%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO634+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 07:18:16 AM UTC 2026
% Result : Theorem 97.35s 13.47s
% Output : CNFRefutation 97.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 29
% Syntax : Number of formulae : 199 ( 95 unt; 0 def)
% Number of atoms : 395 ( 0 equ)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 302 ( 106 ~; 102 |; 64 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 12 con; 0-0 aty)
% Number of variables : 388 ( 42 sgn 146 !; 12 ?)
% 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(exemplo6GDDFULL8110997,conjecture,
! [A,B,C,O,A1,P,Q,S,D,G,NWPNT1,NWPNT2] :
( ( coll(G,A,B)
& perp(G,Q,A,B)
& coll(D,B,C)
& perp(D,Q,B,C)
& coll(S,A,Q)
& coll(S,B,C)
& circle(O,A,Q,NWPNT2)
& eqangle(Q,A,A,B,C,A,A,A1)
& coll(P,A,A1)
& circle(O,A,P,NWPNT1)
& midp(A1,C,B)
& circle(O,A,B,C) )
=> perp(D,G,P,A) ),
file('theBenchmark.p',exemplo6GDDFULL8110997) ).
fof(exemplo6GDDFULL8110997_neg,negated_conjecture,
~ ! [A,B,C,O,A1,P,Q,S,D,G,NWPNT1,NWPNT2] :
( ( coll(G,A,B)
& perp(G,Q,A,B)
& coll(D,B,C)
& perp(D,Q,B,C)
& coll(S,A,Q)
& coll(S,B,C)
& circle(O,A,Q,NWPNT2)
& eqangle(Q,A,A,B,C,A,A,A1)
& coll(P,A,A1)
& circle(O,A,P,NWPNT1)
& midp(A1,C,B)
& circle(O,A,B,C) )
=> perp(D,G,P,A) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL8110997]) ).
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_187,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,O,A1,P,Q,S,D,G,NWPNT1,NWPNT2] :
( ~ perp(D,G,P,A)
& coll(G,A,B)
& perp(G,Q,A,B)
& coll(D,B,C)
& perp(D,Q,B,C)
& coll(S,A,Q)
& coll(S,B,C)
& circle(O,A,Q,NWPNT2)
& eqangle(Q,A,A,B,C,A,A,A1)
& coll(P,A,A1)
& circle(O,A,P,NWPNT1)
& midp(A1,C,B)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL8110997_neg]) ).
fof(sk_exemplo6GDDFULL8110997_neg,plain,
( ~ perp(sK0,sK1,sK2,sK3)
& coll(sK1,sK3,sK4)
& perp(sK1,sK10,sK3,sK4)
& coll(sK0,sK4,sK6)
& perp(sK0,sK10,sK4,sK6)
& coll(sK5,sK3,sK10)
& coll(sK5,sK4,sK6)
& circle(sK8,sK3,sK10,sK11)
& eqangle(sK10,sK3,sK3,sK4,sK6,sK3,sK3,sK7)
& coll(sK2,sK3,sK7)
& circle(sK8,sK3,sK2,sK9)
& midp(sK7,sK6,sK4)
& circle(sK8,sK3,sK4,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK3,sK4,sK6,sK7,sK2,sK9,sK10,sK11,sK5,sK0,sK1]),skolemize(A,sK3),skolemize(B,sK4),skolemize(C,sK6),skolemize(O,sK8),skolemize(A1,sK7),skolemize(P,sK2),skolemize(Q,sK10),skolemize(S,sK5),skolemize(D,sK0),skolemize(G,sK1),skolemize(NWPNT1,sK9),skolemize(NWPNT2,sK11)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ perp(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110997_neg]) ).
cnf(c_193,negated_conjecture,
coll(sK1,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110997_neg]) ).
cnf(c_198,negated_conjecture,
coll(sK5,sK4,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110997_neg]) ).
cnf(c_201,negated_conjecture,
midp(sK7,sK6,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110997_neg]) ).
