%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO618+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 : n014.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 07:18:14 AM UTC 2026
% Result : Theorem 14.29s 2.51s
% Output : CNFRefutation 14.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 21
% Syntax : Number of formulae : 122 ( 48 unt; 0 def)
% Number of atoms : 253 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 213 ( 82 ~; 78 |; 31 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 315 ( 36 sgn 117 !; 8 ?)
% 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(ruleD11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('theBenchmark.p',ruleD11) ).
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(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(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(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(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(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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('theBenchmark.p',ruleD73) ).
fof(ruleX14,axiom,
! [A,B,C,D] :
? [O] :
( ( cyclic(A,B,C,D)
& perp(A,C,C,B) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleX14) ).
fof(exemplo6GDDFULL618080,conjecture,
! [A,B,C,U,O,T] :
( ( coll(T,B,C)
& perp(A,O,A,T)
& circle(O,A,B,C)
& coll(U,B,C)
& eqangle(U,A,A,C,U,A,A,B) )
=> cong(T,A,T,U) ),
file('theBenchmark.p',exemplo6GDDFULL618080) ).
fof(exemplo6GDDFULL618080_neg,negated_conjecture,
~ ! [A,B,C,U,O,T] :
( ( coll(T,B,C)
& perp(A,O,A,T)
& circle(O,A,B,C)
& coll(U,B,C)
& eqangle(U,A,A,C,U,A,A,B) )
=> cong(T,A,T,U) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618080]) ).
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_90,plain,
! [A,B,C,D] :
? [O] :
( circle(O,A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(fof_nnf,[status(thm)],[ruleX14]) ).
fof(sk_ruleX14,plain,
! [A,B,C,D] :
( circle(sK0(A,B,C,D),A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(O,sK0(A,B,C,D))],[nnf_90]) ).
cnf(c_108,plain,
( circle(sK0(A,C,B,D),A,C,B)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(split_conjunct,[status(thm)],[sk_ruleX14]) ).
cnf(c_127,plain,
( midp(E,C,B)
| ~ eqangle(A,C,A,B,sK0(A,C,B,D),C,sK0(A,C,B,D),E)
| ~ coll(E,C,B)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(resolve,[status(thm)],[c_108,c_100]) ).
fof(nnf_95,plain,
? [A,B,C,U,O,T] :
( ~ cong(T,A,T,U)
& coll(T,B,C)
& perp(A,O,A,T)
& circle(O,A,B,C)
& coll(U,B,C)
& eqangle(U,A,A,C,U,A,A,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618080_neg]) ).
fof(sk_exemplo6GDDFULL618080_neg,plain,
( ~ cong(sK1,sK2,sK1,sK3)
& coll(sK1,sK4,sK5)
& perp(sK2,sK6,sK2,sK1)
& circle(sK6,sK2,sK4,sK5)
& coll(sK3,sK4,sK5)
& eqangle(sK3,sK2,sK2,sK5,sK3,sK2,sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK5,sK4,sK6,sK1]),skolemize(A,sK2),skolemize(B,sK4),skolemize(C,sK5),skolemize(U,sK3),skolemize(O,sK6),skolemize(T,sK1)],[nnf_95]) ).
cnf(c_162,negated_conjecture,
~ cong(sK1,sK2,sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618080_neg]) ).
cnf(c_165,negated_conjecture,
coll(sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618080_neg]) ).
cnf(c_166,negated_conjecture,
eqangle(sK3,sK2,sK2,sK5,sK3,sK2,sK2,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618080_neg]) ).
cnf(c_199,plain,
( para(A,B,C,D)
| ~ para(E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD73]) ).
cnf(c_205,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_214,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_216,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_223,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_224,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_226,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_227,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_228,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_246,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_248,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_250,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_251,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_252,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_253,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_255,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_263,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_265,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_313,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,E,D,E,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_223]) ).
cnf(c_314,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_250]) ).
