%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO602+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 : n003.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 07:18:12 AM UTC 2026
% Result : Theorem 12.32s 2.19s
% Output : CNFRefutation 12.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 27
% Syntax : Number of formulae : 158 ( 66 unt; 0 def)
% Number of atoms : 331 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 265 ( 92 ~; 88 |; 57 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 18 ( 18 usr; 17 con; 0-4 aty)
% Number of variables : 463 ( 64 sgn 166 !; 19 ?)
% 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(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(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(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(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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('theBenchmark.p',ruleD67) ).
fof(ruleD74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('theBenchmark.p',ruleD74) ).
fof(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(exemplo6GDDFULL618064,conjecture,
! [A,B,E,F,D,M,E1,F1,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( circle(A,E,F1,NWPNT9)
& coll(F1,F,M)
& coll(E1,E,M)
& circle(A,E,E1,NWPNT8)
& circle(B,E,M,NWPNT7)
& coll(D,E,F)
& coll(D,A,B)
& circle(A,E,F,NWPNT6)
& circle(B,E,F,NWPNT5)
& circle(A,E,NWPNT3,NWPNT4)
& circle(B,E,NWPNT1,NWPNT2) )
=> perp(E1,F1,M,B) ),
file('theBenchmark.p',exemplo6GDDFULL618064) ).
fof(exemplo6GDDFULL618064_neg,negated_conjecture,
~ ! [A,B,E,F,D,M,E1,F1,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( circle(A,E,F1,NWPNT9)
& coll(F1,F,M)
& coll(E1,E,M)
& circle(A,E,E1,NWPNT8)
& circle(B,E,M,NWPNT7)
& coll(D,E,F)
& coll(D,A,B)
& circle(A,E,F,NWPNT6)
& circle(B,E,F,NWPNT5)
& circle(A,E,NWPNT3,NWPNT4)
& circle(B,E,NWPNT1,NWPNT2) )
=> perp(E1,F1,M,B) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618064]) ).
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,E,F,D,M,E1,F1,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ~ perp(E1,F1,M,B)
& circle(A,E,F1,NWPNT9)
& coll(F1,F,M)
& coll(E1,E,M)
& circle(A,E,E1,NWPNT8)
& circle(B,E,M,NWPNT7)
& coll(D,E,F)
& coll(D,A,B)
& circle(A,E,F,NWPNT6)
& circle(B,E,F,NWPNT5)
& circle(A,E,NWPNT3,NWPNT4)
& circle(B,E,NWPNT1,NWPNT2) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618064_neg]) ).
fof(sk_exemplo6GDDFULL618064_neg,plain,
( ~ perp(sK8,sK9,sK10,sK1)
& circle(sK5,sK2,sK9,sK17)
& coll(sK9,sK11,sK10)
& coll(sK8,sK2,sK10)
& circle(sK5,sK2,sK8,sK16)
& circle(sK1,sK2,sK10,sK15)
& coll(sK14,sK2,sK11)
& coll(sK14,sK5,sK1)
& circle(sK5,sK2,sK11,sK13)
& circle(sK1,sK2,sK11,sK12)
& circle(sK5,sK2,sK6,sK7)
& circle(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK11,sK12,sK13,sK14,sK10,sK15,sK8,sK16,sK9,sK17]),skolemize(A,sK5),skolemize(B,sK1),skolemize(E,sK2),skolemize(F,sK11),skolemize(D,sK14),skolemize(M,sK10),skolemize(E1,sK8),skolemize(F1,sK9),skolemize(NWPNT1,sK3),skolemize(NWPNT2,sK4),skolemize(NWPNT3,sK6),skolemize(NWPNT4,sK7),skolemize(NWPNT5,sK12),skolemize(NWPNT6,sK13),skolemize(NWPNT7,sK15),skolemize(NWPNT8,sK16),skolemize(NWPNT9,sK17)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618064_neg]) ).
cnf(c_110,negated_conjecture,
circle(sK5,sK2,sK6,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618064_neg]) ).
cnf(c_191,negated_conjecture,
perp(sK0(sK2,sK6,sK7,sK5),sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_110,c_102]) ).
cnf(c_205,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_252,negated_conjecture,
~ perp(sK8,sK9,sK10,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618064_neg]) ).
cnf(c_288,plain,
( perp(A,B,C,D)
| ~ perp(E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD74]) ).
cnf(c_294,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_295,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_297,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_304,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_305,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_308,plain,
( cong(A,D,B,D)
| ~ midp(D,A,C)
| ~ perp(A,B,B,C) ),
inference(clausify,[status(thm)],[ruleD52]) ).
