%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO546+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 : n007.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 07:18:04 AM UTC 2026
% Result : Theorem 7.59s 1.43s
% Output : CNFRefutation 7.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 33
% Syntax : Number of formulae : 208 ( 93 unt; 0 def)
% Number of atoms : 412 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 333 ( 129 ~; 125 |; 45 &)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 485 ( 49 sgn 166 !; 6 ?)
% 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(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(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(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(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(ruleD55,axiom,
! [A,B,M,O] :
( ( perp(O,M,A,B)
& midp(M,A,B) )
=> cong(O,A,O,B) ),
file('theBenchmark.p',ruleD55) ).
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(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(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(exemplo6GDDFULL012006,conjecture,
! [A,B,C,E,F,H] :
( ( coll(H,A,F)
& coll(H,C,E)
& coll(F,B,C)
& perp(F,A,B,C)
& coll(E,A,B)
& perp(E,C,A,B) )
=> perp(B,H,A,C) ),
file('theBenchmark.p',exemplo6GDDFULL012006) ).
fof(exemplo6GDDFULL012006_neg,negated_conjecture,
~ ! [A,B,C,E,F,H] :
( ( coll(H,A,F)
& coll(H,C,E)
& coll(F,B,C)
& perp(F,A,B,C)
& coll(E,A,B)
& perp(E,C,A,B) )
=> perp(B,H,A,C) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012006]) ).
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_143,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]) ).
fof(nnf_95,plain,
? [A,B,C,E,F,H] :
( ~ perp(B,H,A,C)
& coll(H,A,F)
& coll(H,C,E)
& coll(F,B,C)
& perp(F,A,B,C)
& coll(E,A,B)
& perp(E,C,A,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012006_neg]) ).
fof(sk_exemplo6GDDFULL012006_neg,plain,
( ~ perp(sK0,sK1,sK2,sK3)
& coll(sK1,sK2,sK4)
& coll(sK1,sK3,sK5)
& coll(sK4,sK0,sK3)
& perp(sK4,sK2,sK0,sK3)
& coll(sK5,sK2,sK0)
& perp(sK5,sK3,sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK3,sK2,sK0,sK4,sK1]),skolemize(A,sK2),skolemize(B,sK0),skolemize(C,sK3),skolemize(E,sK5),skolemize(F,sK4),skolemize(H,sK1)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ perp(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012006_neg]) ).
cnf(c_148,negated_conjecture,
coll(sK1,sK2,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012006_neg]) ).
cnf(c_151,negated_conjecture,
perp(sK4,sK2,sK0,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012006_neg]) ).
cnf(c_152,negated_conjecture,
coll(sK5,sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012006_neg]) ).
cnf(c_153,negated_conjecture,
perp(sK5,sK3,sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012006_neg]) ).
cnf(c_184,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_185,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_192,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_193,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_194,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_201,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_202,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_203,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_205,plain,
( cong(A,D,B,D)
| ~ midp(D,A,C)
| ~ perp(A,B,B,C) ),
inference(clausify,[status(thm)],[ruleD52]) ).
cnf(c_208,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_210,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_211,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_214,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_215,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_230,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_231,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_233,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_235,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_237,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_238,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_239,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_240,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_244,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_245,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_246,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_248,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_249,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_250,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_251,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_252,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_268,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_143]) ).
cnf(c_292,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_194]) ).
cnf(c_295,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_201]) ).
cnf(c_301,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_237]) ).
cnf(c_306,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_250]) ).
cnf(c_339,plain,
( para(sK4,sK2,A,B)
| ~ perp(sK0,sK3,A,B) ),
inference(resolve,[status(thm)],[c_244,c_151]) ).
cnf(c_340,plain,
( para(A,B,sK2,sK0)
| ~ perp(A,B,sK5,sK3) ),
inference(resolve,[status(thm)],[c_244,c_153]) ).
cnf(c_342,plain,
perp(sK2,sK0,sK5,sK3),
inference(resolve,[status(thm)],[c_245,c_153]) ).
