2026
% Result : Theorem 139.63s 19.16s
% Output : CNFRefutation 139.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 26
% Syntax : Number of formulae : 132 ( 51 unt; 0 def)
% Number of atoms : 289 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 236 ( 79 ~; 75 |; 55 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 468 ( 71 sgn 160 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('theBenchmark.p',ruleD3) ).
fof(ruleD4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('theBenchmark.p',ruleD4) ).
fof(ruleD5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('theBenchmark.p',ruleD5) ).
fof(ruleD7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('theBenchmark.p',ruleD7) ).
fof(ruleD8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('theBenchmark.p',ruleD8) ).
fof(ruleD9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('theBenchmark.p',ruleD9) ).
fof(ruleD14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('theBenchmark.p',ruleD14) ).
fof(ruleD15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('theBenchmark.p',ruleD15) ).
fof(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('theBenchmark.p',ruleD16) ).
fof(ruleD17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('theBenchmark.p',ruleD17) ).
fof(ruleD18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('theBenchmark.p',ruleD18) ).
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) ),
file('theBenchmark.p',ruleD19) ).
fof(ruleD21,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('theBenchmark.p',ruleD21) ).
fof(ruleD22,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('theBenchmark.p',ruleD22) ).
fof(ruleD39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('theBenchmark.p',ruleD39) ).
fof(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('theBenchmark.p',ruleD40) ).
fof(ruleD41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('theBenchmark.p',ruleD41) ).
fof(ruleD42b,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('theBenchmark.p',ruleD42b) ).
fof(ruleD43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('theBenchmark.p',ruleD43) ).
fof(ruleD46,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
file('theBenchmark.p',ruleD46) ).
fof(ruleD48,axiom,
! [A,B,C,O,X] :
( ( perp(O,A,A,X)
& circle(O,A,B,C) )
=> eqangle(A,X,A,B,C,A,C,B) ),
file('theBenchmark.p',ruleD48) ).
fof(ruleD56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('theBenchmark.p',ruleD56) ).
fof(ruleD57,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('theBenchmark.p',ruleD57) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleX14,axiom,
! [A,B,C,D] :
? [O] :
( ( cyclic(A,B,C,D)
& perp(A,C,C,B) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleX14) ).
fof(exemplo6GDDFULL416046,conjecture,
! [A,B,C,O,D,E,Q,P,S,R,NWPNT1,NWPNT2] :
( ( coll(R,C,D)
& perp(R,E,C,D)
& coll(S,A,D)
& perp(S,E,A,D)
& coll(P,A,B)
& perp(P,E,A,B)
& coll(Q,B,C)
& perp(Q,E,B,C)
& circle(O,A,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> eqangle(E,P,P,S,E,Q,Q,R) ),
file('theBenchmark.p',exemplo6GDDFULL416046) ).
fof(exemplo6GDDFULL416046_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,Q,P,S,R,NWPNT1,NWPNT2] :
( ( coll(R,C,D)
& perp(R,E,C,D)
& coll(S,A,D)
& perp(S,E,A,D)
& coll(P,A,B)
& perp(P,E,A,B)
& coll(Q,B,C)
& perp(Q,E,B,C)
& circle(O,A,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> eqangle(E,P,P,S,E,Q,Q,R) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416046]) ).
cnf(c_96,plain,
( eqangle(B,E,B,C,D,B,D,C)
| ~ perp(A,B,B,E)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD48]) ).
fof(nnf_90,plain,
! [A,B,C,D] :
? [O] :
( circle(O,A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(fof_nnf,[status(thm)],[ruleX14]) ).
fof(sk_ruleX14,plain,
! [A,B,C,D] :
( circle(sK0(A,B,C,D),A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(O,sK0(A,B,C,D))],[nnf_90]) ).
cnf(c_108,plain,
( circle(sK0(A,C,B,D),A,C,B)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(split_conjunct,[status(thm)],[sk_ruleX14]) ).
cnf(c_154,plain,
( eqangle(A,E,A,C,B,A,B,C)
| ~ perp(sK0(A,C,B,D),A,A,E)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(resolve,[status(thm)],[c_108,c_96]) ).
fof(nnf_95,plain,
? [A,B,C,O,D,E,Q,P,S,R,NWPNT1,NWPNT2] :
( ~ eqangle(E,P,P,S,E,Q,Q,R)
& coll(R,C,D)
& perp(R,E,C,D)
& coll(S,A,D)
& perp(S,E,A,D)
& coll(P,A,B)
& perp(P,E,A,B)
& coll(Q,B,C)
& perp(Q,E,B,C)
& circle(O,A,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL416046_neg]) ).
