%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO611+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 : n006.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 07:18:13 AM UTC 2026
% Result : Theorem 18.38s 7.97s
% Output : CNFRefutation 18.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 29
% Syntax : Number of formulae : 198 ( 92 unt; 0 def)
% Number of atoms : 390 ( 0 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 308 ( 116 ~; 112 |; 50 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 445 ( 53 sgn 161 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
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(ruleD10,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(A,B,E,F) ),
file('theBenchmark.p',ruleD10) ).
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(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(ruleD44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('theBenchmark.p',ruleD44) ).
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(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(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(exemplo6GDDFULL618073,conjecture,
! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2] :
( ( coll(H,E,G)
& circle(D,E,H,NWPNT2)
& coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) )
=> para(G,F,H,C) ),
file('theBenchmark.p',exemplo6GDDFULL618073) ).
fof(exemplo6GDDFULL618073_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2] :
( ( coll(H,E,G)
& circle(D,E,H,NWPNT2)
& coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) )
=> para(G,F,H,C) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618073]) ).
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]) ).
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_95,plain,
? [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2] :
( ~ para(G,F,H,C)
& coll(H,E,G)
& circle(D,E,H,NWPNT2)
& coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618073_neg]) ).
fof(sk_exemplo6GDDFULL618073_neg,plain,
( ~ para(sK8,sK9,sK6,sK4)
& coll(sK6,sK5,sK8)
& circle(sK1,sK5,sK6,sK7)
& coll(sK8,sK2,sK3)
& perp(sK8,sK5,sK2,sK3)
& coll(sK9,sK2,sK4)
& perp(sK9,sK5,sK2,sK4)
& circle(sK1,sK2,sK5,sK10)
& circle(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK10,sK9,sK8,sK6,sK7]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4),skolemize(D,sK1),skolemize(E,sK5),skolemize(F,sK9),skolemize(G,sK8),skolemize(H,sK6),skolemize(NWPNT1,sK10),skolemize(NWPNT2,sK7)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618073_neg]) ).
cnf(c_111,negated_conjecture,
circle(sK1,sK5,sK6,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618073_neg]) ).
cnf(c_117,negated_conjecture,
perp(sK0(sK5,sK6,sK7,sK1),sK5,sK5,sK1),
inference(resolve,[status(thm)],[c_111,c_102]) ).
cnf(c_145,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
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,
~ para(sK8,sK9,sK6,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618073_neg]) ).
cnf(c_193,negated_conjecture,
coll(sK6,sK5,sK8),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618073_neg]) ).
cnf(c_195,negated_conjecture,
perp(sK8,sK5,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618073_neg]) ).
cnf(c_197,negated_conjecture,
perp(sK9,sK5,sK2,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618073_neg]) ).
cnf(c_228,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_236,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_237,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_238,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_245,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_246,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_253,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_254,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_255,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_258,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_259,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_275,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_279,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_281,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_282,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_283,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_284,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_287,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_288,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_289,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_290,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_292,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_293,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_294,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_296,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_312,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_336,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_238]) ).
cnf(c_341,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_253]) ).
cnf(c_343,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,D,D,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_254]) ).
cnf(c_345,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_281]) ).
cnf(c_350,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_294]) ).
cnf(c_445,plain,
( para(sK9,sK5,A,B)
| ~ perp(sK2,sK4,A,B) ),
inference(resolve,[status(thm)],[c_288,c_197]) ).
cnf(c_446,plain,
( para(sK8,sK5,A,B)
| ~ perp(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_288,c_195]) ).
cnf(c_452,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_288,c_145]) ).
cnf(c_454,plain,
( para(A,B,sK5,sK1)
| ~ perp(A,B,sK0(sK5,sK6,sK7,sK1),sK5) ),
inference(resolve,[status(thm)],[c_288,c_117]) ).
cnf(c_455,plain,
perp(sK2,sK4,sK9,sK5),
inference(resolve,[status(thm)],[c_289,c_197]) ).
cnf(c_456,plain,
perp(sK2,sK3,sK8,sK5),
inference(resolve,[status(thm)],[c_289,c_195]) ).
cnf(c_457,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_289,c_145]) ).
cnf(c_459,plain,
perp(sK5,sK1,sK0(sK5,sK6,sK7,sK1),sK5),
inference(resolve,[status(thm)],[c_289,c_117]) ).
cnf(c_476,plain,
coll(sK6,sK8,sK5),
inference(resolve,[status(thm)],[c_296,c_193]) ).
cnf(c_500,plain,
coll(sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_476,c_350]) ).
cnf(c_550,plain,
coll(sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_500,c_296]) ).
