%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO654+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 : n020.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 07:18:19 AM UTC 2026
% Result : Theorem 13.44s 2.14s
% Output : CNFRefutation 13.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 30
% Syntax : Number of formulae : 218 ( 104 unt; 0 def)
% Number of atoms : 431 ( 0 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 340 ( 127 ~; 123 |; 59 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 18 ( 18 usr; 17 con; 0-4 aty)
% Number of variables : 489 ( 50 sgn 181 !; 19 ?)
% 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(ruleD6,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
file('theBenchmark.p',ruleD6) ).
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(exemplo6GDDFULLmoreE0228,conjecture,
! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( perp(C,E,E,H)
& circle(A,B,G,NWPNT9)
& coll(B,E,G)
& circle(A,D,F,NWPNT8)
& coll(D,E,F)
& circle(C,B,E,NWPNT7)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(H,E,G,F) ),
file('theBenchmark.p',exemplo6GDDFULLmoreE0228) ).
fof(exemplo6GDDFULLmoreE0228_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( perp(C,E,E,H)
& circle(A,B,G,NWPNT9)
& coll(B,E,G)
& circle(A,D,F,NWPNT8)
& coll(D,E,F)
& circle(C,B,E,NWPNT7)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(H,E,G,F) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULLmoreE0228]) ).
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,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ~ para(H,E,G,F)
& perp(C,E,E,H)
& circle(A,B,G,NWPNT9)
& coll(B,E,G)
& circle(A,D,F,NWPNT8)
& coll(D,E,F)
& circle(C,B,E,NWPNT7)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULLmoreE0228_neg]) ).
fof(sk_exemplo6GDDFULLmoreE0228_neg,plain,
( ~ para(sK11,sK12,sK13,sK9)
& perp(sK5,sK12,sK12,sK11)
& circle(sK1,sK2,sK13,sK17)
& coll(sK2,sK12,sK13)
& circle(sK1,sK8,sK9,sK10)
& coll(sK8,sK12,sK9)
& circle(sK5,sK2,sK12,sK16)
& circle(sK5,sK2,sK8,sK15)
& circle(sK1,sK2,sK8,sK14)
& circle(sK5,sK2,sK6,sK7)
& circle(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK14,sK15,sK12,sK16,sK9,sK10,sK13,sK17,sK11]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK5),skolemize(D,sK8),skolemize(E,sK12),skolemize(F,sK9),skolemize(G,sK13),skolemize(H,sK11),skolemize(NWPNT1,sK3),skolemize(NWPNT2,sK4),skolemize(NWPNT3,sK6),skolemize(NWPNT4,sK7),skolemize(NWPNT5,sK14),skolemize(NWPNT6,sK15),skolemize(NWPNT7,sK16),skolemize(NWPNT8,sK10),skolemize(NWPNT9,sK17)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0228_neg]) ).
cnf(c_110,negated_conjecture,
circle(sK5,sK2,sK6,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0228_neg]) ).
cnf(c_114,negated_conjecture,
circle(sK1,sK8,sK9,sK10),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0228_neg]) ).
cnf(c_135,negated_conjecture,
perp(sK0(sK8,sK9,sK10,sK1),sK8,sK8,sK1),
inference(resolve,[status(thm)],[c_114,c_102]) ).
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_248,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_252,negated_conjecture,
~ para(sK11,sK12,sK13,sK9),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0228_neg]) ).
cnf(c_253,negated_conjecture,
perp(sK5,sK12,sK12,sK11),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0228_neg]) ).
cnf(c_255,negated_conjecture,
coll(sK8,sK12,sK9),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0228_neg]) ).
cnf(c_286,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_294,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_295,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_296,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_303,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_304,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_311,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_312,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_313,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_316,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_317,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(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_337,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_339,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_340,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_341,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_342,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_345,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_346,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_347,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_348,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_349,plain,
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD6]) ).