cnf(c_237,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_238,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_239,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_242,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_250,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_251,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_257,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_258,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_259,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_261,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_262,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_283,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_285,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_286,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_287,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_288,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_289,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_290,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_291,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_292,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_293,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_296,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_297,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_298,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_299,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_300,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_315,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_187]) ).
cnf(c_345,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_257]) ).
cnf(c_346,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_258]) ).
cnf(c_347,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_258]) ).
cnf(c_349,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_285]) ).
cnf(c_350,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_289]) ).
cnf(c_354,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_298]) ).
cnf(c_362,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_346]) ).
cnf(c_363,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_350]) ).
cnf(c_634,plain,
coll(sK7,sK6,sK4),
inference(resolve,[status(thm)],[c_237,c_201]) ).
cnf(c_635,plain,
cong(sK7,sK6,sK7,sK4),
inference(resolve,[status(thm)],[c_238,c_201]) ).
cnf(c_672,plain,
( para(sK7,A,sK4,B)
| ~ midp(A,sK6,B) ),
inference(resolve,[status(thm)],[c_257,c_201]) ).
cnf(c_685,plain,
midp(sK7,sK4,sK6),
inference(resolve,[status(thm)],[c_290,c_201]) ).
cnf(c_722,plain,
coll(sK4,sK5,sK6),
inference(resolve,[status(thm)],[c_299,c_198]) ).
cnf(c_769,plain,
coll(sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_354,c_198]) ).
cnf(c_772,plain,
coll(sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_354,c_193]) ).
cnf(c_30426,plain,
( ~ cong(sK7,sK6,sK7,sK4)
| perp(sK6,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_634,c_315]) ).
cnf(c_785,plain,
perp(sK6,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_635,c_30426]) ).
cnf(c_786,plain,
coll(sK7,sK4,sK6),
inference(resolve,[status(thm)],[c_634,c_300]) ).
cnf(c_787,plain,
coll(sK6,sK7,sK4),
inference(resolve,[status(thm)],[c_634,c_299]) ).
cnf(c_825,plain,
cong(sK7,sK4,sK7,sK6),
inference(resolve,[status(thm)],[c_685,c_238]) ).
cnf(c_897,plain,
coll(sK6,sK6,sK4),
inference(resolve,[status(thm)],[c_722,c_354]) ).
cnf(c_1291,plain,
coll(sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_769,c_300]) ).
cnf(c_1408,plain,
coll(sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_772,c_300]) ).
cnf(c_1471,plain,
coll(sK6,sK6,sK7),
inference(resolve,[status(thm)],[c_786,c_354]) ).
cnf(c_30427,plain,
( ~ cong(sK7,sK4,sK7,sK6)
| perp(sK4,sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_786,c_315]) ).
cnf(c_1483,plain,
perp(sK4,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_825,c_30427]) ).
cnf(c_1503,plain,
coll(sK4,sK4,sK6),
inference(resolve,[status(thm)],[c_787,c_354]) ).
cnf(c_1632,plain,
coll(sK6,sK4,sK6),
inference(resolve,[status(thm)],[c_897,c_300]) ).
cnf(c_2379,plain,
coll(sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_1291,c_354]) ).
cnf(c_2625,plain,
coll(sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_1408,c_354]) ).
cnf(c_2768,plain,
coll(sK6,sK7,sK6),
inference(resolve,[status(thm)],[c_1471,c_300]) ).
cnf(c_2842,plain,
coll(sK4,sK6,sK4),
inference(resolve,[status(thm)],[c_1503,c_300]) ).
cnf(c_3070,plain,
coll(sK4,sK6,sK6),
inference(resolve,[status(thm)],[c_1632,c_299]) ).
cnf(c_3961,plain,
( midp(sK6,sK6,sK6)
| ~ cong(sK6,sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_2379,c_239]) ).
cnf(c_4288,plain,
( cyclic(A,sK4,sK4,sK4)
| ~ eqangle(sK4,A,sK4,sK4,sK4,A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_2625,c_259]) ).
