%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO604+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 95.69s 13.60s
% Output : CNFRefutation 95.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 29
% Syntax : Number of formulae : 199 ( 95 unt; 0 def)
% Number of atoms : 371 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 278 ( 106 ~; 102 |; 40 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 373 ( 42 sgn 136 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('theBenchmark.p',ruleD2) ).
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('theBenchmark.p',ruleD3) ).
fof(ruleD4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('theBenchmark.p',ruleD4) ).
fof(ruleD5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('theBenchmark.p',ruleD5) ).
fof(ruleD8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('theBenchmark.p',ruleD8) ).
fof(ruleD9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('theBenchmark.p',ruleD9) ).
fof(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(ruleD11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('theBenchmark.p',ruleD11) ).
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(ruleD13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('theBenchmark.p',ruleD13) ).
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(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(ruleD41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('theBenchmark.p',ruleD41) ).
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(ruleD53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('theBenchmark.p',ruleD53) ).
fof(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(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(ruleD67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('theBenchmark.p',ruleD67) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('theBenchmark.p',ruleD68) ).
fof(ruleD69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD69) ).
fof(exemplo6GDDFULL618066,conjecture,
! [A,B,C,D,E,F,G] :
( ( midp(G,C,B)
& midp(F,A,E)
& coll(E,C,D)
& perp(B,C,A,E)
& coll(D,A,B)
& perp(D,C,A,B) )
=> perp(D,G,D,F) ),
file('theBenchmark.p',exemplo6GDDFULL618066) ).
fof(exemplo6GDDFULL618066_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( midp(G,C,B)
& midp(F,A,E)
& coll(E,C,D)
& perp(B,C,A,E)
& coll(D,A,B)
& perp(D,C,A,B) )
=> perp(D,G,D,F) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618066]) ).
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_101,plain,
( perp(B,C,C,D)
| ~ coll(A,B,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD53]) ).
cnf(c_142,plain,
( ~ cong(A,B,A,C)
| ~ cong(A,B,A,D)
| perp(B,D,D,C)
| ~ coll(A,B,C) ),
inference(resolve,[status(thm)],[c_101,c_97]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G] :
( ~ perp(D,G,D,F)
& midp(G,C,B)
& midp(F,A,E)
& coll(E,C,D)
& perp(B,C,A,E)
& coll(D,A,B)
& perp(D,C,A,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618066_neg]) ).
fof(sk_exemplo6GDDFULL618066_neg,plain,
( ~ perp(sK0,sK1,sK0,sK2)
& midp(sK1,sK6,sK5)
& midp(sK2,sK3,sK4)
& coll(sK4,sK6,sK0)
& perp(sK5,sK6,sK3,sK4)
& coll(sK0,sK3,sK5)
& perp(sK0,sK6,sK3,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK6,sK3,sK5,sK4,sK2,sK1]),skolemize(A,sK3),skolemize(B,sK5),skolemize(C,sK6),skolemize(D,sK0),skolemize(E,sK4),skolemize(F,sK2),skolemize(G,sK1)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ perp(sK0,sK1,sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618066_neg]) ).
cnf(c_149,negated_conjecture,
midp(sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618066_neg]) ).
cnf(c_152,negated_conjecture,
coll(sK0,sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618066_neg]) ).
cnf(c_189,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_190,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_191,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
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_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_209,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
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_213,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
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_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_241,plain,
( cyclic(B,C,D,E)
| ~ cong(A,B,A,E)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD13]) ).
cnf(c_242,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_243,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
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_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_267,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_142]) ).
cnf(c_297,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_209]) ).
cnf(c_298,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_210]) ).
cnf(c_299,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_210]) ).
cnf(c_301,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_237]) ).
cnf(c_302,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_241]) ).
cnf(c_306,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_250]) ).
cnf(c_314,plain,
( cong(A,B,D,D)
| ~ eqangle(C,A,C,B,D,D,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_298]) ).
cnf(c_315,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_302]) ).
cnf(c_446,plain,
coll(sK2,sK3,sK4),
inference(resolve,[status(thm)],[c_189,c_149]) ).
cnf(c_448,plain,
cong(sK2,sK3,sK2,sK4),
inference(resolve,[status(thm)],[c_190,c_149]) ).
cnf(c_474,plain,
( para(sK2,A,sK4,B)
| ~ midp(A,sK3,B) ),
inference(resolve,[status(thm)],[c_209,c_149]) ).