cnf(c_350,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_351,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_352,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_354,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_370,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_248]) ).
cnf(c_394,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_296]) ).
cnf(c_399,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_311]) ).
cnf(c_400,plain,
( cong(A,B,D,D)
| ~ eqangle(C,A,C,B,E,D,E,D)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_312]) ).
cnf(c_401,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_312]) ).
cnf(c_403,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_339]) ).
cnf(c_408,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_352]) ).
cnf(c_586,plain,
( para(sK5,sK12,A,B)
| ~ perp(sK12,sK11,A,B) ),
inference(resolve,[status(thm)],[c_346,c_253]) ).
cnf(c_594,plain,
( para(A,B,sK12,sK11)
| ~ perp(A,B,sK5,sK12) ),
inference(resolve,[status(thm)],[c_346,c_253]) ).
cnf(c_595,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_346,c_205]) ).
cnf(c_596,plain,
( para(A,B,sK2,sK5)
| ~ perp(A,B,sK0(sK2,sK6,sK7,sK5),sK2) ),
inference(resolve,[status(thm)],[c_346,c_191]) ).
cnf(c_600,plain,
( para(A,B,sK8,sK1)
| ~ perp(A,B,sK0(sK8,sK9,sK10,sK1),sK8) ),
inference(resolve,[status(thm)],[c_346,c_135]) ).
cnf(c_602,plain,
perp(sK12,sK11,sK5,sK12),
inference(resolve,[status(thm)],[c_347,c_253]) ).
cnf(c_603,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_347,c_205]) ).
cnf(c_604,plain,
perp(sK2,sK5,sK0(sK2,sK6,sK7,sK5),sK2),
inference(resolve,[status(thm)],[c_347,c_191]) ).
cnf(c_608,plain,
perp(sK8,sK1,sK0(sK8,sK9,sK10,sK1),sK8),
inference(resolve,[status(thm)],[c_347,c_135]) ).
cnf(c_610,plain,
perp(sK5,sK12,sK11,sK12),
inference(resolve,[status(thm)],[c_348,c_253]) ).
cnf(c_624,plain,
coll(sK8,sK9,sK12),
inference(resolve,[status(thm)],[c_354,c_255]) ).
cnf(c_636,plain,
coll(sK12,sK12,sK8),
inference(resolve,[status(thm)],[c_624,c_408]) ).
cnf(c_668,plain,
coll(sK12,sK8,sK12),
inference(resolve,[status(thm)],[c_636,c_354]) ).
cnf(c_714,plain,
coll(sK12,sK12,sK12),
inference(resolve,[status(thm)],[c_668,c_408]) ).
cnf(c_770,plain,
perp(sK12,sK11,sK12,sK5),
inference(resolve,[status(thm)],[c_602,c_348]) ).
cnf(c_784,plain,
perp(sK11,sK12,sK5,sK12),
inference(resolve,[status(thm)],[c_610,c_347]) ).
cnf(c_1080,plain,
para(sK5,sK12,sK12,sK5),
inference(resolve,[status(thm)],[c_586,c_770]) ).
cnf(c_1081,plain,
para(sK5,sK12,sK5,sK12),
inference(resolve,[status(thm)],[c_586,c_602]) ).
cnf(c_1086,plain,
para(sK12,sK5,sK5,sK12),
inference(resolve,[status(thm)],[c_1080,c_350]) ).
cnf(c_1091,plain,
( eqratio(A,sK5,sK5,sK12,A,sK12,sK12,sK5)
| ~ coll(A,sK12,sK5)
| ~ coll(A,sK5,sK12) ),
inference(resolve,[status(thm)],[c_1080,c_295]) ).
cnf(c_1101,plain,
eqangle(sK5,sK12,A,B,sK5,sK12,A,B),
inference(resolve,[status(thm)],[c_1081,c_316]) ).
cnf(c_1104,plain,
coll(sK5,sK12,sK12),
inference(resolve,[status(thm)],[c_1081,c_294]) ).
