%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO642+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 : n016.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 07:18:17 AM UTC 2026
% Result : Theorem 104.81s 14.60s
% Output : CNFRefutation 104.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 29
% Syntax : Number of formulae : 199 ( 95 unt; 0 def)
% Number of atoms : 399 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 306 ( 106 ~; 102 |; 68 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 17 ( 17 usr; 17 con; 0-0 aty)
% Number of variables : 403 ( 42 sgn 156 !; 17 ?)
% 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(exemplo6GDDFULL81109108,conjecture,
! [A,B,O,C,P,D,G,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ( coll(F,C,P)
& coll(F,A,D)
& coll(E,B,P)
& coll(E,A,C)
& coll(G,A,D)
& coll(G,B,P)
& circle(C,B,D,NWPNT8)
& circle(O,A,D,NWPNT7)
& circle(C,B,NWPNT5,NWPNT6)
& circle(O,A,P,NWPNT4)
& circle(O,A,C,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,B,A) )
=> perp(E,F,A,D) ),
file('theBenchmark.p',exemplo6GDDFULL81109108) ).
fof(exemplo6GDDFULL81109108_neg,negated_conjecture,
~ ! [A,B,O,C,P,D,G,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ( coll(F,C,P)
& coll(F,A,D)
& coll(E,B,P)
& coll(E,A,C)
& coll(G,A,D)
& coll(G,B,P)
& circle(C,B,D,NWPNT8)
& circle(O,A,D,NWPNT7)
& circle(C,B,NWPNT5,NWPNT6)
& circle(O,A,P,NWPNT4)
& circle(O,A,C,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,B,A) )
=> perp(E,F,A,D) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL81109108]) ).
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_232,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,O,C,P,D,G,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ~ perp(E,F,A,D)
& coll(F,C,P)
& coll(F,A,D)
& coll(E,B,P)
& coll(E,A,C)
& coll(G,A,D)
& coll(G,B,P)
& circle(C,B,D,NWPNT8)
& circle(O,A,D,NWPNT7)
& circle(C,B,NWPNT5,NWPNT6)
& circle(O,A,P,NWPNT4)
& circle(O,A,C,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,B,A) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL81109108_neg]) ).
fof(sk_exemplo6GDDFULL81109108_neg,plain,
( ~ perp(sK0,sK1,sK2,sK3)
& coll(sK1,sK10,sK6)
& coll(sK1,sK2,sK3)
& coll(sK0,sK5,sK6)
& coll(sK0,sK2,sK10)
& coll(sK4,sK2,sK3)
& coll(sK4,sK5,sK6)
& circle(sK10,sK5,sK3,sK16)
& circle(sK7,sK2,sK3,sK15)
& circle(sK10,sK5,sK13,sK14)
& circle(sK7,sK2,sK6,sK12)
& circle(sK7,sK2,sK10,sK11)
& circle(sK7,sK2,sK8,sK9)
& midp(sK7,sK5,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK5,sK2,sK8,sK9,sK10,sK11,sK6,sK12,sK13,sK14,sK3,sK15,sK16,sK4,sK0,sK1]),skolemize(A,sK2),skolemize(B,sK5),skolemize(O,sK7),skolemize(C,sK10),skolemize(P,sK6),skolemize(D,sK3),skolemize(G,sK4),skolemize(E,sK0),skolemize(F,sK1),skolemize(NWPNT1,sK8),skolemize(NWPNT2,sK9),skolemize(NWPNT3,sK11),skolemize(NWPNT4,sK12),skolemize(NWPNT5,sK13),skolemize(NWPNT6,sK14),skolemize(NWPNT7,sK15),skolemize(NWPNT8,sK16)],[nnf_95]) ).
cnf(c_237,negated_conjecture,
~ perp(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109108_neg]) ).
cnf(c_243,negated_conjecture,
coll(sK4,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109108_neg]) ).