cnf(c_616,plain,
coll(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_550,c_350]) ).
cnf(c_692,plain,
perp(sK2,sK4,sK5,sK9),
inference(resolve,[status(thm)],[c_455,c_290]) ).
cnf(c_706,plain,
perp(sK2,sK3,sK5,sK8),
inference(resolve,[status(thm)],[c_456,c_290]) ).
cnf(c_1060,plain,
para(sK9,sK5,sK5,sK9),
inference(resolve,[status(thm)],[c_445,c_692]) ).
cnf(c_1061,plain,
para(sK9,sK5,sK9,sK5),
inference(resolve,[status(thm)],[c_445,c_455]) ).
cnf(c_1062,plain,
para(sK8,sK5,sK5,sK8),
inference(resolve,[status(thm)],[c_446,c_706]) ).
cnf(c_1112,plain,
para(sK5,sK9,sK9,sK5),
inference(resolve,[status(thm)],[c_1060,c_292]) ).
cnf(c_1117,plain,
( eqratio(A,sK9,sK9,sK5,A,sK5,sK5,sK9)
| ~ coll(A,sK5,sK9)
| ~ coll(A,sK9,sK5) ),
inference(resolve,[status(thm)],[c_1060,c_237]) ).
cnf(c_1124,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_457,c_452]) ).
cnf(c_1144,plain,
eqangle(sK9,sK5,A,B,sK9,sK5,A,B),
inference(resolve,[status(thm)],[c_1061,c_258]) ).
cnf(c_1147,plain,
coll(sK9,sK5,sK5),
inference(resolve,[status(thm)],[c_1061,c_236]) ).
cnf(c_1154,plain,
coll(sK5,sK5,sK9),
inference(resolve,[status(thm)],[c_1147,c_350]) ).
cnf(c_1162,plain,
coll(sK9,sK9,sK5),
inference(resolve,[status(thm)],[c_1154,c_350]) ).
cnf(c_1167,plain,
coll(sK9,sK5,sK9),
inference(resolve,[status(thm)],[c_1162,c_296]) ).
cnf(c_1189,plain,
para(sK5,sK1,sK5,sK1),
inference(resolve,[status(thm)],[c_459,c_454]) ).
cnf(c_1225,plain,
para(sK5,sK8,sK8,sK5),
inference(resolve,[status(thm)],[c_1062,c_292]) ).
cnf(c_1339,plain,
para(sK5,sK9,sK5,sK9),
inference(resolve,[status(thm)],[c_1112,c_293]) ).
cnf(c_1354,plain,
para(sK2,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_1124,c_293]) ).
cnf(c_1355,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_1124,c_258]) ).
cnf(c_1410,plain,
( midp(A,sK1,sK1)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1189,c_336]) ).
cnf(c_1413,plain,
para(sK5,sK1,sK1,sK5),
inference(resolve,[status(thm)],[c_1189,c_293]) ).
cnf(c_1465,plain,
para(sK5,sK8,sK5,sK8),
inference(resolve,[status(thm)],[c_1225,c_293]) ).
cnf(c_1531,plain,
( midp(A,sK9,sK9)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1339,c_336]) ).
cnf(c_1534,plain,
eqangle(sK5,sK9,A,B,sK5,sK9,A,B),
inference(resolve,[status(thm)],[c_1339,c_258]) ).
cnf(c_1547,plain,
para(sK1,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_1354,c_292]) ).
cnf(c_1563,plain,
para(sK1,sK5,sK5,sK1),
inference(resolve,[status(thm)],[c_1413,c_292]) ).
cnf(c_1578,plain,
eqangle(sK5,sK8,A,B,sK5,sK8,A,B),
inference(resolve,[status(thm)],[c_1465,c_258]) ).
cnf(c_1591,plain,
para(sK1,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_1547,c_293]) ).
cnf(c_1607,plain,
para(sK1,sK5,sK1,sK5),
inference(resolve,[status(thm)],[c_1563,c_293]) ).
cnf(c_1622,plain,
eqangle(sK1,sK2,A,B,sK1,sK2,A,B),
inference(resolve,[status(thm)],[c_1591,c_258]) ).
cnf(c_1634,plain,
eqangle(sK1,sK5,A,B,sK1,sK5,A,B),
inference(resolve,[status(thm)],[c_1607,c_258]) ).
cnf(c_13012,plain,
( eqratio(sK9,sK9,sK9,sK5,sK9,sK5,sK5,sK9)
| ~ coll(sK9,sK5,sK9) ),
inference(resolve,[status(thm)],[c_1117,c_1162]) ).