cnf(c_1117,plain,
coll(sK12,sK12,sK5),
inference(resolve,[status(thm)],[c_1104,c_408]) ).
cnf(c_1133,plain,
coll(sK5,sK5,sK12),
inference(resolve,[status(thm)],[c_1117,c_408]) ).
cnf(c_1192,plain,
coll(sK5,sK12,sK5),
inference(resolve,[status(thm)],[c_1133,c_354]) ).
cnf(c_1606,plain,
para(sK12,sK5,sK12,sK5),
inference(resolve,[status(thm)],[c_1086,c_351]) ).
cnf(c_1618,plain,
( midp(A,sK5,sK5)
| ~ midp(A,sK12,sK12) ),
inference(resolve,[status(thm)],[c_1606,c_394]) ).
cnf(c_1621,plain,
eqangle(sK12,sK5,A,B,sK12,sK5,A,B),
inference(resolve,[status(thm)],[c_1606,c_316]) ).
cnf(c_1630,plain,
para(sK11,sK12,sK12,sK11),
inference(resolve,[status(thm)],[c_594,c_784]) ).
cnf(c_1631,plain,
para(sK12,sK11,sK12,sK11),
inference(resolve,[status(thm)],[c_594,c_602]) ).
cnf(c_1636,plain,
para(sK11,sK12,sK11,sK12),
inference(resolve,[status(thm)],[c_1630,c_351]) ).
cnf(c_1638,plain,
( para(sK11,sK12,A,B)
| ~ para(sK12,sK11,A,B) ),
inference(resolve,[status(thm)],[c_1630,c_349]) ).
cnf(c_1649,plain,
( midp(A,sK11,sK11)
| ~ midp(A,sK12,sK12) ),
inference(resolve,[status(thm)],[c_1631,c_394]) ).
cnf(c_1652,plain,
eqangle(sK12,sK11,A,B,sK12,sK11,A,B),
inference(resolve,[status(thm)],[c_1631,c_316]) ).
cnf(c_1804,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_603,c_595]) ).
cnf(c_1868,plain,
para(sK2,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_604,c_596]) ).
cnf(c_1989,plain,
para(sK8,sK1,sK8,sK1),
inference(resolve,[status(thm)],[c_608,c_600]) ).
cnf(c_2433,plain,
eqangle(sK11,sK12,A,B,sK11,sK12,A,B),
inference(resolve,[status(thm)],[c_1636,c_316]) ).
cnf(c_2457,plain,
( midp(A,sK1,sK1)
| ~ midp(A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_1804,c_394]) ).
cnf(c_2460,plain,
para(sK2,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_1804,c_351]) ).
cnf(c_2461,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_1804,c_316]) ).
cnf(c_3428,plain,
para(sK2,sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_1868,c_351]) ).
cnf(c_3441,plain,
para(sK8,sK1,sK1,sK8),
inference(resolve,[status(thm)],[c_1989,c_351]) ).
cnf(c_3455,plain,
para(sK1,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_2460,c_350]) ).
cnf(c_3471,plain,
para(sK5,sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_3428,c_350]) ).
cnf(c_3487,plain,
para(sK1,sK8,sK8,sK1),
inference(resolve,[status(thm)],[c_3441,c_350]) ).
cnf(c_3503,plain,
para(sK1,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_3455,c_351]) ).
cnf(c_3519,plain,
para(sK5,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_3471,c_351]) ).
cnf(c_3535,plain,
para(sK1,sK8,sK1,sK8),
inference(resolve,[status(thm)],[c_3487,c_351]) ).
cnf(c_3550,plain,
eqangle(sK1,sK2,A,B,sK1,sK2,A,B),
inference(resolve,[status(thm)],[c_3503,c_316]) ).
cnf(c_3559,plain,
( midp(A,sK2,sK2)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_3519,c_394]) ).