cnf(c_480,plain,
midp(sK2,sK4,sK3),
inference(resolve,[status(thm)],[c_242,c_149]) ).
cnf(c_498,plain,
coll(sK0,sK5,sK3),
inference(resolve,[status(thm)],[c_252,c_152]) ).
cnf(c_528,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_446,c_306]) ).
cnf(c_29281,plain,
( ~ cong(sK2,sK3,sK2,sK4)
| perp(sK3,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_446,c_267]) ).
cnf(c_540,plain,
perp(sK3,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_448,c_29281]) ).
cnf(c_541,plain,
coll(sK2,sK4,sK3),
inference(resolve,[status(thm)],[c_446,c_252]) ).
cnf(c_542,plain,
coll(sK3,sK2,sK4),
inference(resolve,[status(thm)],[c_446,c_251]) ).
cnf(c_613,plain,
cong(sK2,sK4,sK2,sK3),
inference(resolve,[status(thm)],[c_480,c_190]) ).
cnf(c_762,plain,
coll(sK3,sK3,sK0),
inference(resolve,[status(thm)],[c_498,c_306]) ).
cnf(c_931,plain,
coll(sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_528,c_252]) ).
cnf(c_955,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_541,c_306]) ).
cnf(c_29282,plain,
( ~ cong(sK2,sK4,sK2,sK3)
| perp(sK4,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_541,c_267]) ).
cnf(c_967,plain,
perp(sK4,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_613,c_29282]) ).
cnf(c_968,plain,
coll(sK4,sK2,sK3),
inference(resolve,[status(thm)],[c_541,c_251]) ).
cnf(c_987,plain,
coll(sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_542,c_306]) ).
cnf(c_1304,plain,
coll(sK3,sK0,sK3),
inference(resolve,[status(thm)],[c_762,c_252]) ).
cnf(c_1647,plain,
coll(sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_931,c_306]) ).
cnf(c_1706,plain,
coll(sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_955,c_252]) ).
cnf(c_1730,plain,
coll(sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_968,c_306]) ).
cnf(c_1782,plain,
coll(sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_987,c_252]) ).
cnf(c_2379,plain,
coll(sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_1304,c_306]) ).
cnf(c_2774,plain,
( cyclic(A,sK4,sK4,sK4)
| ~ eqangle(sK4,A,sK4,sK4,sK4,A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_1647,c_211]) ).
cnf(c_2778,plain,
( midp(sK4,sK4,sK4)
| ~ cong(sK4,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_1647,c_191]) ).
cnf(c_2885,plain,
( ~ cong(sK3,sK2,sK3,sK3)
| perp(sK2,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_1706,c_267]) ).
cnf(c_2886,plain,
coll(sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_1706,c_251]) ).
cnf(c_2925,plain,
coll(sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_1730,c_252]) ).
cnf(c_2999,plain,
coll(sK3,sK4,sK4),
inference(resolve,[status(thm)],[c_1782,c_251]) ).
cnf(c_3567,plain,
( midp(sK3,sK3,sK3)
| ~ cong(sK3,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_2379,c_191]) ).
cnf(c_3926,plain,
( midp(sK2,sK3,sK3)
| ~ cong(sK2,sK3,sK2,sK3) ),
inference(resolve,[status(thm)],[c_2886,c_191]) ).
cnf(c_3954,plain,
coll(sK4,sK3,sK3),
inference(resolve,[status(thm)],[c_2925,c_251]) ).
cnf(c_4006,plain,
( midp(sK3,sK4,sK4)
| ~ cong(sK3,sK4,sK3,sK4) ),
inference(resolve,[status(thm)],[c_2999,c_191]) ).
cnf(c_4486,plain,
( midp(sK4,sK3,sK3)
| ~ cong(sK4,sK3,sK4,sK3) ),
inference(resolve,[status(thm)],[c_3954,c_191]) ).
cnf(c_4582,plain,
cyclic(sK3,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_448,c_315]) ).
cnf(c_4998,plain,
( cong(sK3,sK4,sK3,sK4)
| ~ midp(sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_540,c_203]) ).
cnf(c_5128,plain,
cyclic(sK4,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_613,c_315]) ).
cnf(c_5412,plain,
( cong(sK4,sK3,sK4,sK3)
| ~ midp(sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_967,c_203]) ).