cnf(c_244,negated_conjecture,
midp(sK7,sK5,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109108_neg]) ).
cnf(c_280,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_281,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_282,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_285,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_293,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_294,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_300,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_301,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_302,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_304,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_305,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_326,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_328,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_329,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_330,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_331,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_332,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_333,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_334,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_335,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_336,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_339,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_340,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_341,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_342,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_343,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_358,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_232]) ).
cnf(c_388,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_300]) ).
cnf(c_389,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_301]) ).
cnf(c_390,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_301]) ).
cnf(c_392,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_328]) ).
cnf(c_393,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_332]) ).
cnf(c_397,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_341]) ).
cnf(c_405,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_389]) ).
cnf(c_406,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_393]) ).
cnf(c_766,plain,
coll(sK7,sK5,sK2),
inference(resolve,[status(thm)],[c_280,c_244]) ).
cnf(c_767,plain,
cong(sK7,sK5,sK7,sK2),
inference(resolve,[status(thm)],[c_281,c_244]) ).
cnf(c_811,plain,
( para(sK7,A,sK2,B)
| ~ midp(A,sK5,B) ),
inference(resolve,[status(thm)],[c_300,c_244]) ).
cnf(c_819,plain,
midp(sK7,sK2,sK5),
inference(resolve,[status(thm)],[c_333,c_244]) ).
cnf(c_868,plain,
coll(sK4,sK6,sK5),
inference(resolve,[status(thm)],[c_343,c_243]) ).
cnf(c_923,plain,
coll(sK2,sK2,sK7),
inference(resolve,[status(thm)],[c_766,c_397]) ).
cnf(c_30524,plain,
( ~ cong(sK7,sK5,sK7,sK2)
| perp(sK5,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_766,c_358]) ).
cnf(c_935,plain,
perp(sK5,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_767,c_30524]) ).
cnf(c_936,plain,
coll(sK7,sK2,sK5),
inference(resolve,[status(thm)],[c_766,c_343]) ).
cnf(c_937,plain,
coll(sK5,sK7,sK2),
inference(resolve,[status(thm)],[c_766,c_342]) ).
cnf(c_975,plain,
cong(sK7,sK2,sK7,sK5),
inference(resolve,[status(thm)],[c_819,c_281]) ).
cnf(c_1228,plain,
coll(sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_868,c_397]) ).
cnf(c_1705,plain,
coll(sK2,sK7,sK2),
inference(resolve,[status(thm)],[c_923,c_343]) ).
cnf(c_1729,plain,
coll(sK5,sK5,sK7),
inference(resolve,[status(thm)],[c_936,c_397]) ).
cnf(c_30525,plain,
( ~ cong(sK7,sK2,sK7,sK5)
| perp(sK2,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_936,c_358]) ).
cnf(c_1741,plain,
perp(sK2,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_975,c_30525]) ).
cnf(c_1742,plain,
coll(sK2,sK7,sK5),
inference(resolve,[status(thm)],[c_936,c_342]) ).
cnf(c_1761,plain,
coll(sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_937,c_397]) ).
cnf(c_2198,plain,
coll(sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_1228,c_343]) ).
cnf(c_3160,plain,
coll(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_1705,c_397]) ).
cnf(c_3223,plain,
coll(sK5,sK7,sK5),
inference(resolve,[status(thm)],[c_1729,c_343]) ).
cnf(c_3247,plain,
coll(sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_1742,c_397]) ).
cnf(c_3299,plain,
coll(sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_1761,c_343]) ).
cnf(c_4126,plain,
coll(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_2198,c_397]) ).
cnf(c_5062,plain,
( cyclic(A,sK2,sK2,sK2)
| ~ eqangle(sK2,A,sK2,sK2,sK2,A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_3160,c_302]) ).
cnf(c_5066,plain,
( midp(sK2,sK2,sK2)
| ~ cong(sK2,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_3160,c_282]) ).