cnf(c_319,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_263]) ).
cnf(c_438,plain,
eqangle(sK3,sK2,sK3,sK2,sK2,sK5,sK2,sK4),
inference(resolve,[status(thm)],[c_246,c_166]) ).
cnf(c_440,plain,
eqangle(sK2,sK5,sK3,sK2,sK2,sK4,sK3,sK2),
inference(resolve,[status(thm)],[c_248,c_166]) ).
cnf(c_458,plain,
coll(sK3,sK5,sK4),
inference(resolve,[status(thm)],[c_265,c_165]) ).
cnf(c_549,plain,
coll(sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_458,c_319]) ).
cnf(c_833,plain,
( coll(A,sK3,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_549,c_263]) ).
cnf(c_834,plain,
( coll(sK3,A,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_549,c_263]) ).
cnf(c_3350,plain,
( para(sK3,sK2,sK3,sK2)
| ~ para(sK2,sK5,sK2,sK4) ),
inference(resolve,[status(thm)],[c_438,c_199]) ).
cnf(c_3393,plain,
para(sK2,sK5,sK2,sK4),
inference(resolve,[status(thm)],[c_440,c_228]) ).
cnf(c_3396,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_3393,c_3350]) ).
cnf(c_3410,plain,
coll(sK2,sK5,sK4),
inference(resolve,[status(thm)],[c_3393,c_205]) ).
cnf(c_3434,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_3410,c_319]) ).
cnf(c_3476,plain,
coll(sK3,sK2,sK4),
inference(resolve,[status(thm)],[c_3434,c_834]) ).
cnf(c_3477,plain,
coll(sK2,sK3,sK4),
inference(resolve,[status(thm)],[c_3434,c_833]) ).
cnf(c_3804,plain,
coll(sK3,sK4,sK2),
inference(resolve,[status(thm)],[c_3476,c_265]) ).
cnf(c_3845,plain,
coll(sK2,sK4,sK3),
inference(resolve,[status(thm)],[c_3477,c_265]) ).
cnf(c_4245,plain,
coll(sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_3804,c_319]) ).
cnf(c_4293,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_3845,c_319]) ).
cnf(c_5366,plain,
coll(sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_4245,c_265]) ).
cnf(c_5446,plain,
( cyclic(A,sK2,sK3,sK3)
| ~ eqangle(sK3,A,sK3,sK2,sK3,A,sK3,sK2) ),
inference(resolve,[status(thm)],[c_4293,c_224]) ).
cnf(c_5916,plain,
( midp(sK2,sK3,sK2)
| ~ eqangle(A,sK3,A,sK2,sK0(A,sK3,sK2,B),sK3,sK0(A,sK3,sK2,B),sK2)
| ~ cyclic(A,sK3,sK2,B)
| ~ perp(A,sK2,sK2,sK3) ),
inference(resolve,[status(thm)],[c_5366,c_127]) ).
cnf(c_6057,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_3396,c_227]) ).
cnf(c_6571,plain,
( cong(sK2,sK3,sK2,sK3)
| ~ cyclic(sK2,sK3,sK3,sK3)
| ~ cyclic(sK2,sK3,sK3,sK2) ),
inference(resolve,[status(thm)],[c_6057,c_313]) ).
cnf(c_6574,plain,
eqangle(A,B,sK3,sK2,A,B,sK3,sK2),
inference(resolve,[status(thm)],[c_6057,c_248]) ).
cnf(c_6577,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,sK3)
| ~ cyclic(sK2,A,sK3,A)
| ~ cyclic(sK2,A,sK3,sK2) ),
inference(resolve,[status(thm)],[c_6057,c_223]) ).
cnf(c_6585,plain,
cyclic(A,sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_6574,c_5446]) ).
cnf(c_6612,plain,
cyclic(sK2,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_6585,c_314]) ).
cnf(c_6620,plain,
cyclic(A,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_6585,c_252]) ).