fof(sk_exemplo6GDDFULL416046_neg,plain,
( ~ eqangle(sK1,sK2,sK2,sK3,sK1,sK4,sK4,sK5)
& coll(sK5,sK7,sK10)
& perp(sK5,sK1,sK7,sK10)
& coll(sK3,sK9,sK10)
& perp(sK3,sK1,sK9,sK10)
& coll(sK2,sK9,sK6)
& perp(sK2,sK1,sK9,sK6)
& coll(sK4,sK6,sK7)
& perp(sK4,sK1,sK6,sK7)
& circle(sK8,sK9,sK1,sK12)
& circle(sK8,sK9,sK10,sK11)
& circle(sK8,sK9,sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK6,sK7,sK10,sK11,sK1,sK12,sK4,sK2,sK3,sK5]),skolemize(A,sK9),skolemize(B,sK6),skolemize(C,sK7),skolemize(O,sK8),skolemize(D,sK10),skolemize(E,sK1),skolemize(Q,sK4),skolemize(P,sK2),skolemize(S,sK3),skolemize(R,sK5),skolemize(NWPNT1,sK11),skolemize(NWPNT2,sK12)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ eqangle(sK1,sK2,sK2,sK3,sK1,sK4,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416046_neg]) ).
cnf(c_200,negated_conjecture,
perp(sK4,sK1,sK6,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416046_neg]) ).
cnf(c_239,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_248,plain,
( perp(B,A,A,D)
| ~ cyclic(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD57]) ).
cnf(c_249,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_254,plain,
( eqangle(A,B,B,C,B,C,A,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD46]) ).
cnf(c_257,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,F,D,F,E)
| ~ cyclic(A,B,C,F)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD43]) ).
cnf(c_258,plain,
( cyclic(B,C,A,D)
| ~ coll(A,D,C)
| ~ eqangle(A,B,A,C,D,B,D,C) ),
inference(clausify,[status(thm)],[ruleD42b]) ).
cnf(c_260,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_261,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_262,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_279,plain,
( eqangle(A,B,C,D,V8,V9,V10,V11)
| ~ eqangle(E,F,V6,V7,V8,V9,V10,V11)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD22]) ).
cnf(c_280,plain,
( eqangle(A,B,E,F,C,D,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD21]) ).
cnf(c_282,plain,
( eqangle(C,D,A,B,V6,V7,E,F)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD19]) ).
cnf(c_283,plain,
( eqangle(B,A,C,D,E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD18]) ).
cnf(c_284,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_285,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_286,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_287,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_291,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_292,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_293,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_295,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_296,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_297,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_342,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_248]) ).
cnf(c_348,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_284]) ).
cnf(c_353,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_297]) ).
cnf(c_470,plain,
( para(sK4,sK1,A,B)
| ~ perp(sK6,sK7,A,B) ),
inference(resolve,[status(thm)],[c_291,c_200]) ).
cnf(c_484,plain,
perp(sK6,sK7,sK4,sK1),
inference(resolve,[status(thm)],[c_292,c_200]) ).
cnf(c_798,plain,
perp(sK6,sK7,sK1,sK4),
inference(resolve,[status(thm)],[c_484,c_293]) ).
cnf(c_2406,plain,
para(sK4,sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_470,c_798]) ).
cnf(c_2407,plain,
para(sK4,sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_470,c_484]) ).
cnf(c_2412,plain,
para(sK1,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_2406,c_295]) ).
cnf(c_2427,plain,
eqangle(sK4,sK1,A,B,sK4,sK1,A,B),
inference(resolve,[status(thm)],[c_2407,c_261]) ).
cnf(c_3094,plain,
para(sK1,sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_2412,c_296]) ).
cnf(c_3109,plain,
eqangle(sK1,sK4,A,B,sK1,sK4,A,B),
inference(resolve,[status(thm)],[c_3094,c_261]) ).
cnf(c_3128,plain,
eqangle(A,B,sK4,sK1,A,B,sK4,sK1),
inference(resolve,[status(thm)],[c_2427,c_282]) ).
cnf(c_3130,plain,
( cyclic(sK1,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_2427,c_258]) ).
cnf(c_3131,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,sK4)
| ~ cyclic(sK1,A,sK4,A)
| ~ cyclic(sK1,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_2427,c_257]) ).
cnf(c_3151,plain,
( cyclic(sK4,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3109,c_258]) ).
cnf(c_3170,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_3128,c_262]) ).
cnf(c_3195,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_3170,c_239]) ).
cnf(c_3215,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_3195,c_353]) ).
cnf(c_3223,plain,
cyclic(sK4,A,sK1,sK1),
inference(resolve,[status(thm)],[c_3215,c_3151]) ).
cnf(c_3224,plain,
cyclic(sK1,A,sK4,sK4),
inference(resolve,[status(thm)],[c_3215,c_3130]) ).