cnf(c_5483,plain,
cyclic(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_4582,c_301]) ).
cnf(c_5726,plain,
cyclic(sK3,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_5128,c_301]) ).
cnf(c_5846,plain,
( cong(sK4,sK4,sK4,sK4)
| ~ eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_5483,c_314]) ).
cnf(c_5854,plain,
eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_5483,c_213]) ).
cnf(c_5877,plain,
cong(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_5854,c_5846]) ).
cnf(c_5879,plain,
midp(sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_5877,c_2778]) ).
cnf(c_5880,plain,
cong(sK3,sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_5879,c_4998]) ).
cnf(c_5884,plain,
midp(sK3,sK4,sK4),
inference(resolve,[status(thm)],[c_5880,c_4006]) ).
cnf(c_5896,plain,
para(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_5879,c_297]) ).
cnf(c_6406,plain,
( cong(sK3,sK3,sK3,sK3)
| ~ eqangle(sK3,sK3,sK3,sK3,sK3,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_5726,c_314]) ).
cnf(c_6414,plain,
eqangle(sK3,sK3,sK3,sK3,sK3,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_5726,c_213]) ).
cnf(c_6437,plain,
cong(sK3,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_6414,c_6406]) ).
cnf(c_6439,plain,
midp(sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_6437,c_3567]) ).
cnf(c_6440,plain,
cong(sK4,sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_6439,c_5412]) ).
cnf(c_6444,plain,
midp(sK4,sK3,sK3),
inference(resolve,[status(thm)],[c_6440,c_4486]) ).
cnf(c_7154,plain,
eqangle(sK4,sK4,A,B,sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_5896,c_214]) ).
cnf(c_15739,plain,
para(sK2,sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_474,c_6444]) ).
cnf(c_15740,plain,
para(sK2,sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_474,c_6439]) ).
cnf(c_15746,plain,
para(sK4,sK3,sK2,sK4),
inference(resolve,[status(thm)],[c_15739,c_248]) ).
cnf(c_15760,plain,
para(sK2,sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_15740,c_249]) ).
cnf(c_15782,plain,
para(sK4,sK3,sK4,sK2),
inference(resolve,[status(thm)],[c_15746,c_249]) ).
cnf(c_15797,plain,
para(sK3,sK4,sK2,sK3),
inference(resolve,[status(thm)],[c_15760,c_248]) ).
cnf(c_15832,plain,
para(sK4,sK2,sK4,sK3),
inference(resolve,[status(thm)],[c_15782,c_248]) ).
cnf(c_29283,plain,
( midp(A,sK2,sK3)
| ~ para(sK4,sK2,sK4,sK3)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_15782,c_194]) ).
cnf(c_15839,plain,
( midp(A,sK2,sK3)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_15832,c_29283]) ).
cnf(c_15845,plain,
para(sK3,sK4,sK3,sK2),
inference(resolve,[status(thm)],[c_15797,c_249]) ).
cnf(c_15898,plain,
para(sK3,sK2,sK3,sK4),
inference(resolve,[status(thm)],[c_15845,c_248]) ).
cnf(c_29284,plain,
( midp(A,sK2,sK4)
| ~ para(sK3,sK2,sK3,sK4)
| ~ midp(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_15845,c_194]) ).
cnf(c_15905,plain,
( midp(A,sK2,sK4)
| ~ midp(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_15898,c_29284]) ).
cnf(c_15943,plain,
midp(sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_15839,c_5884]) ).
cnf(c_15965,plain,
cong(sK3,sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_15943,c_190]) ).
cnf(c_15978,plain,
perp(sK2,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_15965,c_2885]) ).
cnf(c_29285,plain,
( cong(sK2,sK3,sK2,sK3)
| ~ midp(sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_15978,c_203]) ).
cnf(c_16107,plain,
cong(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_6439,c_29285]) ).
cnf(c_16129,plain,
midp(sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_16107,c_3926]) ).
cnf(c_18348,plain,
midp(sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_15905,c_16129]) ).
cnf(c_18374,plain,
midp(sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_18348,c_242]) ).
cnf(c_18383,plain,
cong(sK2,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_18348,c_190]) ).
cnf(c_18476,plain,
cong(sK2,sK4,sK2,sK2),
inference(resolve,[status(thm)],[c_18374,c_190]) ).