cnf(c_4292,plain,
( midp(sK4,sK4,sK4)
| ~ cong(sK4,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_2625,c_239]) ).
cnf(c_4480,plain,
( ~ cong(sK6,sK7,sK6,sK6)
| perp(sK7,sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_2768,c_315]) ).
cnf(c_4481,plain,
coll(sK7,sK6,sK6),
inference(resolve,[status(thm)],[c_2768,c_299]) ).
cnf(c_4555,plain,
coll(sK6,sK4,sK4),
inference(resolve,[status(thm)],[c_2842,c_299]) ).
cnf(c_4733,plain,
( midp(sK4,sK6,sK6)
| ~ cong(sK4,sK6,sK4,sK6) ),
inference(resolve,[status(thm)],[c_3070,c_239]) ).
cnf(c_5775,plain,
( midp(sK7,sK6,sK6)
| ~ cong(sK7,sK6,sK7,sK6) ),
inference(resolve,[status(thm)],[c_4481,c_239]) ).
cnf(c_5815,plain,
( midp(sK6,sK4,sK4)
| ~ cong(sK6,sK4,sK6,sK4) ),
inference(resolve,[status(thm)],[c_4555,c_239]) ).
cnf(c_6191,plain,
cyclic(sK6,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_635,c_363]) ).
cnf(c_6438,plain,
( cong(sK6,sK4,sK6,sK4)
| ~ midp(sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_785,c_251]) ).
cnf(c_6530,plain,
cyclic(sK4,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_825,c_363]) ).
cnf(c_6645,plain,
( cong(sK4,sK6,sK4,sK6)
| ~ midp(sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_1483,c_251]) ).
cnf(c_6678,plain,
cyclic(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_6191,c_349]) ).
cnf(c_6848,plain,
cyclic(sK6,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_6530,c_349]) ).
cnf(c_6895,plain,
( cong(sK4,sK4,sK4,sK4)
| ~ eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_6678,c_362]) ).
cnf(c_6903,plain,
eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_6678,c_261]) ).
cnf(c_6926,plain,
cong(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_6903,c_6895]) ).
cnf(c_6928,plain,
midp(sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_6926,c_4292]) ).
cnf(c_6929,plain,
cong(sK6,sK4,sK6,sK4),
inference(resolve,[status(thm)],[c_6928,c_6438]) ).
cnf(c_6933,plain,
midp(sK6,sK4,sK4),
inference(resolve,[status(thm)],[c_6929,c_5815]) ).
cnf(c_6945,plain,
para(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_6928,c_345]) ).
cnf(c_7220,plain,
( cong(sK6,sK6,sK6,sK6)
| ~ eqangle(sK6,sK6,sK6,sK6,sK6,sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_6848,c_362]) ).
cnf(c_7228,plain,
eqangle(sK6,sK6,sK6,sK6,sK6,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_6848,c_261]) ).
cnf(c_7251,plain,
cong(sK6,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_7228,c_7220]) ).
cnf(c_7253,plain,
midp(sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_7251,c_3961]) ).
cnf(c_7254,plain,
cong(sK4,sK6,sK4,sK6),
inference(resolve,[status(thm)],[c_7253,c_6645]) ).
cnf(c_7258,plain,
midp(sK4,sK6,sK6),
inference(resolve,[status(thm)],[c_7254,c_4733]) ).
cnf(c_7723,plain,
eqangle(sK4,sK4,A,B,sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_6945,c_262]) ).
cnf(c_19926,plain,
para(sK7,sK4,sK4,sK6),
inference(resolve,[status(thm)],[c_672,c_7258]) ).
cnf(c_19927,plain,
para(sK7,sK6,sK4,sK6),
inference(resolve,[status(thm)],[c_672,c_7253]) ).
cnf(c_19929,plain,
para(sK4,sK6,sK7,sK4),
inference(resolve,[status(thm)],[c_19926,c_296]) ).