cnf(c_3379,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A)
| ~ cyclic(sK1,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_3224,c_3131]) ).
cnf(c_3433,plain,
cyclic(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_3223,c_348]) ).
cnf(c_3435,plain,
cyclic(sK4,sK1,A,sK1),
inference(resolve,[status(thm)],[c_3223,c_286]) ).
cnf(c_3583,plain,
cyclic(sK1,A,sK1,sK1),
inference(resolve,[status(thm)],[c_3433,c_285]) ).
cnf(c_3596,plain,
cyclic(sK4,sK1,sK1,A),
inference(resolve,[status(thm)],[c_3435,c_287]) ).
cnf(c_3597,plain,
cyclic(sK1,sK4,A,sK1),
inference(resolve,[status(thm)],[c_3435,c_285]) ).
cnf(c_3851,plain,
cyclic(sK1,sK1,A,sK1),
inference(resolve,[status(thm)],[c_3583,c_286]) ).
cnf(c_3852,plain,
( cyclic(A,sK1,B,sK1)
| ~ cyclic(sK1,A,sK1,B) ),
inference(resolve,[status(thm)],[c_3583,c_284]) ).
cnf(c_3864,plain,
cyclic(sK1,sK1,A,A),
inference(resolve,[status(thm)],[c_3596,c_348]) ).
cnf(c_6362,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK4,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3596,c_284]) ).
cnf(c_3866,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_3596,c_6362]) ).
cnf(c_3880,plain,
cyclic(sK1,A,sK4,sK1),
inference(resolve,[status(thm)],[c_3597,c_286]) ).
cnf(c_3896,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A) ),
inference(resolve,[status(thm)],[c_3880,c_3379]) ).
cnf(c_6363,plain,
( cyclic(sK1,A,sK1,B)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_3851,c_284]) ).
cnf(c_4073,plain,
cyclic(sK1,A,sK1,B),
inference(resolve,[status(thm)],[c_3866,c_6363]) ).
cnf(c_4086,plain,
cyclic(A,sK1,B,sK1),
inference(resolve,[status(thm)],[c_4073,c_3852]) ).
cnf(c_4088,plain,
( perp(A,sK1,sK1,A)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_3864,c_342]) ).
cnf(c_6364,plain,
( cyclic(sK1,A,B,A)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_3864,c_284]) ).
cnf(c_4089,plain,
cyclic(sK1,A,B,A),
inference(resolve,[status(thm)],[c_3866,c_6364]) ).
cnf(c_4102,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_4089,c_3896]) ).
cnf(c_4103,plain,
perp(A,sK1,sK1,A),
inference(resolve,[status(thm)],[c_4102,c_4088]) ).
cnf(c_6365,plain,
( perp(A,sK1,sK1,B)
| ~ cong(sK1,B,sK1,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_3866,c_248]) ).
cnf(c_6366,plain,
( perp(B,sK1,sK1,A)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_4102,c_6365]) ).
cnf(c_4151,plain,
perp(A,sK1,sK1,B),
inference(resolve,[status(thm)],[c_4102,c_6366]) ).
cnf(c_6367,plain,
( eqangle(sK1,C,sK1,sK1,A,sK1,A,sK1)
| ~ perp(sK0(sK1,sK1,A,B),sK1,sK1,C)
| ~ perp(sK1,A,A,sK1) ),
inference(resolve,[status(thm)],[c_3866,c_154]) ).
cnf(c_4159,plain,
( eqangle(sK1,B,sK1,sK1,A,sK1,A,sK1)
| ~ perp(sK1,A,A,sK1) ),
inference(resolve,[status(thm)],[c_4151,c_6367]) ).
cnf(c_4491,plain,
eqangle(A,B,A,sK1,sK1,B,sK1,sK1),
inference(resolve,[status(thm)],[c_4086,c_260]) ).
cnf(c_4517,plain,
eqangle(A,sK1,A,B,B,sK1,B,B),
inference(resolve,[status(thm)],[c_4089,c_260]) ).
cnf(c_4562,plain,
eqangle(sK1,A,A,A,A,A,sK1,A),
inference(resolve,[status(thm)],[c_4102,c_254]) ).
cnf(c_6368,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_4102,c_249]) ).
cnf(c_4563,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_4102,c_6368]) ).
cnf(c_4600,plain,
perp(sK1,A,A,sK1),
inference(resolve,[status(thm)],[c_4103,c_292]) ).
cnf(c_4616,plain,
eqangle(sK1,A,sK1,sK1,B,sK1,B,sK1),
inference(resolve,[status(thm)],[c_4600,c_4159]) ).