cnf(c_3210,plain,
eqratio(sK9,sK9,sK9,sK5,sK9,sK5,sK5,sK9),
inference(resolve,[status(thm)],[c_1167,c_13012]) ).
cnf(c_13013,plain,
( ~ cong(sK9,sK9,sK9,sK5)
| midp(sK5,sK5,sK5)
| ~ coll(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1144,c_312]) ).
cnf(c_3321,plain,
( ~ cong(sK9,sK9,sK9,sK5)
| midp(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_616,c_13013]) ).
cnf(c_3322,plain,
eqangle(A,B,sK9,sK5,A,B,sK9,sK5),
inference(resolve,[status(thm)],[c_1144,c_279]) ).
cnf(c_3324,plain,
( cyclic(sK5,A,sK9,sK9)
| ~ coll(sK9,sK9,A) ),
inference(resolve,[status(thm)],[c_1144,c_255]) ).
cnf(c_4222,plain,
( cyclic(sK1,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1355,c_255]) ).
cnf(c_4223,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,sK2)
| ~ cyclic(sK1,A,sK2,A)
| ~ cyclic(sK1,A,sK2,sK1) ),
inference(resolve,[status(thm)],[c_1355,c_254]) ).
cnf(c_5041,plain,
( cyclic(sK9,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_1534,c_255]) ).
cnf(c_5042,plain,
( cong(sK9,A,sK9,A)
| ~ cyclic(sK9,A,sK5,sK5)
| ~ cyclic(sK9,A,sK5,A)
| ~ cyclic(sK9,A,sK5,sK9) ),
inference(resolve,[status(thm)],[c_1534,c_254]) ).
cnf(c_5069,plain,
( cyclic(sK8,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_1578,c_255]) ).
cnf(c_5105,plain,
( cyclic(sK2,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1622,c_255]) ).
cnf(c_5119,plain,
( cyclic(sK5,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1634,c_255]) ).
cnf(c_5254,plain,
( cong(sK9,sK9,sK9,sK5)
| ~ cong(sK9,sK5,sK5,sK9) ),
inference(resolve,[status(thm)],[c_3210,c_228]) ).
cnf(c_5269,plain,
( cong(sK9,sK5,sK9,sK5)
| ~ cyclic(sK9,sK5,sK9,sK5)
| ~ cyclic(sK9,sK5,sK9,sK9) ),
inference(resolve,[status(thm)],[c_3322,c_343]) ).
cnf(c_5272,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_3322,c_259]) ).
cnf(c_13014,plain,
( cyclic(A,sK5,sK9,sK9)
| ~ coll(sK9,sK9,sK5) ),
inference(resolve,[status(thm)],[c_3322,c_255]) ).
cnf(c_5274,plain,
cyclic(A,sK5,sK9,sK9),
inference(resolve,[status(thm)],[c_1162,c_13014]) ).
cnf(c_5285,plain,
( cong(sK9,sK5,sK9,sK5)
| ~ cyclic(sK9,sK5,sK9,sK5) ),
inference(resolve,[status(thm)],[c_5274,c_5269]) ).
cnf(c_5297,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_5272,c_236]) ).
cnf(c_5498,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_5297,c_350]) ).
cnf(c_5506,plain,
cyclic(sK5,A,sK1,sK1),
inference(resolve,[status(thm)],[c_5498,c_5119]) ).
cnf(c_5507,plain,
cyclic(sK2,A,sK1,sK1),
inference(resolve,[status(thm)],[c_5498,c_5105]) ).
cnf(c_5508,plain,
cyclic(sK8,A,sK5,sK5),
inference(resolve,[status(thm)],[c_5498,c_5069]) ).
cnf(c_5509,plain,
cyclic(sK9,A,sK5,sK5),
inference(resolve,[status(thm)],[c_5498,c_5041]) ).
cnf(c_5513,plain,
cyclic(sK1,A,sK2,sK2),
inference(resolve,[status(thm)],[c_5498,c_4222]) ).
cnf(c_5521,plain,
cyclic(sK5,A,sK9,sK9),
inference(resolve,[status(thm)],[c_5498,c_3324]) ).
cnf(c_5676,plain,
( cong(sK9,A,sK9,A)
| ~ cyclic(sK9,A,sK5,A)
| ~ cyclic(sK9,A,sK5,sK9) ),
inference(resolve,[status(thm)],[c_5509,c_5042]) ).
cnf(c_5688,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,A)
| ~ cyclic(sK1,A,sK2,sK1) ),
inference(resolve,[status(thm)],[c_5513,c_4223]) ).
cnf(c_6130,plain,
cyclic(A,sK9,sK5,sK9),
inference(resolve,[status(thm)],[c_5274,c_283]) ).