cnf(c_343,plain,
perp(sK0,sK3,sK4,sK2),
inference(resolve,[status(thm)],[c_245,c_151]) ).
cnf(c_344,plain,
perp(sK5,sK3,sK0,sK2),
inference(resolve,[status(thm)],[c_246,c_153]) ).
cnf(c_354,plain,
coll(sK2,sK5,sK0),
inference(resolve,[status(thm)],[c_251,c_152]) ).
cnf(c_357,plain,
coll(sK2,sK1,sK4),
inference(resolve,[status(thm)],[c_251,c_148]) ).
cnf(c_358,plain,
coll(sK5,sK0,sK2),
inference(resolve,[status(thm)],[c_252,c_152]) ).
cnf(c_366,plain,
coll(sK0,sK0,sK2),
inference(resolve,[status(thm)],[c_354,c_306]) ).
cnf(c_378,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_357,c_306]) ).
cnf(c_382,plain,
coll(sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_358,c_306]) ).
cnf(c_414,plain,
coll(sK2,sK2,sK0),
inference(resolve,[status(thm)],[c_366,c_306]) ).
cnf(c_439,plain,
coll(sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_378,c_252]) ).
cnf(c_446,plain,
coll(sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_382,c_252]) ).
cnf(c_494,plain,
coll(sK2,sK0,sK2),
inference(resolve,[status(thm)],[c_414,c_252]) ).
cnf(c_527,plain,
para(sK2,sK0,sK2,sK0),
inference(resolve,[status(thm)],[c_342,c_340]) ).
cnf(c_546,plain,
coll(sK2,sK4,sK4),
inference(resolve,[status(thm)],[c_439,c_251]) ).
cnf(c_554,plain,
coll(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_446,c_306]) ).
cnf(c_562,plain,
para(sK4,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_343,c_339]) ).
cnf(c_577,plain,
perp(sK0,sK2,sK5,sK3),
inference(resolve,[status(thm)],[c_344,c_245]) ).
cnf(c_705,plain,
para(sK2,sK0,sK0,sK2),
inference(resolve,[status(thm)],[c_527,c_249]) ).
cnf(c_706,plain,
eqangle(sK2,sK0,A,B,sK2,sK0,A,B),
inference(resolve,[status(thm)],[c_527,c_214]) ).
cnf(c_758,plain,
para(sK4,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_562,c_249]) ).
cnf(c_759,plain,
eqangle(sK4,sK2,A,B,sK4,sK2,A,B),
inference(resolve,[status(thm)],[c_562,c_214]) ).
cnf(c_761,plain,
( eqratio(A,sK4,sK4,sK4,A,sK2,sK2,sK2)
| ~ coll(A,sK2,sK2)
| ~ coll(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_562,c_193]) ).
cnf(c_782,plain,
para(sK0,sK2,sK2,sK0),
inference(resolve,[status(thm)],[c_577,c_340]) ).
cnf(c_820,plain,
( eqratio(A,sK2,sK2,sK0,A,sK0,sK0,sK2)
| ~ coll(A,sK0,sK2)
| ~ coll(A,sK2,sK0) ),
inference(resolve,[status(thm)],[c_705,c_193]) ).
cnf(c_1218,plain,
para(sK2,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_758,c_248]) ).
cnf(c_1248,plain,
para(sK0,sK2,sK0,sK2),
inference(resolve,[status(thm)],[c_782,c_249]) ).
cnf(c_1335,plain,
para(sK2,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_1218,c_249]) ).
cnf(c_1363,plain,
eqangle(sK0,sK2,A,B,sK0,sK2,A,B),
inference(resolve,[status(thm)],[c_1248,c_214]) ).
cnf(c_1399,plain,
eqangle(sK2,sK4,A,B,sK2,sK4,A,B),
inference(resolve,[status(thm)],[c_1335,c_214]) ).
cnf(c_1411,plain,
eqangle(A,B,sK2,sK0,A,B,sK2,sK0),
inference(resolve,[status(thm)],[c_706,c_235]) ).
