%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO586+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 07:18:10 AM UTC 2026
% Result : Theorem 13.03s 2.27s
% Output : CNFRefutation 12.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 31
% Syntax : Number of formulae : 181 ( 71 unt; 0 def)
% Number of atoms : 376 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 322 ( 127 ~; 123 |; 40 &)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-5 aty)
% Number of variables : 511 ( 88 sgn 173 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('theBenchmark.p',ruleD2) ).
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(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(ruleD12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleD12) ).
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(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(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('theBenchmark.p',ruleD23) ).
fof(ruleD24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('theBenchmark.p',ruleD24) ).
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(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(ruleD45,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('theBenchmark.p',ruleD45) ).
fof(ruleD51,axiom,
! [A,B,C,O,M] :
( ( eqangle(A,B,A,C,O,B,O,M)
& coll(M,B,C)
& circle(O,A,B,C) )
=> midp(M,B,C) ),
file('theBenchmark.p',ruleD51) ).
fof(ruleD52,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('theBenchmark.p',ruleD52) ).
fof(ruleD53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('theBenchmark.p',ruleD53) ).
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(ruleD64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('theBenchmark.p',ruleD64) ).
fof(ruleD65,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('theBenchmark.p',ruleD65) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('theBenchmark.p',ruleD75) ).
fof(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(ruleX13,axiom,
! [A,B,C,D,M] :
? [O] :
( ( midp(M,A,B)
& para(A,B,C,D)
& cyclic(A,B,C,D) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleX13) ).
fof(exemplo6GDDFULL416048,conjecture,
! [A,B,C,O,D,E,I,NWPNT1] :
( ( circle(I,A,B,E)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> perp(I,E,C,D) ),
file('theBenchmark.p',exemplo6GDDFULL416048) ).
fof(exemplo6GDDFULL416048_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,I,NWPNT1] :
( ( circle(I,A,B,E)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> perp(I,E,C,D) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416048]) ).
cnf(c_97,plain,
( circle(A,B,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD12]) ).
cnf(c_100,plain,
( midp(E,C,D)
| ~ eqangle(B,C,B,D,A,C,A,E)
| ~ coll(E,C,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD51]) ).
cnf(c_101,plain,
( perp(B,C,C,D)
| ~ coll(A,B,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD53]) ).
fof(nnf_87,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[ruleX11]) ).
fof(sk_ruleX11,plain,
! [A,B,C,O] :
( perp(sK0(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0(A,B,C,O))],[nnf_87]) ).
cnf(c_102,plain,
( perp(sK0(B,C,D,A),B,B,A)
| ~ circle(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_ruleX11]) ).
fof(nnf_89,plain,
! [A,B,C,D,M] :
? [O] :
( circle(O,A,B,C)
| ~ midp(M,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(fof_nnf,[status(thm)],[ruleX13]) ).
fof(sk_ruleX13,plain,
! [A,B,C,D,M] :
( circle(sK1(A,B,C,D,M),A,B,C)
| ~ midp(M,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(O,sK1(A,B,C,D,M))],[nnf_89]) ).
cnf(c_107,plain,
( circle(sK1(A,B,C,D,E),A,B,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_ruleX13]) ).
fof(nnf_95,plain,
? [A,B,C,O,D,E,I,NWPNT1] :
( ~ perp(I,E,C,D)
& circle(I,A,B,E)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL416048_neg]) ).
fof(sk_exemplo6GDDFULL416048_neg,plain,
( ~ perp(sK6,sK7,sK5,sK8)
& circle(sK6,sK3,sK4,sK7)
& coll(sK7,sK4,sK8)
& coll(sK7,sK3,sK5)
& circle(sK2,sK3,sK8,sK9)
& circle(sK2,sK3,sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK8,sK9,sK7,sK6]),skolemize(A,sK3),skolemize(B,sK4),skolemize(C,sK5),skolemize(O,sK2),skolemize(D,sK8),skolemize(E,sK7),skolemize(I,sK6),skolemize(NWPNT1,sK9)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK2,sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416048_neg]) ).
cnf(c_111,negated_conjecture,
circle(sK6,sK3,sK4,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416048_neg]) ).
cnf(c_117,negated_conjecture,
perp(sK0(sK3,sK4,sK7,sK6),sK3,sK3,sK6),
inference(resolve,[status(thm)],[c_111,c_102]) ).