cnf(c_3574,plain,
eqangle(sK1,sK8,A,B,sK1,sK8,A,B),
inference(resolve,[status(thm)],[c_3535,c_316]) ).
cnf(c_13175,plain,
( eqratio(sK5,sK5,sK5,sK12,sK5,sK12,sK12,sK5)
| ~ coll(sK5,sK5,sK12) ),
inference(resolve,[status(thm)],[c_1091,c_1192]) ).
cnf(c_3818,plain,
eqratio(sK5,sK5,sK5,sK12,sK5,sK12,sK12,sK5),
inference(resolve,[status(thm)],[c_1133,c_13175]) ).
cnf(c_13176,plain,
( ~ cong(sK5,sK5,sK5,sK12)
| midp(sK12,sK12,sK12)
| ~ coll(sK12,sK12,sK12) ),
inference(resolve,[status(thm)],[c_1101,c_370]) ).
cnf(c_3871,plain,
( ~ cong(sK5,sK5,sK5,sK12)
| midp(sK12,sK12,sK12) ),
inference(resolve,[status(thm)],[c_714,c_13176]) ).
cnf(c_3872,plain,
eqangle(A,B,sK5,sK12,A,B,sK5,sK12),
inference(resolve,[status(thm)],[c_1101,c_337]) ).
cnf(c_6444,plain,
( cyclic(sK5,A,sK12,sK12)
| ~ coll(sK12,sK12,A) ),
inference(resolve,[status(thm)],[c_1621,c_313]) ).
cnf(c_6461,plain,
( cong(sK11,sK11,sK11,sK11)
| ~ cyclic(sK11,sK11,sK12,sK12)
| ~ cyclic(sK11,sK11,sK12,sK11) ),
inference(resolve,[status(thm)],[c_1652,c_400]) ).
cnf(c_6465,plain,
( cyclic(sK11,A,sK12,sK12)
| ~ coll(sK12,sK12,A) ),
inference(resolve,[status(thm)],[c_1652,c_313]) ).
cnf(c_6466,plain,
( cong(sK11,A,sK11,A)
| ~ cyclic(sK11,A,sK12,sK12)
| ~ cyclic(sK11,A,sK12,A)
| ~ cyclic(sK11,A,sK12,sK11) ),
inference(resolve,[status(thm)],[c_1652,c_312]) ).
cnf(c_6479,plain,
( cyclic(sK12,A,sK11,sK11)
| ~ coll(sK11,sK11,A) ),
inference(resolve,[status(thm)],[c_2433,c_313]) ).
cnf(c_6514,plain,
( cyclic(sK1,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_2461,c_313]) ).
cnf(c_6515,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_2461,c_312]) ).
cnf(c_6600,plain,
( cyclic(sK2,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3550,c_313]) ).
cnf(c_6654,plain,
( cyclic(sK8,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3574,c_313]) ).
cnf(c_6685,plain,
( cong(sK5,sK5,sK5,sK12)
| ~ cong(sK5,sK12,sK12,sK5) ),
inference(resolve,[status(thm)],[c_3818,c_286]) ).
cnf(c_6742,plain,
( cong(sK5,sK12,sK5,sK12)
| ~ cyclic(sK5,sK12,sK5,sK12)
| ~ cyclic(sK5,sK12,sK5,sK5) ),
inference(resolve,[status(thm)],[c_3872,c_401]) ).
cnf(c_6745,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_3872,c_317]) ).
cnf(c_13177,plain,
( cyclic(A,sK12,sK5,sK5)
| ~ coll(sK5,sK5,sK12) ),
inference(resolve,[status(thm)],[c_3872,c_313]) ).
cnf(c_6747,plain,
cyclic(A,sK12,sK5,sK5),
inference(resolve,[status(thm)],[c_1133,c_13177]) ).
cnf(c_6758,plain,
( cong(sK5,sK12,sK5,sK12)
| ~ cyclic(sK5,sK12,sK5,sK12) ),
inference(resolve,[status(thm)],[c_6747,c_6742]) ).