cnf(c_18536,plain,
cyclic(sK2,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_18383,c_315]) ).
cnf(c_18677,plain,
cyclic(sK4,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_18476,c_315]) ).
cnf(c_18815,plain,
cyclic(sK4,sK2,sK4,sK4),
inference(resolve,[status(thm)],[c_18536,c_238]) ).
cnf(c_18861,plain,
cyclic(sK2,sK4,sK2,sK2),
inference(resolve,[status(thm)],[c_18677,c_238]) ).
cnf(c_18928,plain,
cyclic(sK4,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_18815,c_239]) ).
cnf(c_18987,plain,
cyclic(sK2,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_18861,c_239]) ).
cnf(c_19038,plain,
cyclic(sK4,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_18928,c_240]) ).
cnf(c_19039,plain,
( cyclic(sK4,sK2,A,sK4)
| ~ cyclic(sK4,sK4,sK2,A) ),
inference(resolve,[status(thm)],[c_18928,c_237]) ).
cnf(c_19068,plain,
cyclic(sK2,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_18987,c_240]) ).
cnf(c_19082,plain,
cyclic(sK4,sK4,sK2,sK2),
inference(resolve,[status(thm)],[c_19038,c_301]) ).
cnf(c_19090,plain,
( cyclic(sK4,sK4,sK2,A)
| ~ cyclic(sK4,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_19038,c_237]) ).
cnf(c_19111,plain,
cyclic(sK2,sK2,sK4,sK4),
inference(resolve,[status(thm)],[c_19068,c_301]) ).
cnf(c_19146,plain,
cyclic(sK4,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_19082,c_239]) ).
cnf(c_19148,plain,
( cyclic(sK4,sK2,sK2,A)
| ~ cyclic(sK4,sK4,sK2,A) ),
inference(resolve,[status(thm)],[c_19082,c_237]) ).
cnf(c_19171,plain,
( cyclic(sK2,sK4,A,sK4)
| ~ cyclic(sK2,sK2,sK4,A) ),
inference(resolve,[status(thm)],[c_19111,c_237]) ).
cnf(c_19192,plain,
cyclic(sK4,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_19146,c_240]) ).
cnf(c_19213,plain,
( cyclic(sK2,sK2,sK4,A)
| ~ cyclic(sK4,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_19192,c_237]) ).
cnf(c_22310,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_7154,c_299]) ).
cnf(c_22312,plain,
eqangle(A,B,sK4,sK4,A,B,sK4,sK4),
inference(resolve,[status(thm)],[c_7154,c_235]) ).
cnf(c_22319,plain,
cyclic(A,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_22312,c_2774]) ).
cnf(c_22327,plain,
cyclic(sK4,A,sK4,sK4),
inference(resolve,[status(thm)],[c_22319,c_238]) ).
cnf(c_22330,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_22327,c_22310]) ).
cnf(c_22342,plain,
cyclic(sK4,sK4,A,sK4),
inference(resolve,[status(thm)],[c_22327,c_239]) ).
cnf(c_22354,plain,
cyclic(sK4,sK4,sK4,A),
inference(resolve,[status(thm)],[c_22342,c_240]) ).
cnf(c_22358,plain,
cyclic(sK4,sK4,sK2,A),
inference(resolve,[status(thm)],[c_22354,c_19090]) ).
cnf(c_22372,plain,
cyclic(sK4,sK2,sK2,A),
inference(resolve,[status(thm)],[c_22358,c_19148]) ).
cnf(c_22378,plain,
cyclic(sK4,sK2,A,sK4),
inference(resolve,[status(thm)],[c_22358,c_19039]) ).
cnf(c_22398,plain,
cyclic(sK2,sK2,sK4,A),
inference(resolve,[status(thm)],[c_22372,c_19213]) ).
cnf(c_22433,plain,
cyclic(sK2,sK4,A,sK4),
inference(resolve,[status(thm)],[c_22398,c_19171]) ).
cnf(c_29286,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK4,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_22354,c_237]) ).
cnf(c_22587,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_22354,c_29286]) ).
cnf(c_29287,plain,
( cyclic(sK4,sK2,A,B)
| ~ cyclic(sK4,sK4,sK2,A) ),
inference(resolve,[status(thm)],[c_22358,c_237]) ).
cnf(c_22600,plain,
cyclic(sK4,sK2,A,B),
inference(resolve,[status(thm)],[c_22587,c_29287]) ).