cnf(c_6159,plain,
cyclic(sK5,sK1,A,sK1),
inference(resolve,[status(thm)],[c_5506,c_283]) ).
cnf(c_6175,plain,
cyclic(sK2,sK1,A,sK1),
inference(resolve,[status(thm)],[c_5507,c_283]) ).
cnf(c_6192,plain,
cyclic(sK8,sK5,A,sK5),
inference(resolve,[status(thm)],[c_5508,c_283]) ).
cnf(c_6208,plain,
cyclic(sK9,sK5,A,sK5),
inference(resolve,[status(thm)],[c_5509,c_283]) ).
cnf(c_6223,plain,
cong(sK9,sK5,sK9,sK5),
inference(resolve,[status(thm)],[c_6208,c_5285]) ).
cnf(c_6367,plain,
cyclic(A,sK9,sK9,sK9),
inference(resolve,[status(thm)],[c_5521,c_345]) ).
cnf(c_6416,plain,
cyclic(sK9,A,sK5,sK9),
inference(resolve,[status(thm)],[c_6130,c_282]) ).
cnf(c_6432,plain,
( cong(sK9,A,sK9,A)
| ~ cyclic(sK9,A,sK5,A) ),
inference(resolve,[status(thm)],[c_6416,c_5676]) ).
cnf(c_6514,plain,
cyclic(sK5,sK1,sK1,A),
inference(resolve,[status(thm)],[c_6159,c_284]) ).
cnf(c_6547,plain,
cyclic(sK1,sK2,A,sK1),
inference(resolve,[status(thm)],[c_6175,c_282]) ).
cnf(c_6592,plain,
cyclic(sK8,sK5,sK5,A),
inference(resolve,[status(thm)],[c_6192,c_284]) ).
cnf(c_6634,plain,
cyclic(sK5,sK9,A,sK5),
inference(resolve,[status(thm)],[c_6208,c_282]) ).
cnf(c_6696,plain,
cong(sK9,sK5,sK5,sK9),
inference(resolve,[status(thm)],[c_6223,c_275]) ).
cnf(c_6712,plain,
cong(sK9,sK9,sK9,sK5),
inference(resolve,[status(thm)],[c_6696,c_5254]) ).
cnf(c_6715,plain,
midp(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_6712,c_3321]) ).
cnf(c_6717,plain,
midp(sK5,sK9,sK9),
inference(resolve,[status(thm)],[c_6715,c_1531]) ).
cnf(c_6718,plain,
midp(sK5,sK1,sK1),
inference(resolve,[status(thm)],[c_6715,c_1410]) ).
cnf(c_6766,plain,
para(sK5,sK5,sK9,sK9),
inference(resolve,[status(thm)],[c_6717,c_341]) ).
cnf(c_6782,plain,
para(sK5,sK5,sK1,sK1),
inference(resolve,[status(thm)],[c_6718,c_341]) ).
cnf(c_7156,plain,
cyclic(sK9,A,sK9,sK9),
inference(resolve,[status(thm)],[c_6367,c_282]) ).
cnf(c_7358,plain,
cyclic(sK1,sK1,A,A),
inference(resolve,[status(thm)],[c_6514,c_345]) ).
cnf(c_13015,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK5,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_6514,c_281]) ).
cnf(c_7360,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_6514,c_13015]) ).
cnf(c_7593,plain,
cyclic(sK1,A,sK2,sK1),
inference(resolve,[status(thm)],[c_6547,c_283]) ).
cnf(c_7609,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,A) ),
inference(resolve,[status(thm)],[c_7593,c_5688]) ).
cnf(c_13016,plain,
( cyclic(sK5,sK5,A,B)
| ~ cyclic(sK8,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_6592,c_281]) ).
cnf(c_7755,plain,
cyclic(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_6592,c_13016]) ).
cnf(c_7970,plain,
( cyclic(sK9,A,sK5,B)
| ~ cyclic(sK5,sK9,A,B) ),
inference(resolve,[status(thm)],[c_6634,c_281]) ).
cnf(c_8066,plain,
para(sK9,sK9,sK5,sK5),
inference(resolve,[status(thm)],[c_6766,c_292]) ).
cnf(c_8096,plain,
( perp(sK5,sK5,A,B)
| ~ perp(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_6782,c_287]) ).
cnf(c_9073,plain,
cyclic(sK9,sK9,A,sK9),
inference(resolve,[status(thm)],[c_7156,c_283]) ).
cnf(c_13017,plain,
( cyclic(sK1,A,B,A)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_7358,c_281]) ).