cnf(c_5173,plain,
( ~ cong(sK5,sK7,sK5,sK5)
| perp(sK7,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_3223,c_358]) ).
cnf(c_5174,plain,
coll(sK7,sK5,sK5),
inference(resolve,[status(thm)],[c_3223,c_342]) ).
cnf(c_5213,plain,
coll(sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_3247,c_343]) ).
cnf(c_5287,plain,
coll(sK5,sK2,sK2),
inference(resolve,[status(thm)],[c_3299,c_342]) ).
cnf(c_5910,plain,
( midp(sK5,sK5,sK5)
| ~ cong(sK5,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_4126,c_282]) ).
cnf(c_6667,plain,
( midp(sK7,sK5,sK5)
| ~ cong(sK7,sK5,sK7,sK5) ),
inference(resolve,[status(thm)],[c_5174,c_282]) ).
cnf(c_6695,plain,
coll(sK2,sK5,sK5),
inference(resolve,[status(thm)],[c_5213,c_342]) ).
cnf(c_6747,plain,
( midp(sK5,sK2,sK2)
| ~ cong(sK5,sK2,sK5,sK2) ),
inference(resolve,[status(thm)],[c_5287,c_282]) ).
cnf(c_7227,plain,
( midp(sK2,sK5,sK5)
| ~ cong(sK2,sK5,sK2,sK5) ),
inference(resolve,[status(thm)],[c_6695,c_282]) ).
cnf(c_7243,plain,
cyclic(sK5,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_767,c_406]) ).
cnf(c_7418,plain,
( cong(sK5,sK2,sK5,sK2)
| ~ midp(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_935,c_294]) ).
cnf(c_7510,plain,
cyclic(sK2,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_975,c_406]) ).
cnf(c_7641,plain,
( cong(sK2,sK5,sK2,sK5)
| ~ midp(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1741,c_294]) ).
cnf(c_7674,plain,
cyclic(sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_7243,c_392]) ).
cnf(c_7772,plain,
cyclic(sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_7510,c_392]) ).
cnf(c_7819,plain,
( cong(sK2,sK2,sK2,sK2)
| ~ eqangle(sK2,sK2,sK2,sK2,sK2,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_7674,c_405]) ).
cnf(c_7827,plain,
eqangle(sK2,sK2,sK2,sK2,sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_7674,c_304]) ).
cnf(c_7850,plain,
cong(sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_7827,c_7819]) ).
cnf(c_7852,plain,
midp(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_7850,c_5066]) ).
cnf(c_7853,plain,
cong(sK5,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_7852,c_7418]) ).
cnf(c_7857,plain,
midp(sK5,sK2,sK2),
inference(resolve,[status(thm)],[c_7853,c_6747]) ).
cnf(c_7869,plain,
para(sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_7852,c_388]) ).
cnf(c_8079,plain,
( cong(sK5,sK5,sK5,sK5)
| ~ eqangle(sK5,sK5,sK5,sK5,sK5,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_7772,c_405]) ).
cnf(c_8087,plain,
eqangle(sK5,sK5,sK5,sK5,sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_7772,c_304]) ).
cnf(c_8110,plain,
cong(sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_8087,c_8079]) ).
cnf(c_8112,plain,
midp(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_8110,c_5910]) ).
cnf(c_8113,plain,
cong(sK2,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_8112,c_7641]) ).
cnf(c_8117,plain,
midp(sK2,sK5,sK5),
inference(resolve,[status(thm)],[c_8113,c_7227]) ).
cnf(c_8587,plain,
eqangle(sK2,sK2,A,B,sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_7869,c_305]) ).
cnf(c_20114,plain,
para(sK7,sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_811,c_8117]) ).
cnf(c_20115,plain,
para(sK7,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_811,c_8112]) ).
cnf(c_20117,plain,
para(sK2,sK5,sK7,sK2),
inference(resolve,[status(thm)],[c_20114,c_339]) ).