cnf(c_19941,plain,
para(sK7,sK6,sK6,sK4),
inference(resolve,[status(thm)],[c_19927,c_297]) ).
cnf(c_19959,plain,
para(sK4,sK6,sK4,sK7),
inference(resolve,[status(thm)],[c_19929,c_297]) ).
cnf(c_19970,plain,
para(sK6,sK4,sK7,sK6),
inference(resolve,[status(thm)],[c_19941,c_296]) ).
cnf(c_19999,plain,
para(sK4,sK7,sK4,sK6),
inference(resolve,[status(thm)],[c_19959,c_296]) ).
cnf(c_30428,plain,
( midp(A,sK7,sK6)
| ~ para(sK4,sK7,sK4,sK6)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_19959,c_242]) ).
cnf(c_20006,plain,
( midp(A,sK7,sK6)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_19999,c_30428]) ).
cnf(c_20010,plain,
para(sK6,sK4,sK6,sK7),
inference(resolve,[status(thm)],[c_19970,c_297]) ).
cnf(c_20057,plain,
para(sK6,sK7,sK6,sK4),
inference(resolve,[status(thm)],[c_20010,c_296]) ).
cnf(c_30429,plain,
( midp(A,sK7,sK4)
| ~ para(sK6,sK7,sK6,sK4)
| ~ midp(A,sK6,sK6) ),
inference(resolve,[status(thm)],[c_20010,c_242]) ).
cnf(c_20064,plain,
( midp(A,sK7,sK4)
| ~ midp(A,sK6,sK6) ),
inference(resolve,[status(thm)],[c_20057,c_30429]) ).
cnf(c_20098,plain,
midp(sK6,sK7,sK6),
inference(resolve,[status(thm)],[c_20006,c_6933]) ).
cnf(c_20116,plain,
cong(sK6,sK7,sK6,sK6),
inference(resolve,[status(thm)],[c_20098,c_238]) ).
cnf(c_20123,plain,
perp(sK7,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_20116,c_4480]) ).
cnf(c_30430,plain,
( cong(sK7,sK6,sK7,sK6)
| ~ midp(sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_20123,c_251]) ).
cnf(c_20227,plain,
cong(sK7,sK6,sK7,sK6),
inference(resolve,[status(thm)],[c_7253,c_30430]) ).
cnf(c_20243,plain,
midp(sK7,sK6,sK6),
inference(resolve,[status(thm)],[c_20227,c_5775]) ).
cnf(c_21940,plain,
midp(sK7,sK7,sK4),
inference(resolve,[status(thm)],[c_20064,c_20243]) ).
cnf(c_21950,plain,
midp(sK7,sK4,sK7),
inference(resolve,[status(thm)],[c_21940,c_290]) ).
cnf(c_21959,plain,
cong(sK7,sK7,sK7,sK4),
inference(resolve,[status(thm)],[c_21940,c_238]) ).
cnf(c_22015,plain,
cong(sK7,sK4,sK7,sK7),
inference(resolve,[status(thm)],[c_21950,c_238]) ).
cnf(c_22054,plain,
cyclic(sK7,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_21959,c_363]) ).
cnf(c_22154,plain,
cyclic(sK4,sK7,sK7,sK7),
inference(resolve,[status(thm)],[c_22015,c_363]) ).
cnf(c_22256,plain,
cyclic(sK4,sK7,sK4,sK4),
inference(resolve,[status(thm)],[c_22054,c_286]) ).
cnf(c_22297,plain,
cyclic(sK7,sK4,sK7,sK7),
inference(resolve,[status(thm)],[c_22154,c_286]) ).
cnf(c_22350,plain,
cyclic(sK4,sK4,sK7,sK4),
inference(resolve,[status(thm)],[c_22256,c_287]) ).
cnf(c_22404,plain,
cyclic(sK7,sK7,sK4,sK7),
inference(resolve,[status(thm)],[c_22297,c_287]) ).
cnf(c_22448,plain,
cyclic(sK4,sK4,sK4,sK7),
inference(resolve,[status(thm)],[c_22350,c_288]) ).