cnf(c_1413,plain,
( cyclic(sK0,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_706,c_211]) ).
cnf(c_1414,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK2,sK2)
| ~ cyclic(sK0,A,sK2,A)
| ~ cyclic(sK0,A,sK2,sK0) ),
inference(resolve,[status(thm)],[c_706,c_210]) ).
cnf(c_8309,plain,
( ~ cong(sK4,sK4,sK4,sK2)
| midp(sK2,sK2,sK2)
| ~ coll(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_759,c_268]) ).
cnf(c_1551,plain,
( ~ cong(sK4,sK4,sK4,sK2)
| midp(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_554,c_8309]) ).
cnf(c_1554,plain,
( cyclic(sK2,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_759,c_211]) ).
cnf(c_1555,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK4,sK4)
| ~ cyclic(sK2,A,sK4,A)
| ~ cyclic(sK2,A,sK4,sK2) ),
inference(resolve,[status(thm)],[c_759,c_210]) ).
cnf(c_8310,plain,
( eqratio(sK2,sK4,sK4,sK4,sK2,sK2,sK2,sK2)
| ~ coll(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_761,c_546]) ).
cnf(c_1566,plain,
eqratio(sK2,sK4,sK4,sK4,sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_554,c_8310]) ).
cnf(c_8311,plain,
( eqratio(sK2,sK2,sK2,sK0,sK2,sK0,sK0,sK2)
| ~ coll(sK2,sK2,sK0) ),
inference(resolve,[status(thm)],[c_820,c_494]) ).
cnf(c_1618,plain,
eqratio(sK2,sK2,sK2,sK0,sK2,sK0,sK0,sK2),
inference(resolve,[status(thm)],[c_414,c_8311]) ).
cnf(c_1717,plain,
( cyclic(sK2,A,sK0,sK0)
| ~ coll(sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_1363,c_211]) ).
cnf(c_1759,plain,
( cyclic(sK4,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1399,c_211]) ).
cnf(c_1770,plain,
eqangle(A,B,A,B,sK2,sK0,sK2,sK0),
inference(resolve,[status(thm)],[c_1411,c_233]) ).
cnf(c_1771,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_1411,c_215]) ).
cnf(c_8312,plain,
( cyclic(A,sK0,sK2,sK2)
| ~ coll(sK2,sK2,sK0) ),
inference(resolve,[status(thm)],[c_1411,c_211]) ).
cnf(c_1773,plain,
cyclic(A,sK0,sK2,sK2),
inference(resolve,[status(thm)],[c_414,c_8312]) ).
cnf(c_8313,plain,
( cong(A,sK0,A,sK0)
| ~ cyclic(A,sK0,sK2,sK2)
| ~ cyclic(A,sK0,sK2,sK0)
| ~ cyclic(A,sK0,sK2,A) ),
inference(resolve,[status(thm)],[c_1411,c_210]) ).
cnf(c_1774,plain,
( cong(A,sK0,A,sK0)
| ~ cyclic(A,sK0,sK2,sK0)
| ~ cyclic(A,sK0,sK2,A) ),
inference(resolve,[status(thm)],[c_1773,c_8313]) ).
cnf(c_1779,plain,
( ~ cong(sK2,sK2,sK2,sK0)
| ~ cong(sK2,sK2,sK2,A)
| midp(sK0,A,sK0)
| ~ coll(sK0,A,sK0) ),
inference(resolve,[status(thm)],[c_1411,c_143]) ).
cnf(c_1786,plain,
( midp(A,C,C)
| ~ midp(A,B,B) ),
inference(resolve,[status(thm)],[c_1771,c_292]) ).
cnf(c_1794,plain,
( midp(C,B,C)
| ~ coll(C,B,C)
| ~ midp(A,B,A) ),
inference(resolve,[status(thm)],[c_1771,c_208]) ).
cnf(c_1796,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_1771,c_192]) ).
cnf(c_1876,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_1796,c_306]) ).