cnf(c_313,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_314,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_317,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_318,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_333,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_334,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_336,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_338,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_340,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_341,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_342,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_343,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_347,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_348,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_349,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_351,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_352,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_353,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_398,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_304]) ).
cnf(c_404,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_340]) ).
cnf(c_409,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_353]) ).
cnf(c_573,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_347,c_205]) ).
cnf(c_574,plain,
( para(A,B,sK2,sK5)
| ~ perp(A,B,sK0(sK2,sK6,sK7,sK5),sK2) ),
inference(resolve,[status(thm)],[c_347,c_191]) ).
cnf(c_580,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_348,c_205]) ).
cnf(c_581,plain,
perp(sK2,sK5,sK0(sK2,sK6,sK7,sK5),sK2),
inference(resolve,[status(thm)],[c_348,c_191]) ).
cnf(c_1556,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_580,c_573]) ).
cnf(c_1620,plain,
para(sK2,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_581,c_574]) ).
cnf(c_3477,plain,
para(sK2,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_1556,c_352]) ).
cnf(c_3478,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_1556,c_317]) ).
cnf(c_3490,plain,
para(sK2,sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_1620,c_352]) ).
cnf(c_3491,plain,
eqangle(sK2,sK5,A,B,sK2,sK5,A,B),
inference(resolve,[status(thm)],[c_1620,c_317]) ).
cnf(c_3504,plain,
para(sK1,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_3477,c_351]) ).
cnf(c_3535,plain,
para(sK5,sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_3490,c_351]) ).
cnf(c_3551,plain,
para(sK1,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_3504,c_352]) ).
cnf(c_3567,plain,
para(sK5,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_3535,c_352]) ).
cnf(c_3582,plain,
eqangle(sK1,sK2,A,B,sK1,sK2,A,B),
inference(resolve,[status(thm)],[c_3551,c_317]) ).
cnf(c_3594,plain,
eqangle(sK5,sK2,A,B,sK5,sK2,A,B),
inference(resolve,[status(thm)],[c_3567,c_317]) ).
cnf(c_6394,plain,
eqangle(A,B,sK2,sK1,A,B,sK2,sK1),
inference(resolve,[status(thm)],[c_3478,c_338]) ).
cnf(c_6396,plain,
( cyclic(sK1,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_3478,c_314]) ).
cnf(c_6397,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_3478,c_313]) ).
cnf(c_6410,plain,
( cyclic(sK5,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_3491,c_314]) ).
cnf(c_6411,plain,
( cong(sK5,A,sK5,A)
| ~ cyclic(sK5,A,sK2,sK2)
| ~ cyclic(sK5,A,sK2,A)
| ~ cyclic(sK5,A,sK2,sK5) ),
inference(resolve,[status(thm)],[c_3491,c_313]) ).
cnf(c_6477,plain,
( cyclic(sK2,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3582,c_314]) ).
cnf(c_6491,plain,
( cyclic(sK2,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_3594,c_314]) ).
cnf(c_6492,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK5,sK5)
| ~ cyclic(sK2,A,sK5,A)
| ~ cyclic(sK2,A,sK5,sK2) ),
inference(resolve,[status(thm)],[c_3594,c_313]) ).
cnf(c_6502,plain,
eqangle(A,B,A,B,sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_6394,c_336]) ).
cnf(c_6503,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_6394,c_318]) ).
cnf(c_6528,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_6503,c_295]) ).
cnf(c_6641,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_6528,c_409]) ).
cnf(c_6649,plain,
cyclic(sK2,A,sK5,sK5),
inference(resolve,[status(thm)],[c_6641,c_6491]) ).
cnf(c_6650,plain,
cyclic(sK2,A,sK1,sK1),
inference(resolve,[status(thm)],[c_6641,c_6477]) ).
cnf(c_6651,plain,
cyclic(sK5,A,sK2,sK2),
inference(resolve,[status(thm)],[c_6641,c_6410]) ).
cnf(c_6652,plain,
cyclic(sK1,A,sK2,sK2),
inference(resolve,[status(thm)],[c_6641,c_6396]) ).
cnf(c_6866,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK5,A)
| ~ cyclic(sK2,A,sK5,sK2) ),
inference(resolve,[status(thm)],[c_6649,c_6492]) ).
cnf(c_6872,plain,
( cong(sK5,A,sK5,A)
| ~ cyclic(sK5,A,sK2,A)
| ~ cyclic(sK5,A,sK2,sK5) ),
inference(resolve,[status(thm)],[c_6651,c_6411]) ).
cnf(c_6875,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,A)
| ~ cyclic(sK1,A,sK2,sK1) ),
inference(resolve,[status(thm)],[c_6652,c_6397]) ).
cnf(c_11383,plain,
( coll(B,C,A)
| ~ coll(A,A,B) ),
inference(resolve,[status(thm)],[c_6641,c_353]) ).