cnf(c_6770,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_6745,c_294]) ).
cnf(c_6841,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_6770,c_408]) ).
cnf(c_6849,plain,
cyclic(sK8,A,sK1,sK1),
inference(resolve,[status(thm)],[c_6841,c_6654]) ).
cnf(c_6851,plain,
cyclic(sK2,A,sK1,sK1),
inference(resolve,[status(thm)],[c_6841,c_6600]) ).
cnf(c_6854,plain,
cyclic(sK1,A,sK2,sK2),
inference(resolve,[status(thm)],[c_6841,c_6514]) ).
cnf(c_6855,plain,
cyclic(sK12,A,sK11,sK11),
inference(resolve,[status(thm)],[c_6841,c_6479]) ).
cnf(c_6856,plain,
cyclic(sK11,A,sK12,sK12),
inference(resolve,[status(thm)],[c_6841,c_6465]) ).
cnf(c_6857,plain,
cyclic(sK5,A,sK12,sK12),
inference(resolve,[status(thm)],[c_6841,c_6444]) ).
cnf(c_7009,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,A)
| ~ cyclic(sK1,A,sK2,sK1) ),
inference(resolve,[status(thm)],[c_6854,c_6515]) ).
cnf(c_7015,plain,
( cong(sK11,A,sK11,A)
| ~ cyclic(sK11,A,sK12,A)
| ~ cyclic(sK11,A,sK12,sK11) ),
inference(resolve,[status(thm)],[c_6856,c_6466]) ).
cnf(c_7016,plain,
( cong(sK11,sK11,sK11,sK11)
| ~ cyclic(sK11,sK11,sK12,sK11) ),
inference(resolve,[status(thm)],[c_6856,c_6461]) ).
cnf(c_7366,plain,
cyclic(sK8,sK1,A,sK1),
inference(resolve,[status(thm)],[c_6849,c_341]) ).
cnf(c_7399,plain,
cyclic(sK2,sK1,A,sK1),
inference(resolve,[status(thm)],[c_6851,c_341]) ).
cnf(c_7476,plain,
cyclic(A,sK11,sK11,sK11),
inference(resolve,[status(thm)],[c_6855,c_403]) ).
cnf(c_7478,plain,
cyclic(sK12,sK11,A,sK11),
inference(resolve,[status(thm)],[c_6855,c_341]) ).
cnf(c_7479,plain,
cyclic(A,sK12,sK11,sK11),
inference(resolve,[status(thm)],[c_6855,c_340]) ).
cnf(c_7511,plain,
cyclic(sK5,sK12,A,sK12),
inference(resolve,[status(thm)],[c_6857,c_341]) ).
cnf(c_7526,plain,
cong(sK5,sK12,sK5,sK12),
inference(resolve,[status(thm)],[c_7511,c_6758]) ).
cnf(c_7755,plain,
cyclic(sK8,sK1,sK1,A),
inference(resolve,[status(thm)],[c_7366,c_342]) ).
cnf(c_7834,plain,
cyclic(sK1,sK2,A,sK1),
inference(resolve,[status(thm)],[c_7399,c_340]) ).
cnf(c_7985,plain,
cyclic(sK11,A,sK11,sK11),
inference(resolve,[status(thm)],[c_7476,c_340]) ).
cnf(c_7998,plain,
cyclic(sK12,sK11,sK11,A),
inference(resolve,[status(thm)],[c_7478,c_342]) ).
cnf(c_7999,plain,
cyclic(sK11,sK12,A,sK11),
inference(resolve,[status(thm)],[c_7478,c_340]) ).
cnf(c_8017,plain,
cyclic(A,sK11,sK12,sK11),
inference(resolve,[status(thm)],[c_7479,c_341]) ).
cnf(c_8029,plain,
cong(sK11,sK11,sK11,sK11),
inference(resolve,[status(thm)],[c_8017,c_7016]) ).