cnf(c_1877,plain,
coll(A,B,A),
inference(resolve,[status(thm)],[c_1796,c_251]) ).
cnf(c_1884,plain,
cyclic(sK4,A,sK2,sK2),
inference(resolve,[status(thm)],[c_1876,c_1759]) ).
cnf(c_1887,plain,
cyclic(sK2,A,sK0,sK0),
inference(resolve,[status(thm)],[c_1876,c_1717]) ).
cnf(c_1888,plain,
cyclic(sK2,A,sK4,sK4),
inference(resolve,[status(thm)],[c_1876,c_1554]) ).
cnf(c_1891,plain,
cyclic(sK0,A,sK2,sK2),
inference(resolve,[status(thm)],[c_1876,c_1413]) ).
cnf(c_1953,plain,
( midp(C,B,C)
| ~ midp(A,B,A) ),
inference(resolve,[status(thm)],[c_1877,c_1794]) ).
cnf(c_1954,plain,
( ~ cong(sK2,sK2,sK2,sK0)
| ~ cong(sK2,sK2,sK2,A)
| midp(sK0,A,sK0) ),
inference(resolve,[status(thm)],[c_1877,c_1779]) ).
cnf(c_1983,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK4,A)
| ~ cyclic(sK2,A,sK4,sK2) ),
inference(resolve,[status(thm)],[c_1888,c_1555]) ).
cnf(c_1992,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK2,A)
| ~ cyclic(sK0,A,sK2,sK0) ),
inference(resolve,[status(thm)],[c_1891,c_1414]) ).
cnf(c_2073,plain,
cyclic(A,sK2,sK0,sK2),
inference(resolve,[status(thm)],[c_1773,c_239]) ).
cnf(c_2093,plain,
cyclic(sK4,sK2,A,sK2),
inference(resolve,[status(thm)],[c_1884,c_239]) ).
cnf(c_2143,plain,
cyclic(sK2,sK0,A,sK0),
inference(resolve,[status(thm)],[c_1887,c_239]) ).
cnf(c_2144,plain,
cyclic(A,sK2,sK0,sK0),
inference(resolve,[status(thm)],[c_1887,c_238]) ).
cnf(c_2210,plain,
cyclic(sK0,sK2,A,sK2),
inference(resolve,[status(thm)],[c_1891,c_239]) ).
cnf(c_2225,plain,
cyclic(sK2,A,sK0,sK2),
inference(resolve,[status(thm)],[c_2073,c_238]) ).
cnf(c_2305,plain,
cyclic(sK4,sK2,sK2,A),
inference(resolve,[status(thm)],[c_2093,c_240]) ).
cnf(c_2306,plain,
cyclic(sK2,sK4,A,sK2),
inference(resolve,[status(thm)],[c_2093,c_238]) ).
cnf(c_2429,plain,
cyclic(sK2,sK0,sK0,A),
inference(resolve,[status(thm)],[c_2143,c_240]) ).
cnf(c_2430,plain,
cyclic(sK0,sK2,A,sK0),
inference(resolve,[status(thm)],[c_2143,c_238]) ).
cnf(c_2446,plain,
cyclic(A,sK0,sK2,sK0),
inference(resolve,[status(thm)],[c_2144,c_239]) ).
cnf(c_2459,plain,
( cong(A,sK0,A,sK0)
| ~ cyclic(A,sK0,sK2,A) ),
inference(resolve,[status(thm)],[c_2446,c_1774]) ).
cnf(c_2629,plain,
cyclic(sK2,sK0,A,sK2),
inference(resolve,[status(thm)],[c_2210,c_238]) ).
cnf(c_2662,plain,
( cyclic(A,sK0,sK2,B)
| ~ cyclic(sK2,A,sK0,B) ),
inference(resolve,[status(thm)],[c_2225,c_237]) ).
cnf(c_2751,plain,
cyclic(sK2,sK2,A,A),
inference(resolve,[status(thm)],[c_2305,c_301]) ).