cnf(c_6907,plain,
coll(A,B,C),
inference(resolve,[status(thm)],[c_6641,c_11383]) ).
cnf(c_6939,plain,
( midp(A,B,C)
| ~ cong(A,B,A,C) ),
inference(resolve,[status(thm)],[c_6907,c_294]) ).
cnf(c_7201,plain,
cyclic(sK2,sK5,A,sK5),
inference(resolve,[status(thm)],[c_6649,c_342]) ).
cnf(c_7218,plain,
cyclic(sK2,sK1,A,sK1),
inference(resolve,[status(thm)],[c_6650,c_342]) ).
cnf(c_7236,plain,
cyclic(sK5,sK2,A,sK2),
inference(resolve,[status(thm)],[c_6651,c_342]) ).
cnf(c_7503,plain,
cyclic(sK2,sK5,sK5,A),
inference(resolve,[status(thm)],[c_7201,c_343]) ).
cnf(c_7504,plain,
cyclic(sK5,sK2,A,sK5),
inference(resolve,[status(thm)],[c_7201,c_341]) ).
cnf(c_7550,plain,
cyclic(sK2,sK1,sK1,A),
inference(resolve,[status(thm)],[c_7218,c_343]) ).
cnf(c_7551,plain,
cyclic(sK1,sK2,A,sK1),
inference(resolve,[status(thm)],[c_7218,c_341]) ).
cnf(c_7646,plain,
cyclic(sK2,sK5,A,sK2),
inference(resolve,[status(thm)],[c_7236,c_341]) ).
cnf(c_7956,plain,
cyclic(sK5,sK5,A,A),
inference(resolve,[status(thm)],[c_7503,c_404]) ).
cnf(c_11384,plain,
( cyclic(sK5,sK5,A,B)
| ~ cyclic(sK2,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_7503,c_340]) ).
cnf(c_7958,plain,
cyclic(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_7503,c_11384]) ).
cnf(c_7981,plain,
cyclic(sK5,A,sK2,sK5),
inference(resolve,[status(thm)],[c_7504,c_342]) ).
cnf(c_7983,plain,
( cyclic(sK2,A,sK5,B)
| ~ cyclic(sK5,sK2,A,B) ),
inference(resolve,[status(thm)],[c_7504,c_340]) ).
cnf(c_7997,plain,
( cong(sK5,A,sK5,A)
| ~ cyclic(sK5,A,sK2,A) ),
inference(resolve,[status(thm)],[c_7981,c_6872]) ).
cnf(c_8207,plain,
cyclic(sK1,sK1,A,A),
inference(resolve,[status(thm)],[c_7550,c_404]) ).
cnf(c_11385,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK2,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_7550,c_340]) ).
cnf(c_8209,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_7550,c_11385]) ).
cnf(c_8223,plain,
cyclic(sK1,A,sK2,sK1),
inference(resolve,[status(thm)],[c_7551,c_342]) ).
cnf(c_8239,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,A) ),
inference(resolve,[status(thm)],[c_8223,c_6875]) ).
cnf(c_8363,plain,
cyclic(sK2,A,sK5,sK2),
inference(resolve,[status(thm)],[c_7646,c_342]) ).
cnf(c_8379,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK5,A) ),
inference(resolve,[status(thm)],[c_8363,c_6866]) ).
cnf(c_11386,plain,
( cyclic(sK5,A,B,A)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_7956,c_340]) ).
cnf(c_8619,plain,
cyclic(sK5,A,B,A),
inference(resolve,[status(thm)],[c_7958,c_11386]) ).
cnf(c_8632,plain,
cong(sK5,A,sK5,A),
inference(resolve,[status(thm)],[c_8619,c_7997]) ).
cnf(c_11387,plain,
( cyclic(sK5,A,B,C)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_7958,c_340]) ).
cnf(c_8674,plain,
cyclic(sK5,A,B,C),
inference(resolve,[status(thm)],[c_7958,c_11387]) ).
cnf(c_8686,plain,
cyclic(sK2,A,sK5,B),
inference(resolve,[status(thm)],[c_8674,c_7983]) ).
cnf(c_8714,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_8686,c_8379]) ).
cnf(c_8842,plain,
( perp(A,sK1,sK1,A)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_8207,c_398]) ).
cnf(c_11388,plain,
( cyclic(sK1,A,B,A)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_8207,c_340]) ).
cnf(c_8843,plain,
cyclic(sK1,A,B,A),
inference(resolve,[status(thm)],[c_8209,c_11388]) ).
cnf(c_8856,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_8843,c_8239]) ).
cnf(c_8857,plain,
perp(A,sK1,sK1,A),
inference(resolve,[status(thm)],[c_8856,c_8842]) ).