cnf(c_8153,plain,
cong(sK5,sK12,sK12,sK5),
inference(resolve,[status(thm)],[c_7526,c_333]) ).
cnf(c_8169,plain,
cong(sK5,sK5,sK5,sK12),
inference(resolve,[status(thm)],[c_8153,c_6685]) ).
cnf(c_8172,plain,
midp(sK12,sK12,sK12),
inference(resolve,[status(thm)],[c_8169,c_3871]) ).
cnf(c_8173,plain,
midp(sK12,sK11,sK11),
inference(resolve,[status(thm)],[c_8172,c_1649]) ).
cnf(c_8174,plain,
midp(sK12,sK5,sK5),
inference(resolve,[status(thm)],[c_8172,c_1618]) ).
cnf(c_8189,plain,
para(sK12,sK12,sK11,sK11),
inference(resolve,[status(thm)],[c_8173,c_399]) ).
cnf(c_8204,plain,
midp(sK12,sK2,sK2),
inference(resolve,[status(thm)],[c_8174,c_3559]) ).
cnf(c_8220,plain,
midp(sK12,sK1,sK1),
inference(resolve,[status(thm)],[c_8204,c_2457]) ).
cnf(c_8238,plain,
para(sK12,sK12,sK1,sK1),
inference(resolve,[status(thm)],[c_8220,c_399]) ).
cnf(c_8524,plain,
cyclic(sK1,sK1,A,A),
inference(resolve,[status(thm)],[c_7755,c_403]) ).
cnf(c_13178,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK8,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_7755,c_339]) ).
cnf(c_8526,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_7755,c_13178]) ).
cnf(c_8939,plain,
cyclic(sK1,A,sK2,sK1),
inference(resolve,[status(thm)],[c_7834,c_341]) ).
cnf(c_8955,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,A) ),
inference(resolve,[status(thm)],[c_8939,c_7009]) ).
cnf(c_9343,plain,
cyclic(sK11,sK11,A,sK11),
inference(resolve,[status(thm)],[c_7985,c_341]) ).
cnf(c_9356,plain,
cyclic(sK11,sK11,A,A),
inference(resolve,[status(thm)],[c_7998,c_403]) ).
cnf(c_13179,plain,
( cyclic(sK11,sK11,A,B)
| ~ cyclic(sK12,sK11,sK11,A) ),
inference(resolve,[status(thm)],[c_7998,c_339]) ).
cnf(c_9358,plain,
cyclic(sK11,sK11,A,B),
inference(resolve,[status(thm)],[c_7998,c_13179]) ).
cnf(c_9372,plain,
cyclic(sK11,A,sK12,sK11),
inference(resolve,[status(thm)],[c_7999,c_341]) ).
cnf(c_9388,plain,
( cong(sK11,A,sK11,A)
| ~ cyclic(sK11,A,sK12,A) ),
inference(resolve,[status(thm)],[c_9372,c_7015]) ).
cnf(c_9761,plain,
para(sK11,sK11,sK12,sK12),
inference(resolve,[status(thm)],[c_8189,c_350]) ).
cnf(c_9824,plain,
( perp(sK12,sK12,A,B)
| ~ perp(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_8238,c_345]) ).
cnf(c_13180,plain,
( cyclic(sK1,A,B,A)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_8524,c_339]) ).
cnf(c_10095,plain,
cyclic(sK1,A,B,A),
inference(resolve,[status(thm)],[c_8526,c_13180]) ).
cnf(c_10108,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_10095,c_8955]) ).
cnf(c_13181,plain,
( perp(A,sK11,sK11,sK11)
| ~ cong(sK11,sK11,sK11,sK11)
| ~ cong(sK11,A,sK11,A) ),
inference(resolve,[status(thm)],[c_9343,c_303]) ).