cnf(c_6621,plain,
cyclic(sK2,A,sK3,sK3),
inference(resolve,[status(thm)],[c_6585,c_251]) ).
cnf(c_6648,plain,
( cong(sK2,sK3,sK2,sK3)
| ~ cyclic(sK2,sK3,sK3,sK2) ),
inference(resolve,[status(thm)],[c_6621,c_6571]) ).
cnf(c_6659,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,A)
| ~ cyclic(sK2,A,sK3,sK2) ),
inference(resolve,[status(thm)],[c_6621,c_6577]) ).
cnf(c_6669,plain,
( cyclic(sK3,sK3,A,sK3)
| ~ cyclic(sK2,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_6612,c_250]) ).
cnf(c_6700,plain,
cyclic(A,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_6620,c_253]) ).
cnf(c_6701,plain,
cyclic(sK3,A,sK2,sK3),
inference(resolve,[status(thm)],[c_6620,c_251]) ).
cnf(c_6729,plain,
cong(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_6700,c_6648]) ).
cnf(c_7130,plain,
cyclic(sK2,sK3,A,sK3),
inference(resolve,[status(thm)],[c_6621,c_252]) ).
cnf(c_7477,plain,
cyclic(sK3,A,sK3,sK2),
inference(resolve,[status(thm)],[c_6700,c_251]) ).
cnf(c_7522,plain,
cyclic(sK3,sK2,A,sK3),
inference(resolve,[status(thm)],[c_6701,c_252]) ).
cnf(c_7523,plain,
( cyclic(A,sK2,B,sK3)
| ~ cyclic(sK3,A,sK2,B) ),
inference(resolve,[status(thm)],[c_6701,c_250]) ).
cnf(c_7615,plain,
( perp(A,sK2,sK2,sK3)
| ~ cyclic(sK2,sK2,A,sK3)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_6729,c_214]) ).
cnf(c_8346,plain,
cyclic(sK2,sK3,sK3,A),
inference(resolve,[status(thm)],[c_7130,c_253]) ).
cnf(c_8378,plain,
cyclic(sK3,sK3,A,sK3),
inference(resolve,[status(thm)],[c_8346,c_6669]) ).
cnf(c_9002,plain,
cyclic(sK3,sK3,A,sK2),
inference(resolve,[status(thm)],[c_7477,c_252]) ).
cnf(c_9004,plain,
( cyclic(A,sK3,sK2,B)
| ~ cyclic(sK3,A,sK3,B) ),
inference(resolve,[status(thm)],[c_7477,c_250]) ).
cnf(c_9041,plain,
( cyclic(sK2,A,sK3,B)
| ~ cyclic(sK3,sK2,A,B) ),
inference(resolve,[status(thm)],[c_7522,c_250]) ).
cnf(c_17742,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK2,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_8346,c_250]) ).
cnf(c_9320,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_8346,c_17742]) ).
cnf(c_17743,plain,
( cyclic(sK3,A,sK3,B)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_8378,c_250]) ).
cnf(c_9441,plain,
cyclic(sK3,A,sK3,B),
inference(resolve,[status(thm)],[c_9320,c_17743]) ).
cnf(c_9473,plain,
cyclic(A,sK3,sK2,B),
inference(resolve,[status(thm)],[c_9441,c_9004]) ).
cnf(c_9478,plain,
( midp(sK2,sK3,sK2)
| ~ eqangle(A,sK3,A,sK2,sK0(A,sK3,sK2,B),sK3,sK0(A,sK3,sK2,B),sK2)
| ~ perp(A,sK2,sK2,sK3) ),
inference(resolve,[status(thm)],[c_9473,c_5916]) ).
cnf(c_17744,plain,
( cyclic(sK3,A,sK2,B)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_9002,c_250]) ).
cnf(c_9687,plain,
cyclic(sK3,A,sK2,B),
inference(resolve,[status(thm)],[c_9320,c_17744]) ).