cnf(c_11389,plain,
( perp(sK5,sK5,A,B)
| ~ cong(sK5,A,sK5,A) ),
inference(resolve,[status(thm)],[c_8632,c_305]) ).
cnf(c_9528,plain,
perp(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_8632,c_11389]) ).
cnf(c_9899,plain,
cong(sK2,A,A,sK2),
inference(resolve,[status(thm)],[c_8714,c_334]) ).
cnf(c_10115,plain,
perp(A,sK1,A,sK1),
inference(resolve,[status(thm)],[c_8857,c_349]) ).
cnf(c_10535,plain,
perp(A,B,sK5,sK5),
inference(resolve,[status(thm)],[c_9528,c_348]) ).
cnf(c_11390,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK5,sK5) ),
inference(resolve,[status(thm)],[c_9528,c_347]) ).
cnf(c_10536,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_10535,c_11390]) ).
cnf(c_11391,plain,
( midp(A,E,D)
| ~ para(B,D,C,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_10536,c_297]) ).
cnf(c_10553,plain,
( midp(A,D,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_10536,c_11391]) ).
cnf(c_10629,plain,
cong(A,sK2,sK2,A),
inference(resolve,[status(thm)],[c_9899,c_333]) ).
cnf(c_10824,plain,
cong(A,sK2,A,sK2),
inference(resolve,[status(thm)],[c_10629,c_334]) ).
cnf(c_11392,plain,
( perp(A,B,A,B)
| ~ perp(sK2,sK1,sK2,sK1) ),
inference(resolve,[status(thm)],[c_6502,c_288]) ).
cnf(c_11065,plain,
perp(A,B,A,B),
inference(resolve,[status(thm)],[c_10115,c_11392]) ).
cnf(c_11068,plain,
perp(A,B,B,A),
inference(resolve,[status(thm)],[c_11065,c_349]) ).
cnf(c_11076,plain,
( cong(B,A,C,A)
| ~ midp(A,B,B) ),
inference(resolve,[status(thm)],[c_11068,c_308]) ).
cnf(c_11126,plain,
midp(A,sK2,sK2),
inference(resolve,[status(thm)],[c_6939,c_10824]) ).
cnf(c_11168,plain,
midp(A,B,C),
inference(resolve,[status(thm)],[c_11126,c_10553]) ).
cnf(c_11183,plain,
cong(A,B,C,B),
inference(resolve,[status(thm)],[c_11168,c_11076]) ).
cnf(c_11393,plain,
( perp(A,C,D,B)
| ~ cong(A,B,C,B) ),
inference(resolve,[status(thm)],[c_11183,c_305]) ).
cnf(c_11381,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_11183,c_11393]) ).
cnf(c_11382,plain,
$false,
inference(resolve,[status(thm)],[c_11381,c_252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO602+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 13:45:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 296696 was started by sandbox2 on n003,
% 0.10/0.36 % Fri Sep 25 13:45:39 2026
% 0.10/0.36 % 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).
% 12.32/2.19
% 12.32/2.19 % given #500 (W,wt=9): 1077 coll(c6,c5,c5). [resolve(1047,a,354,a)].
% 12.32/2.19
% 12.32/2.19 % given #1000 (T,wt=9): 2524 coll(c3,c7,c2). [resolve(2195,a,354,a)].
% 12.32/2.19
% 12.32/2.19 % given #1500 (W,wt=13): 1360 -coll(c3,c7,A) | coll(c5,A,c3). [resolve(1305,a,353,a)].
% 12.32/2.19
% 12.32/2.19 % given #2000 (T,wt=13): 2630 -coll(c5,c4,A) | coll(A,c1,c5). [resolve(2273,a,353,b)].
% 12.32/2.19
% 12.32/2.19 % given #2500 (A,wt=32): 1894 perp(f12(c3,c4,c14,c1),f10(f12(c3,c4,c14,c1),c1,c3,c3),c3,c1). [resolve(590,a,266,a),unit_del(a,1885)].
% 12.32/2.19
% 12.32/2.19 % given #3000 (T,wt=13): 10549 -midp(A,B,C) | midp(D,B,E). [back_unit_del(6937),unit_del(b,10536)].
% 12.32/2.19
% 12.32/2.19 % SZS status Theorem for theBenchmark
% 12.32/2.19
% 12.32/2.19 % Proof 1 at 1.30 (+ 0.45) seconds.
% 12.32/2.19 % Length of proof is 142.
% 12.32/2.19 % Level of proof is 24.
% 12.32/2.19 % Maximum clause weight is 34.000.
% 12.32/2.19 % Given clauses 3052.
% 12.32/2.19
% 12.32/2.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------