cnf(c_22449,plain,
( cyclic(sK4,sK7,A,sK4)
| ~ cyclic(sK4,sK4,sK7,A) ),
inference(resolve,[status(thm)],[c_22350,c_285]) ).
cnf(c_22473,plain,
cyclic(sK7,sK7,sK7,sK4),
inference(resolve,[status(thm)],[c_22404,c_288]) ).
cnf(c_22487,plain,
cyclic(sK4,sK4,sK7,sK7),
inference(resolve,[status(thm)],[c_22448,c_349]) ).
cnf(c_22489,plain,
( cyclic(sK4,sK4,sK7,A)
| ~ cyclic(sK4,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_22448,c_285]) ).
cnf(c_22504,plain,
cyclic(sK7,sK7,sK4,sK4),
inference(resolve,[status(thm)],[c_22473,c_349]) ).
cnf(c_22521,plain,
cyclic(sK4,sK7,sK4,sK7),
inference(resolve,[status(thm)],[c_22487,c_287]) ).
cnf(c_22523,plain,
( cyclic(sK4,sK7,sK7,A)
| ~ cyclic(sK4,sK4,sK7,A) ),
inference(resolve,[status(thm)],[c_22487,c_285]) ).
cnf(c_22536,plain,
( cyclic(sK7,sK4,A,sK4)
| ~ cyclic(sK7,sK7,sK4,A) ),
inference(resolve,[status(thm)],[c_22504,c_285]) ).
cnf(c_22548,plain,
cyclic(sK4,sK7,sK7,sK4),
inference(resolve,[status(thm)],[c_22521,c_288]) ).
cnf(c_22559,plain,
( cyclic(sK7,sK7,sK4,A)
| ~ cyclic(sK4,sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_22548,c_285]) ).
cnf(c_22824,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_7723,c_347]) ).
cnf(c_22826,plain,
eqangle(A,B,sK4,sK4,A,B,sK4,sK4),
inference(resolve,[status(thm)],[c_7723,c_283]) ).
cnf(c_22833,plain,
cyclic(A,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_22826,c_4288]) ).
cnf(c_22840,plain,
cyclic(sK4,A,sK4,sK4),
inference(resolve,[status(thm)],[c_22833,c_286]) ).
cnf(c_22843,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_22840,c_22824]) ).
cnf(c_22855,plain,
cyclic(sK4,sK4,A,sK4),
inference(resolve,[status(thm)],[c_22840,c_287]) ).
cnf(c_22867,plain,
cyclic(sK4,sK4,sK4,A),
inference(resolve,[status(thm)],[c_22855,c_288]) ).
cnf(c_22871,plain,
cyclic(sK4,sK4,sK7,A),
inference(resolve,[status(thm)],[c_22867,c_22489]) ).
cnf(c_22881,plain,
cyclic(sK4,sK7,sK7,A),
inference(resolve,[status(thm)],[c_22871,c_22523]) ).
cnf(c_22883,plain,
cyclic(sK4,sK7,A,sK4),
inference(resolve,[status(thm)],[c_22871,c_22449]) ).
cnf(c_22899,plain,
cyclic(sK7,sK7,sK4,A),
inference(resolve,[status(thm)],[c_22881,c_22559]) ).
cnf(c_22924,plain,
cyclic(sK7,sK4,A,sK4),
inference(resolve,[status(thm)],[c_22899,c_22536]) ).
cnf(c_30431,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK4,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_22867,c_285]) ).
cnf(c_23004,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_22867,c_30431]) ).
cnf(c_30432,plain,
( cyclic(sK4,sK7,A,B)
| ~ cyclic(sK4,sK4,sK7,A) ),
inference(resolve,[status(thm)],[c_22871,c_285]) ).
cnf(c_23017,plain,
cyclic(sK4,sK7,A,B),
inference(resolve,[status(thm)],[c_23004,c_30432]) ).