cnf(c_9211,plain,
cyclic(sK1,A,B,A),
inference(resolve,[status(thm)],[c_7360,c_13017]) ).
cnf(c_9224,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_9211,c_7609]) ).
cnf(c_13018,plain,
( cyclic(sK5,A,B,C)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_7755,c_281]) ).
cnf(c_9606,plain,
cyclic(sK5,A,B,C),
inference(resolve,[status(thm)],[c_7755,c_13018]) ).
cnf(c_9618,plain,
cyclic(sK9,A,sK5,B),
inference(resolve,[status(thm)],[c_9606,c_7970]) ).
cnf(c_9703,plain,
cong(sK9,A,sK9,A),
inference(resolve,[status(thm)],[c_9618,c_6432]) ).
cnf(c_9996,plain,
( perp(sK9,sK9,A,B)
| ~ perp(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_8066,c_287]) ).
cnf(c_13019,plain,
( perp(A,sK9,sK9,sK9)
| ~ cong(sK9,sK9,sK9,sK9)
| ~ cong(sK9,A,sK9,A) ),
inference(resolve,[status(thm)],[c_9073,c_245]) ).
cnf(c_13020,plain,
( perp(A,sK9,sK9,sK9)
| ~ cong(sK9,sK9,sK9,sK9) ),
inference(resolve,[status(thm)],[c_9703,c_13019]) ).
cnf(c_10887,plain,
perp(A,sK9,sK9,sK9),
inference(resolve,[status(thm)],[c_9703,c_13020]) ).
cnf(c_13021,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_9224,c_246]) ).
cnf(c_11161,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_9224,c_13021]) ).
cnf(c_11177,plain,
perp(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_11161,c_8096]) ).
cnf(c_11206,plain,
perp(sK9,sK9,A,B),
inference(resolve,[status(thm)],[c_11177,c_9996]) ).
cnf(c_13022,plain,
( para(C,sK9,A,B)
| ~ perp(sK9,sK9,A,B) ),
inference(resolve,[status(thm)],[c_10887,c_288]) ).
cnf(c_13010,plain,
para(A,sK9,B,C),
inference(resolve,[status(thm)],[c_11206,c_13022]) ).
cnf(c_13011,plain,
$false,
inference(resolve,[status(thm)],[c_13010,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO611+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.57 % Computer : n006.cluster.edu
% 0.11/5.57 % Model : x86_64 x86_64
% 0.11/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.57 % Memory : 8046.5625MB
% 0.11/5.57 % OS : Linux 6.8.0-71-generic
% 0.11/5.57 % CPULimit : 300
% 0.11/5.57 % WCLimit : 300
% 0.11/5.57 % DateTime : Fri Sep 25 13:44:38 UTC 2026
% 0.11/5.57 % CPUTime :
% 0.11/5.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.57 % Process 3037267 was started by sandbox2 on n006,
% 0.11/5.57 % Fri Sep 25 13:44:38 2026
% 0.11/5.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.60
% 0.15/5.60 % From the command line: assign(max_seconds, 300).
% 18.38/7.97
% 18.38/7.97 % given #500 (A,wt=15): 451 -perp(A,B,c7,c5) | para(A,B,c1,c2). [resolve(288,b,195,a)].
% 18.38/7.97
% 18.38/7.97 % given #1000 (T,wt=9): 2883 coll(c8,c6,c2). [resolve(2867,a,295,a)].
% 18.38/7.97
% 18.38/7.97 % given #1500 (A,wt=23): 1126 para(f12(c1,c2,c3,c4),c1,f12(c1,c2,c3,c4),c1). [resolve(457,a,447,a)].
% 18.38/7.97
% 18.38/7.97 % given #2000 (W,wt=13): 2452 -coll(c4,c3,A) | coll(c4,A,c4). [resolve(2218,a,294,a)].
% 18.38/7.97
% 18.38/7.97 % given #2500 (T,wt=9): 5532 coll(c2,A,c3). [back_unit_del(2397),unit_del(a,5498)].
% 18.38/7.97
% 18.38/7.97 % given #3000 (W,wt=10): 8986 cyclic(c7,c7,A,B). [resolve(7124,a,281,b),unit_del(a,7124)].
% 18.38/7.97
% 18.38/7.97 % SZS status Theorem for theBenchmark
% 18.38/7.97
% 18.38/7.97 % Proof 1 at 1.71 (+ 0.60) seconds.
% 18.38/7.97 % Length of proof is 182.
% 18.38/7.97 % Level of proof is 21.
% 18.38/7.97 % Maximum clause weight is 34.000.
% 18.38/7.97 % Given clauses 3306.
% 18.38/7.97
% 18.38/7.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------