cnf(c_9717,plain,
cyclic(A,sK2,B,sK3),
inference(resolve,[status(thm)],[c_9687,c_7523]) ).
cnf(c_9744,plain,
( perp(A,sK2,sK2,sK3)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_9717,c_7615]) ).
cnf(c_17745,plain,
( cyclic(sK3,A,B,C)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_9320,c_250]) ).
cnf(c_10366,plain,
cyclic(sK3,A,B,C),
inference(resolve,[status(thm)],[c_9320,c_17745]) ).
cnf(c_10394,plain,
cyclic(sK2,A,sK3,B),
inference(resolve,[status(thm)],[c_10366,c_9041]) ).
cnf(c_17746,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,A) ),
inference(resolve,[status(thm)],[c_10394,c_6659]) ).
cnf(c_10400,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_10394,c_17746]) ).
cnf(c_10415,plain,
perp(A,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_10400,c_9744]) ).
cnf(c_10445,plain,
( midp(sK2,sK3,sK2)
| ~ eqangle(A,sK3,A,sK2,sK0(A,sK3,sK2,B),sK3,sK0(A,sK3,sK2,B),sK2) ),
inference(resolve,[status(thm)],[c_10415,c_9478]) ).
cnf(c_17747,plain,
( cyclic(A,B,C,D)
| ~ cyclic(sK3,A,B,C) ),
inference(resolve,[status(thm)],[c_10366,c_250]) ).
cnf(c_17446,plain,
cyclic(A,B,C,D),
inference(resolve,[status(thm)],[c_10366,c_17747]) ).
cnf(c_17483,plain,
eqangle(A,B,A,C,D,B,D,C),
inference(resolve,[status(thm)],[c_17446,c_226]) ).
cnf(c_17495,plain,
midp(sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_17483,c_10445]) ).
cnf(c_17577,plain,
midp(sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_17495,c_255]) ).
cnf(c_17748,plain,
( cong(A,sK2,A,sK3)
| ~ perp(A,sK2,sK2,sK3) ),
inference(resolve,[status(thm)],[c_17577,c_216]) ).
cnf(c_17740,plain,
cong(A,sK2,A,sK3),
inference(resolve,[status(thm)],[c_10415,c_17748]) ).
cnf(c_17741,plain,
$false,
inference(resolve,[status(thm)],[c_17740,c_162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO618+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.40 % Computer : n014.cluster.edu
% 0.09/0.40 % Model : x86_64 x86_64
% 0.09/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.40 % Memory : 8046.5625MB
% 0.09/0.40 % OS : Linux 6.8.0-71-generic
% 0.09/0.40 % CPULimit : 300
% 0.09/0.40 % WCLimit : 300
% 0.09/0.40 % DateTime : Fri Sep 25 13:45:03 UTC 2026
% 0.09/0.40 % CPUTime :
% 0.09/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.40 % Process 358221 was started by sandbox on n014,
% 0.09/0.40 % Fri Sep 25 13:45:03 2026
% 0.09/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.43
% 0.09/0.43 % From the command line: assign(max_seconds, 300).
% 14.29/2.51
% 14.29/2.51 % given #500 (W,wt=9): 4525 coll(c4,c3,c1). [resolve(3989,a,265,a)].
% 14.29/2.51
% 14.29/2.51 % given #1000 (T,wt=9): 13153 coll(c5,c1,c5). [resolve(13116,a,264,a)].
% 14.29/2.51
% 14.29/2.51 % SZS status Theorem for theBenchmark
% 14.29/2.51
% 14.29/2.51 % Proof 1 at 1.45 (+ 0.44) seconds.
% 14.29/2.51 % Length of proof is 110.
% 14.29/2.51 % Level of proof is 23.
% 14.29/2.51 % Maximum clause weight is 45.000.
% 14.29/2.51 % Given clauses 1124.
% 14.29/2.51
% 14.29/2.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------