cnf(c_30433,plain,
( cyclic(sK7,A,sK4,B)
| ~ cyclic(sK4,sK7,A,B) ),
inference(resolve,[status(thm)],[c_22883,c_285]) ).
cnf(c_23123,plain,
cyclic(sK7,A,sK4,B),
inference(resolve,[status(thm)],[c_23017,c_30433]) ).
cnf(c_30434,plain,
( cyclic(sK7,sK4,A,B)
| ~ cyclic(sK7,sK7,sK4,A) ),
inference(resolve,[status(thm)],[c_22899,c_285]) ).
cnf(c_23174,plain,
cyclic(sK7,sK4,A,B),
inference(resolve,[status(thm)],[c_23123,c_30434]) ).
cnf(c_30435,plain,
( cyclic(sK4,A,sK4,B)
| ~ cyclic(sK7,sK4,A,B) ),
inference(resolve,[status(thm)],[c_22924,c_285]) ).
cnf(c_23259,plain,
cyclic(sK4,A,sK4,B),
inference(resolve,[status(thm)],[c_23174,c_30435]) ).
cnf(c_23265,plain,
cong(sK4,A,sK4,A),
inference(resolve,[status(thm)],[c_23259,c_22843]) ).
cnf(c_30436,plain,
( perp(sK4,sK4,A,B)
| ~ cong(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_23265,c_250]) ).
cnf(c_25828,plain,
perp(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_23265,c_30436]) ).
cnf(c_30422,plain,
perp(A,B,sK4,sK4),
inference(resolve,[status(thm)],[c_25828,c_293]) ).
cnf(c_30437,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK4,sK4) ),
inference(resolve,[status(thm)],[c_25828,c_292]) ).
cnf(c_30423,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_30422,c_30437]) ).
cnf(c_30438,plain,
( perp(A,B,C,D)
| ~ para(A,B,sK4,sK4) ),
inference(resolve,[status(thm)],[c_25828,c_291]) ).
cnf(c_30424,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_30423,c_30438]) ).
cnf(c_30425,plain,
$false,
inference(resolve,[status(thm)],[c_30424,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO634+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n007.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 13:43:38 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1135319 was started by sandbox2 on n007,
% 0.17/0.43 % Fri Sep 25 13:43:38 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 97.35/13.47
% 97.35/13.47 % given #500 (T,wt=9): 9062 coll(c2,c2,c6). [resolve(8873,a,354,a)].
% 97.35/13.47
% 97.35/13.47 % given #1000 (W,wt=13): 1749 -coll(c1,c7,A) | coll(A,c8,c1). [resolve(950,a,298,b)].
% 97.35/13.47
% 97.35/13.47 % given #1500 (T,wt=13): 12520 -coll(c7,c3,A) | coll(c7,A,c7). [resolve(11883,a,298,a)].
% 97.35/13.47
% 97.35/13.47 % given #2000 (T,wt=13): 16814 -coll(c6,c10,A) | coll(c2,A,c6). [resolve(16789,a,298,a)].
% 97.35/13.47
% 97.35/13.47 % given #2500 (W,wt=10): 19926 para(c5,c2,c2,c3). [resolve(672,a,7258,a)].
% 97.35/13.47
% 97.35/13.47 % given #3000 (T,wt=9): 23277 midp(c2,c6,c6). [back_unit_del(9776),unit_del(a,23265)].
% 97.35/13.47
% 97.35/13.47 % given #3500 (T,wt=10): 24647 cong(c6,c5,c6,c3). [resolve(23786,a,238,a)].
% 97.35/13.47
% 97.35/13.47 % SZS status Theorem for theBenchmark
% 97.35/13.47
% 97.35/13.47 % Proof 1 at 3.60 (+ 1.11) seconds.
% 97.35/13.47 % Length of proof is 183.
% 97.35/13.47 % Level of proof is 39.
% 97.35/13.47 % Maximum clause weight is 34.000.
% 97.35/13.47 % Given clauses 3649.
% 97.35/13.47
% 97.35/13.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------