cnf(c_5027,plain,
perp(A,B,sK1,sK1),
inference(resolve,[status(thm)],[c_4563,c_292]) ).
cnf(c_6369,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK1,sK1) ),
inference(resolve,[status(thm)],[c_4563,c_291]) ).
cnf(c_5028,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_5027,c_6369]) ).
cnf(c_5052,plain,
eqangle(A,B,C,D,E,F,C,D),
inference(resolve,[status(thm)],[c_5028,c_261]) ).
cnf(c_5778,plain,
eqangle(A,B,sK1,B,A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_4491,c_280]) ).
cnf(c_5781,plain,
eqangle(sK1,A,A,B,B,sK1,B,B),
inference(resolve,[status(thm)],[c_4517,c_283]) ).
cnf(c_5789,plain,
eqangle(A,sK1,A,A,A,A,sK1,A),
inference(resolve,[status(thm)],[c_4562,c_283]) ).
cnf(c_5803,plain,
eqangle(A,sK1,sK1,sK1,B,sK1,B,sK1),
inference(resolve,[status(thm)],[c_4616,c_283]) ).
cnf(c_5919,plain,
eqangle(A,B,C,D,A,B,E,F),
inference(resolve,[status(thm)],[c_5052,c_282]) ).
cnf(c_6173,plain,
( eqangle(A,F,sK1,F,B,C,D,E)
| ~ eqangle(A,sK1,sK1,sK1,B,C,D,E) ),
inference(resolve,[status(thm)],[c_5778,c_279]) ).
cnf(c_6177,plain,
( eqangle(sK1,F,F,A,B,C,D,E)
| ~ eqangle(A,sK1,A,A,B,C,D,E) ),
inference(resolve,[status(thm)],[c_5781,c_279]) ).
cnf(c_6187,plain,
( eqangle(A,sK1,A,A,B,C,D,E)
| ~ eqangle(A,A,sK1,A,B,C,D,E) ),
inference(resolve,[status(thm)],[c_5789,c_279]) ).
cnf(c_6207,plain,
( eqangle(F,sK1,sK1,sK1,B,C,D,E)
| ~ eqangle(A,sK1,A,sK1,B,C,D,E) ),
inference(resolve,[status(thm)],[c_5803,c_279]) ).
cnf(c_6323,plain,
eqangle(A,B,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_5919,c_280]) ).
cnf(c_6329,plain,
eqangle(A,sK1,sK1,sK1,B,C,D,E),
inference(resolve,[status(thm)],[c_6323,c_6207]) ).
cnf(c_6342,plain,
eqangle(A,B,sK1,B,C,D,E,F),
inference(resolve,[status(thm)],[c_6329,c_6173]) ).
cnf(c_6354,plain,
eqangle(A,sK1,A,A,B,C,D,E),
inference(resolve,[status(thm)],[c_6342,c_6187]) ).
cnf(c_6360,plain,
eqangle(sK1,A,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_6354,c_6177]) ).
cnf(c_6361,plain,
$false,
inference(resolve,[status(thm)],[c_6360,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO584+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:43:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2890583 was started by sandbox2 on n019,
% 0.09/0.36 % Fri Sep 25 13:43:18 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 139.63/19.16
% 139.63/19.16 % given #500 (W,wt=9): 1481 coll(c7,c7,c8). [resolve(1439,a,353,a)].
% 139.63/19.16
% 139.63/19.16 % given #1000 (T,wt=13): 1279 -coll(c2,c7,A) | coll(A,c5,c2). [resolve(1244,a,297,b)].
% 139.63/19.16
% 139.63/19.16 % given #1500 (T,wt=13): 2006 -coll(c9,c8,A) | coll(A,c2,c9). [resolve(1918,a,297,b)].
% 139.63/19.16
% 139.63/19.16 % given #2000 (W,wt=9): 2792 coll(c6,c8,c6). [resolve(2575,a,299,a)].
% 139.63/19.16
% 139.63/19.16 % given #2500 (T,wt=9): 3240 coll(A,c10,c6). [back_unit_del(2836),unit_del(a,3215)].
% 139.63/19.16
% 139.63/19.16 % given #3000 (T,wt=14): 5239 eqangle(c1,c4,c1,c6,c12,c1,c12,c6). [resolve(5221,a,112,a)].
% 139.63/19.16
% 139.63/19.16 % SZS status Theorem for theBenchmark
% 139.63/19.16
% 139.63/19.16 % Proof 1 at 1.92 (+ 0.68) seconds.
% 139.63/19.16 % Length of proof is 119.
% 139.63/19.16 % Level of proof is 25.
% 139.63/19.16 % Maximum clause weight is 38.000.
% 139.63/19.16 % Given clauses 3166.
% 139.63/19.16
% 139.63/19.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------