cnf(c_29288,plain,
( cyclic(sK2,A,sK4,B)
| ~ cyclic(sK4,sK2,A,B) ),
inference(resolve,[status(thm)],[c_22378,c_237]) ).
cnf(c_22741,plain,
cyclic(sK2,A,sK4,B),
inference(resolve,[status(thm)],[c_22600,c_29288]) ).
cnf(c_29289,plain,
( cyclic(sK2,sK4,A,B)
| ~ cyclic(sK2,sK2,sK4,A) ),
inference(resolve,[status(thm)],[c_22398,c_237]) ).
cnf(c_22796,plain,
cyclic(sK2,sK4,A,B),
inference(resolve,[status(thm)],[c_22741,c_29289]) ).
cnf(c_29290,plain,
( cyclic(sK4,A,sK4,B)
| ~ cyclic(sK2,sK4,A,B) ),
inference(resolve,[status(thm)],[c_22433,c_237]) ).
cnf(c_22881,plain,
cyclic(sK4,A,sK4,B),
inference(resolve,[status(thm)],[c_22796,c_29290]) ).
cnf(c_22887,plain,
cong(sK4,A,sK4,A),
inference(resolve,[status(thm)],[c_22881,c_22330]) ).
cnf(c_29291,plain,
( perp(sK4,sK4,A,B)
| ~ cong(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_22887,c_202]) ).
cnf(c_25089,plain,
perp(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_22887,c_29291]) ).
cnf(c_29277,plain,
perp(A,B,sK4,sK4),
inference(resolve,[status(thm)],[c_25089,c_245]) ).
cnf(c_29292,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK4,sK4) ),
inference(resolve,[status(thm)],[c_25089,c_244]) ).
cnf(c_29278,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_29277,c_29292]) ).
cnf(c_29293,plain,
( perp(A,B,C,D)
| ~ para(A,B,sK4,sK4) ),
inference(resolve,[status(thm)],[c_25089,c_243]) ).
cnf(c_29279,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_29278,c_29293]) ).
cnf(c_29280,plain,
$false,
inference(resolve,[status(thm)],[c_29279,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO604+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.48 % Computer : n013.cluster.edu
% 0.09/0.48 % Model : x86_64 x86_64
% 0.09/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.48 % Memory : 8046.5625MB
% 0.09/0.48 % OS : Linux 6.8.0-71-generic
% 0.09/0.48 % CPULimit : 300
% 0.09/0.48 % WCLimit : 300
% 0.09/0.48 % DateTime : Fri Sep 25 13:43:52 UTC 2026
% 0.09/0.49 % CPUTime :
% 0.09/0.49 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.49 % Process 547814 was started by sandbox on n013,
% 0.09/0.49 % Fri Sep 25 13:43:52 2026
% 0.09/0.49 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.51
% 0.09/0.51 % From the command line: assign(max_seconds, 300).
% 95.69/13.60
% 95.69/13.60 % given #500 (T,wt=9): 10245 coll(c7,c7,c1). [resolve(10023,a,306,a)].
% 95.69/13.60
% 95.69/13.60 % given #1000 (T,wt=13): 11403 -coll(c7,c5,A) | coll(A,c4,c7). [resolve(11385,a,250,b)].
% 95.69/13.60
% 95.69/13.60 % given #1500 (W,wt=10): 17312 perp(c1,c6,c1,c6). [resolve(16900,a,246,a)].
% 95.69/13.60
% 95.69/13.60 % given #2000 (T,wt=14): 4182 eqratio(c3,c2,c2,c3,c3,c2,c2,c3). [resolve(3200,a,291,b),unit_del(a,641)].
% 95.69/13.60
% 95.69/13.60 % given #2500 (T,wt=10): 23560 para(c5,c2,c7,c2). [resolve(22989,a,6115,a)].
% 95.69/13.60
% 95.69/13.60 % SZS status Theorem for theBenchmark
% 95.69/13.60
% 95.69/13.60 % Proof 1 at 3.78 (+ 1.20) seconds.
% 95.69/13.60 % Length of proof is 183.
% 95.69/13.60 % Level of proof is 39.
% 95.69/13.60 % Maximum clause weight is 34.000.
% 95.69/13.60 % Given clauses 2790.
% 95.69/13.60
% 95.69/13.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------