cnf(c_8314,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK4,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_2305,c_237]) ).
cnf(c_2753,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_2305,c_8314]) ).
cnf(c_2767,plain,
cyclic(sK2,A,sK4,sK2),
inference(resolve,[status(thm)],[c_2306,c_239]) ).
cnf(c_2783,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK4,A) ),
inference(resolve,[status(thm)],[c_2767,c_1983]) ).
cnf(c_3240,plain,
cyclic(sK0,sK0,A,A),
inference(resolve,[status(thm)],[c_2429,c_301]) ).
cnf(c_3256,plain,
cyclic(sK0,A,sK2,sK0),
inference(resolve,[status(thm)],[c_2430,c_239]) ).
cnf(c_3272,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK2,A) ),
inference(resolve,[status(thm)],[c_3256,c_1992]) ).
cnf(c_3603,plain,
( cyclic(sK0,A,sK2,B)
| ~ cyclic(sK2,sK0,A,B) ),
inference(resolve,[status(thm)],[c_2629,c_237]) ).
cnf(c_3657,plain,
( perp(A,sK2,sK2,A)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_2751,c_295]) ).
cnf(c_8315,plain,
( cyclic(sK2,A,B,A)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_2751,c_237]) ).
cnf(c_3658,plain,
cyclic(sK2,A,B,A),
inference(resolve,[status(thm)],[c_2753,c_8315]) ).
cnf(c_3671,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_3658,c_2783]) ).
cnf(c_3672,plain,
perp(A,sK2,sK2,A),
inference(resolve,[status(thm)],[c_3671,c_3657]) ).
cnf(c_8316,plain,
( cyclic(sK2,A,B,C)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_2753,c_237]) ).
cnf(c_3735,plain,
cyclic(sK2,A,B,C),
inference(resolve,[status(thm)],[c_2753,c_8316]) ).
cnf(c_3747,plain,
cyclic(sK0,A,sK2,B),
inference(resolve,[status(thm)],[c_3735,c_3603]) ).
cnf(c_3751,plain,
cyclic(A,sK0,sK2,B),
inference(resolve,[status(thm)],[c_3735,c_2662]) ).
cnf(c_3805,plain,
cong(sK0,A,sK0,A),
inference(resolve,[status(thm)],[c_3747,c_3272]) ).
cnf(c_3808,plain,
cong(A,sK0,A,sK0),
inference(resolve,[status(thm)],[c_3751,c_2459]) ).
cnf(c_8317,plain,
( perp(A,sK0,sK0,A)
| ~ cong(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_3240,c_295]) ).
cnf(c_4204,plain,
perp(A,sK0,sK0,A),
inference(resolve,[status(thm)],[c_3805,c_8317]) ).
cnf(c_4735,plain,
cong(sK2,A,A,sK2),
inference(resolve,[status(thm)],[c_3671,c_231]) ).
cnf(c_4783,plain,
perp(sK2,A,A,sK2),
inference(resolve,[status(thm)],[c_3672,c_245]) ).
cnf(c_5230,plain,
cong(A,sK0,sK0,A),
inference(resolve,[status(thm)],[c_3808,c_231]) ).
cnf(c_5758,plain,
perp(A,sK0,A,sK0),
inference(resolve,[status(thm)],[c_4204,c_246]) ).
cnf(c_8318,plain,
( cong(sK2,sK4,sK4,sK4)
| ~ cong(sK2,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_1566,c_184]) ).
cnf(c_5861,plain,
cong(sK2,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_4735,c_8318]) ).
cnf(c_8319,plain,
( cong(sK2,sK2,sK2,sK0)
| ~ cong(sK2,sK0,sK0,sK2) ),
inference(resolve,[status(thm)],[c_1618,c_184]) ).
cnf(c_6013,plain,
cong(sK2,sK2,sK2,sK0),
inference(resolve,[status(thm)],[c_5230,c_8319]) ).
cnf(c_6016,plain,
( ~ cong(sK2,sK2,sK2,A)
| midp(sK0,A,sK0) ),
inference(resolve,[status(thm)],[c_6013,c_1954]) ).