cnf(c_11004,plain,
( perp(A,sK11,sK11,sK11)
| ~ cong(sK11,A,sK11,A) ),
inference(resolve,[status(thm)],[c_8029,c_13181]) ).
cnf(c_13182,plain,
( cyclic(sK11,A,B,A)
| ~ cyclic(sK11,sK11,A,B) ),
inference(resolve,[status(thm)],[c_9356,c_339]) ).
cnf(c_11018,plain,
cyclic(sK11,A,B,A),
inference(resolve,[status(thm)],[c_9358,c_13182]) ).
cnf(c_11031,plain,
cong(sK11,A,sK11,A),
inference(resolve,[status(thm)],[c_11018,c_9388]) ).
cnf(c_11033,plain,
perp(A,sK11,sK11,sK11),
inference(resolve,[status(thm)],[c_11031,c_11004]) ).
cnf(c_11429,plain,
( perp(sK11,sK11,A,B)
| ~ perp(sK12,sK12,A,B) ),
inference(resolve,[status(thm)],[c_9761,c_345]) ).
cnf(c_13183,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_10108,c_304]) ).
cnf(c_11743,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_10108,c_13183]) ).
cnf(c_11760,plain,
perp(sK12,sK12,A,B),
inference(resolve,[status(thm)],[c_11743,c_9824]) ).
cnf(c_11790,plain,
perp(sK11,sK11,A,B),
inference(resolve,[status(thm)],[c_11760,c_11429]) ).
cnf(c_13184,plain,
( para(C,sK11,A,B)
| ~ perp(sK11,sK11,A,B) ),
inference(resolve,[status(thm)],[c_11033,c_346]) ).
cnf(c_13125,plain,
para(A,sK11,B,C),
inference(resolve,[status(thm)],[c_11790,c_13184]) ).
cnf(c_13173,plain,
para(sK11,sK12,A,B),
inference(resolve,[status(thm)],[c_13125,c_1638]) ).
cnf(c_13174,plain,
$false,
inference(resolve,[status(thm)],[c_13173,c_252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO654+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 13:47:34 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 3062330 was started by sandbox2 on n020,
% 0.10/0.36 % Fri Sep 25 13:47:34 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 13.44/2.14
% 13.44/2.14 % given #500 (A,wt=41): 477 -perp(c2,c2,f12(c2,c4,c13,c1),c1) | perp(f12(c2,c4,c13,c1),f11(c2,f12(c2,c4,c13,c1),c1,c2),c1,c2). [resolve(263,b,177,a)].
% 13.44/2.14
% 13.44/2.14 % given #1000 (T,wt=9): 1753 coll(c5,c8,c3). [resolve(1703,a,1120,a)].
% 13.44/2.14
% 13.44/2.14 % given #1500 (A,wt=28): 1142 coll(f17(f12(c2,c4,c14,c3),c3,c2,c7,c5),c7,c5). [resolve(1126,a,462,a)].
% 13.44/2.14
% 13.44/2.14 % given #2000 (T,wt=13): 2883 -coll(c7,c1,A) | coll(A,c4,c7). [resolve(2679,a,352,b)].
% 13.44/2.14
% 13.44/2.14 % given #2500 (A,wt=20): 1719 perp(f17(c3,c8,c5,c7,c5),c3,c7,c5). [resolve(1682,a,450,a)].
% 13.44/2.14
% 13.44/2.14 % given #3000 (T,wt=10): 10497 perp(c5,c5,c1,A). [back_unit_del(9858),unit_del(a,10492)].
% 13.44/2.14
% 13.44/2.14 % SZS status Theorem for theBenchmark
% 13.44/2.14
% 13.44/2.14 % Proof 1 at 1.37 (+ 0.33) seconds.
% 13.44/2.14 % Length of proof is 203.
% 13.44/2.14 % Level of proof is 24.
% 13.44/2.14 % Maximum clause weight is 34.000.
% 13.44/2.14 % Given clauses 3062.
% 13.44/2.14
% 13.44/2.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------