cnf(c_145,negated_conjecture,
perp(sK0(sK3,sK4,sK5,sK2),sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_172,plain,
( perp(A,B,B,C)
| ~ coll(sK1(A,B,C,D,E),A,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(resolve,[status(thm)],[c_107,c_101]) ).
cnf(c_188,plain,
( ~ cong(E,D,E,C)
| ~ cong(E,D,E,B)
| midp(A,B,C)
| ~ eqangle(D,B,D,C,E,B,E,A)
| ~ coll(A,B,C) ),
inference(resolve,[status(thm)],[c_100,c_97]) ).
cnf(c_192,negated_conjecture,
~ perp(sK6,sK7,sK5,sK8),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416048_neg]) ).
cnf(c_225,plain,
( cong(A,B,C,D)
| ~ cong(E,F,V6,V7)
| ~ eqratio(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD75]) ).
cnf(c_233,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_234,plain,
( eqratio(E,A,A,C,E,B,B,D)
| ~ coll(E,B,D)
| ~ coll(E,A,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD65]) ).
cnf(c_235,plain,
( midp(A,D,E)
| ~ para(B,E,C,D)
| ~ para(B,D,C,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD64]) ).
cnf(c_243,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_246,plain,
( cong(A,D,B,D)
| ~ midp(D,A,C)
| ~ perp(A,B,B,C) ),
inference(clausify,[status(thm)],[ruleD52]) ).
cnf(c_249,plain,
( midp(D,B,E)
| ~ coll(D,B,E)
| ~ para(A,D,C,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD45]) ).
cnf(c_251,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_252,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_255,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_256,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_271,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_272,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_276,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_278,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_279,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_280,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_281,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_285,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_286,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_289,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_290,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_291,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_292,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_293,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_309,plain,
( ~ cong(D,C,D,B)
| midp(A,B,B)
| ~ eqangle(C,B,C,B,D,B,D,A)
| ~ coll(A,B,B) ),
inference(factor,[status(thm)],[c_188]) ).
cnf(c_342,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_278]) ).
cnf(c_347,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_291]) ).
cnf(c_423,plain,
( para(A,B,sK3,sK2)
| ~ perp(A,B,sK0(sK3,sK4,sK5,sK2),sK3) ),
inference(resolve,[status(thm)],[c_285,c_145]) ).
cnf(c_425,plain,
( para(A,B,sK3,sK6)
| ~ perp(A,B,sK0(sK3,sK4,sK7,sK6),sK3) ),
inference(resolve,[status(thm)],[c_285,c_117]) ).
cnf(c_426,plain,
perp(sK3,sK2,sK0(sK3,sK4,sK5,sK2),sK3),
inference(resolve,[status(thm)],[c_286,c_145]) ).
cnf(c_428,plain,
perp(sK3,sK6,sK0(sK3,sK4,sK7,sK6),sK3),
inference(resolve,[status(thm)],[c_286,c_117]) ).
cnf(c_758,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_426,c_423]) ).
cnf(c_791,plain,
para(sK3,sK6,sK3,sK6),
inference(resolve,[status(thm)],[c_428,c_425]) ).
cnf(c_894,plain,
para(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_758,c_290]) ).
cnf(c_895,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_758,c_255]) ).
cnf(c_897,plain,
( eqratio(A,sK3,sK3,sK3,A,sK2,sK2,sK2)
| ~ coll(A,sK2,sK2)
| ~ coll(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_758,c_234]) ).
cnf(c_898,plain,
coll(sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_758,c_233]) ).
cnf(c_905,plain,
coll(sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_898,c_347]) ).
cnf(c_906,plain,
coll(sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_898,c_292]) ).
cnf(c_915,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_905,c_347]) ).
cnf(c_922,plain,
coll(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_906,c_347]) ).
cnf(c_927,plain,
coll(sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_915,c_293]) ).
cnf(c_947,plain,
coll(sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_927,c_292]) ).
cnf(c_1222,plain,
para(sK3,sK6,sK6,sK3),
inference(resolve,[status(thm)],[c_791,c_290]) ).
cnf(c_1223,plain,
eqangle(sK3,sK6,A,B,sK3,sK6,A,B),
inference(resolve,[status(thm)],[c_791,c_255]) ).