cnf(c_6064,plain,
perp(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_4783,c_246]) ).
cnf(c_6619,plain,
cong(sK4,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_5861,c_230]) ).
cnf(c_6700,plain,
( cong(sK2,sK2,sK2,A)
| ~ midp(A,sK2,A) ),
inference(resolve,[status(thm)],[c_6064,c_203]) ).
cnf(c_8320,plain,
( perp(A,B,A,B)
| ~ perp(sK2,sK0,sK2,sK0) ),
inference(resolve,[status(thm)],[c_1770,c_185]) ).
cnf(c_6736,plain,
perp(A,B,A,B),
inference(resolve,[status(thm)],[c_5758,c_8320]) ).
cnf(c_6931,plain,
cong(sK4,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_6619,c_231]) ).
cnf(c_6935,plain,
midp(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_6931,c_1551]) ).
cnf(c_6936,plain,
midp(sK2,A,A),
inference(resolve,[status(thm)],[c_6935,c_1786]) ).
cnf(c_6996,plain,
perp(A,B,B,A),
inference(resolve,[status(thm)],[c_6736,c_246]) ).
cnf(c_7244,plain,
( cong(B,A,C,A)
| ~ midp(A,B,B) ),
inference(resolve,[status(thm)],[c_6996,c_205]) ).
cnf(c_7438,plain,
midp(A,sK2,A),
inference(resolve,[status(thm)],[c_1953,c_6936]) ).
cnf(c_7441,plain,
cong(sK2,sK2,sK2,A),
inference(resolve,[status(thm)],[c_7438,c_6700]) ).
cnf(c_7468,plain,
midp(sK0,A,sK0),
inference(resolve,[status(thm)],[c_7441,c_6016]) ).
cnf(c_7706,plain,
midp(A,B,A),
inference(resolve,[status(thm)],[c_7468,c_1953]) ).
cnf(c_8110,plain,
midp(A,B,B),
inference(resolve,[status(thm)],[c_7706,c_1786]) ).
cnf(c_8124,plain,
cong(A,B,C,B),
inference(resolve,[status(thm)],[c_8110,c_7244]) ).
cnf(c_8321,plain,
( perp(A,C,D,B)
| ~ cong(A,B,C,B) ),
inference(resolve,[status(thm)],[c_8124,c_202]) ).
cnf(c_8307,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_8124,c_8321]) ).
cnf(c_8308,plain,
$false,
inference(resolve,[status(thm)],[c_8307,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO546+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Computer : n007.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8046.5625MB
% 0.13/0.36 % OS : Linux 6.8.0-71-generic
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Sep 25 13:39:08 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.37 % Process 1125264 was started by sandbox2 on n007,
% 0.13/0.37 % Fri Sep 25 13:39:08 2026
% 0.13/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.40
% 0.13/0.40 % From the command line: assign(max_seconds, 300).
% 7.59/1.43
% 7.59/1.43 % given #500 (T,wt=9): 1031 coll(c4,c6,c2). [resolve(930,a,251,a)].
% 7.59/1.43
% 7.59/1.43 % given #1000 (W,wt=13): 1144 -coll(c2,c3,A) | coll(c1,A,c2). [resolve(1049,a,250,a)].
% 7.59/1.43
% 7.59/1.43 % given #1500 (T,wt=10): 4001 cyclic(c3,A,B,c4). [back_unit_del(3514),unit_del(a,3987)].
% 7.59/1.43
% 7.59/1.43 % SZS status Theorem for theBenchmark
% 7.59/1.43
% 7.59/1.43 % Proof 1 at 0.72 (+ 0.22) seconds.
% 7.59/1.43 % Length of proof is 192.
% 7.59/1.43 % Level of proof is 28.
% 7.59/1.43 % Maximum clause weight is 34.000.
% 7.59/1.43 % Given clauses 1913.
% 7.59/1.43
% 7.59/1.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------