cnf(c_1495,plain,
para(sK2,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_894,c_289]) ).
cnf(c_1632,plain,
para(sK6,sK3,sK3,sK6),
inference(resolve,[status(thm)],[c_1222,c_289]) ).
cnf(c_1673,plain,
para(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_1495,c_290]) ).
cnf(c_1717,plain,
para(sK6,sK3,sK6,sK3),
inference(resolve,[status(thm)],[c_1632,c_290]) ).
cnf(c_1760,plain,
eqangle(sK2,sK3,A,B,sK2,sK3,A,B),
inference(resolve,[status(thm)],[c_1673,c_255]) ).
cnf(c_1790,plain,
eqangle(sK6,sK3,A,B,sK6,sK3,A,B),
inference(resolve,[status(thm)],[c_1717,c_255]) ).
cnf(c_8132,plain,
( ~ cong(sK3,sK3,sK3,sK2)
| midp(sK2,sK2,sK2)
| ~ coll(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_895,c_309]) ).
cnf(c_2575,plain,
( ~ cong(sK3,sK3,sK3,sK2)
| midp(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_922,c_8132]) ).
cnf(c_2576,plain,
eqangle(A,B,sK3,sK2,A,B,sK3,sK2),
inference(resolve,[status(thm)],[c_895,c_276]) ).
cnf(c_8133,plain,
( eqratio(sK2,sK3,sK3,sK3,sK2,sK2,sK2,sK2)
| ~ coll(sK2,sK3,sK3) ),
inference(resolve,[status(thm)],[c_897,c_922]) ).
cnf(c_2592,plain,
eqratio(sK2,sK3,sK3,sK3,sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_947,c_8133]) ).
cnf(c_3748,plain,
( cyclic(sK6,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1223,c_252]) ).
cnf(c_3749,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK3,sK3)
| ~ cyclic(sK6,A,sK3,A)
| ~ cyclic(sK6,A,sK3,sK6) ),
inference(resolve,[status(thm)],[c_1223,c_251]) ).
cnf(c_4230,plain,
( cyclic(sK3,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1760,c_252]) ).
cnf(c_4244,plain,
( cyclic(sK3,A,sK6,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_1790,c_252]) ).
cnf(c_4314,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_2576,c_256]) ).
cnf(c_8134,plain,
( cyclic(A,sK2,sK3,sK3)
| ~ coll(sK3,sK3,sK2) ),
inference(resolve,[status(thm)],[c_2576,c_252]) ).
cnf(c_4316,plain,
cyclic(A,sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_915,c_8134]) ).
cnf(c_8135,plain,
( cong(A,sK2,A,sK2)
| ~ cyclic(A,sK2,sK3,sK3)
| ~ cyclic(A,sK2,sK3,sK2)
| ~ cyclic(A,sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_2576,c_251]) ).
cnf(c_4317,plain,
( cong(A,sK2,A,sK2)
| ~ cyclic(A,sK2,sK3,sK2)
| ~ cyclic(A,sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_4316,c_8135]) ).
cnf(c_4339,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_4314,c_233]) ).
cnf(c_4418,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_4339,c_347]) ).
cnf(c_4426,plain,
cyclic(sK3,A,sK6,sK6),
inference(resolve,[status(thm)],[c_4418,c_4244]) ).
cnf(c_4427,plain,
cyclic(sK3,A,sK2,sK2),
inference(resolve,[status(thm)],[c_4418,c_4230]) ).
cnf(c_4428,plain,
cyclic(sK6,A,sK3,sK3),
inference(resolve,[status(thm)],[c_4418,c_3748]) ).
cnf(c_4541,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK3,A)
| ~ cyclic(sK6,A,sK3,sK6) ),
inference(resolve,[status(thm)],[c_4428,c_3749]) ).
cnf(c_8136,plain,
( coll(B,C,A)
| ~ coll(A,A,B) ),
inference(resolve,[status(thm)],[c_4418,c_291]) ).
cnf(c_4597,plain,
coll(A,B,C),
inference(resolve,[status(thm)],[c_4418,c_8136]) ).
cnf(c_4611,plain,
( midp(D,B,E)
| ~ para(A,D,C,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_4597,c_249]) ).
cnf(c_4618,plain,
( perp(A,B,B,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(resolve,[status(thm)],[c_4597,c_172]) ).
cnf(c_4717,plain,
cyclic(A,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_4316,c_280]) ).
cnf(c_4737,plain,
cyclic(sK3,sK6,A,sK6),
inference(resolve,[status(thm)],[c_4426,c_280]) ).
cnf(c_4763,plain,
cyclic(sK3,sK2,A,sK2),
inference(resolve,[status(thm)],[c_4427,c_280]) ).
cnf(c_4764,plain,
cyclic(A,sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_4427,c_279]) ).
cnf(c_4862,plain,
cyclic(sK3,A,sK2,sK3),
inference(resolve,[status(thm)],[c_4717,c_279]) ).
cnf(c_4942,plain,
cyclic(sK3,sK6,sK6,A),
inference(resolve,[status(thm)],[c_4737,c_281]) ).
cnf(c_4943,plain,
cyclic(sK6,sK3,A,sK6),
inference(resolve,[status(thm)],[c_4737,c_279]) ).
cnf(c_4998,plain,
cyclic(sK3,sK2,sK2,A),
inference(resolve,[status(thm)],[c_4763,c_281]) ).
cnf(c_4999,plain,
cyclic(sK2,sK3,A,sK2),
inference(resolve,[status(thm)],[c_4763,c_279]) ).
cnf(c_5015,plain,
cyclic(A,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_4764,c_280]) ).
cnf(c_5028,plain,
( cong(A,sK2,A,sK2)
| ~ cyclic(A,sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_5015,c_4317]) ).
cnf(c_5213,plain,
( cyclic(A,sK2,sK3,B)
| ~ cyclic(sK3,A,sK2,B) ),
inference(resolve,[status(thm)],[c_4862,c_278]) ).
cnf(c_5313,plain,
cyclic(sK6,sK6,A,A),
inference(resolve,[status(thm)],[c_4942,c_342]) ).
cnf(c_8137,plain,
( cyclic(sK6,sK6,A,B)
| ~ cyclic(sK3,sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_4942,c_278]) ).
cnf(c_5315,plain,
cyclic(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_4942,c_8137]) ).
cnf(c_5329,plain,
cyclic(sK6,A,sK3,sK6),
inference(resolve,[status(thm)],[c_4943,c_280]) ).
cnf(c_5345,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK3,A) ),
inference(resolve,[status(thm)],[c_5329,c_4541]) ).
cnf(c_8138,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK3,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_4998,c_278]) ).
cnf(c_5520,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_4998,c_8138]) ).
cnf(c_5536,plain,
( cyclic(sK3,A,sK2,B)
| ~ cyclic(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_4999,c_278]) ).
cnf(c_8139,plain,
( cyclic(sK6,A,B,A)
| ~ cyclic(sK6,sK6,A,B) ),
inference(resolve,[status(thm)],[c_5313,c_278]) ).
cnf(c_5772,plain,
cyclic(sK6,A,B,A),
inference(resolve,[status(thm)],[c_5315,c_8139]) ).
cnf(c_5785,plain,
cong(sK6,A,sK6,A),
inference(resolve,[status(thm)],[c_5772,c_5345]) ).
cnf(c_8140,plain,
( cyclic(sK6,A,B,C)
| ~ cyclic(sK6,sK6,A,B) ),
inference(resolve,[status(thm)],[c_5315,c_278]) ).
cnf(c_5827,plain,
cyclic(sK6,A,B,C),
inference(resolve,[status(thm)],[c_5315,c_8140]) ).
cnf(c_8141,plain,
( cyclic(sK2,A,B,C)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_5520,c_278]) ).
cnf(c_6025,plain,
cyclic(sK2,A,B,C),
inference(resolve,[status(thm)],[c_5520,c_8141]) ).
cnf(c_6037,plain,
cyclic(sK3,A,sK2,B),
inference(resolve,[status(thm)],[c_6025,c_5536]) ).
cnf(c_6068,plain,
cyclic(A,sK2,sK3,B),
inference(resolve,[status(thm)],[c_6037,c_5213]) ).
cnf(c_6071,plain,
cong(A,sK2,A,sK2),
inference(resolve,[status(thm)],[c_6068,c_5028]) ).
cnf(c_8142,plain,
( perp(sK6,sK6,A,B)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_5785,c_243]) ).
cnf(c_6427,plain,
perp(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_5785,c_8142]) ).
cnf(c_8143,plain,
( cyclic(A,B,C,D)
| ~ cyclic(sK6,A,B,C) ),
inference(resolve,[status(thm)],[c_5827,c_278]) ).
cnf(c_6675,plain,
cyclic(A,B,C,D),
inference(resolve,[status(thm)],[c_5827,c_8143]) ).
cnf(c_6689,plain,
( perp(A,B,B,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D) ),
inference(resolve,[status(thm)],[c_6675,c_4618]) ).
cnf(c_7216,plain,
perp(A,B,sK6,sK6),
inference(resolve,[status(thm)],[c_6427,c_286]) ).
cnf(c_8144,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK6,sK6) ),
inference(resolve,[status(thm)],[c_6427,c_285]) ).
cnf(c_7217,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_7216,c_8144]) ).
cnf(c_7225,plain,
( perp(B,C,C,D)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7217,c_6689]) ).
cnf(c_7238,plain,
( midp(D,B,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7217,c_4611]) ).
cnf(c_8145,plain,
( midp(A,E,D)
| ~ para(B,D,C,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7217,c_235]) ).
cnf(c_7242,plain,
( midp(A,D,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7217,c_8145]) ).
cnf(c_8146,plain,
( cong(sK2,sK3,sK3,sK3)
| ~ cong(sK2,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_2592,c_225]) ).
cnf(c_7635,plain,
cong(sK2,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_6071,c_8146]) ).
cnf(c_7636,plain,
cong(sK3,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_7635,c_271]) ).
cnf(c_7639,plain,
cong(sK3,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_7636,c_272]) ).
cnf(c_7645,plain,
midp(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_7639,c_2575]) ).
cnf(c_7646,plain,
midp(sK2,A,B),
inference(resolve,[status(thm)],[c_7645,c_7242]) ).
cnf(c_7831,plain,
midp(A,B,C),
inference(resolve,[status(thm)],[c_7646,c_7238]) ).
cnf(c_7889,plain,
perp(A,B,B,C),
inference(resolve,[status(thm)],[c_7831,c_7225]) ).
cnf(c_8147,plain,
( cong(B,A,D,A)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7889,c_246]) ).
cnf(c_8001,plain,
cong(A,B,C,B),
inference(resolve,[status(thm)],[c_7831,c_8147]) ).
cnf(c_8148,plain,
( perp(A,C,D,B)
| ~ cong(A,B,C,B) ),
inference(resolve,[status(thm)],[c_8001,c_243]) ).
cnf(c_8130,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_8001,c_8148]) ).
cnf(c_8131,plain,
$false,
inference(resolve,[status(thm)],[c_8130,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO586+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n014.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 13:43:02 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 354702 was started by sandbox on n014,
% 0.17/0.45 % Fri Sep 25 13:43:02 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 13.03/2.27
% 13.03/2.27 % given #500 (T,wt=9): 990 coll(c4,c3,c3). [resolve(958,a,510,a)].
% 13.03/2.27
% 13.03/2.27 % given #1000 (A,wt=31): 827 coll(f10(c4,f12(c1,c2,c3,c4),c1,c1),c1,f12(c1,c2,c3,c4)). [resolve(429,a,205,b),unit_del(a,821)].
% 13.03/2.27
% 13.03/2.27 % given #1500 (T,wt=13): 2104 -coll(c7,c1,A) | coll(A,c4,c7). [resolve(2096,a,291,b)].
% 13.03/2.27
% 13.03/2.27 % given #2000 (A,wt=19): 1738 perp(c1,f10(c1,c6,c2,c2),c2,c6). [resolve(1645,a,204,a),unit_del(a,1729)].
% 13.03/2.27
% 13.03/2.27 % SZS status Theorem for theBenchmark
% 13.03/2.27
% 13.03/2.27 % Proof 1 at 1.24 (+ 0.52) seconds.
% 13.03/2.27 % Length of proof is 157.
% 13.03/2.27 % Level of proof is 27.
% 13.03/2.27 % Maximum clause weight is 38.000.
% 13.03/2.27 % Given clauses 2203.
% 13.03/2.27
% 13.03/2.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------