cnf(c_20129,plain,
para(sK7,sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_20115,c_340]) ).
cnf(c_20147,plain,
para(sK2,sK5,sK2,sK7),
inference(resolve,[status(thm)],[c_20117,c_340]) ).
cnf(c_20158,plain,
para(sK5,sK2,sK7,sK5),
inference(resolve,[status(thm)],[c_20129,c_339]) ).
cnf(c_20187,plain,
para(sK2,sK7,sK2,sK5),
inference(resolve,[status(thm)],[c_20147,c_339]) ).
cnf(c_30526,plain,
( midp(A,sK7,sK5)
| ~ para(sK2,sK7,sK2,sK5)
| ~ midp(A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_20147,c_285]) ).
cnf(c_20194,plain,
( midp(A,sK7,sK5)
| ~ midp(A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_20187,c_30526]) ).
cnf(c_20198,plain,
para(sK5,sK2,sK5,sK7),
inference(resolve,[status(thm)],[c_20158,c_340]) ).
cnf(c_20245,plain,
para(sK5,sK7,sK5,sK2),
inference(resolve,[status(thm)],[c_20198,c_339]) ).
cnf(c_30527,plain,
( midp(A,sK7,sK2)
| ~ para(sK5,sK7,sK5,sK2)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_20198,c_285]) ).
cnf(c_20252,plain,
( midp(A,sK7,sK2)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_20245,c_30527]) ).
cnf(c_20286,plain,
midp(sK5,sK7,sK5),
inference(resolve,[status(thm)],[c_20194,c_7857]) ).
cnf(c_20304,plain,
cong(sK5,sK7,sK5,sK5),
inference(resolve,[status(thm)],[c_20286,c_281]) ).
cnf(c_20311,plain,
perp(sK7,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_20304,c_5173]) ).
cnf(c_30528,plain,
( cong(sK7,sK5,sK7,sK5)
| ~ midp(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_20311,c_294]) ).
cnf(c_20415,plain,
cong(sK7,sK5,sK7,sK5),
inference(resolve,[status(thm)],[c_8112,c_30528]) ).
cnf(c_20431,plain,
midp(sK7,sK5,sK5),
inference(resolve,[status(thm)],[c_20415,c_6667]) ).
cnf(c_22143,plain,
midp(sK7,sK7,sK2),
inference(resolve,[status(thm)],[c_20252,c_20431]) ).
cnf(c_22153,plain,
midp(sK7,sK2,sK7),
inference(resolve,[status(thm)],[c_22143,c_333]) ).
cnf(c_22162,plain,
cong(sK7,sK7,sK7,sK2),
inference(resolve,[status(thm)],[c_22143,c_281]) ).
cnf(c_22222,plain,
cong(sK7,sK2,sK7,sK7),
inference(resolve,[status(thm)],[c_22153,c_281]) ).
cnf(c_22261,plain,
cyclic(sK7,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_22162,c_406]) ).
cnf(c_22365,plain,
cyclic(sK2,sK7,sK7,sK7),
inference(resolve,[status(thm)],[c_22222,c_406]) ).
cnf(c_22467,plain,
cyclic(sK2,sK7,sK2,sK2),
inference(resolve,[status(thm)],[c_22261,c_329]) ).
cnf(c_22508,plain,
cyclic(sK7,sK2,sK7,sK7),
inference(resolve,[status(thm)],[c_22365,c_329]) ).
cnf(c_22561,plain,
cyclic(sK2,sK2,sK7,sK2),
inference(resolve,[status(thm)],[c_22467,c_330]) ).
cnf(c_22619,plain,
cyclic(sK7,sK7,sK2,sK7),
inference(resolve,[status(thm)],[c_22508,c_330]) ).
cnf(c_22663,plain,
cyclic(sK2,sK2,sK2,sK7),
inference(resolve,[status(thm)],[c_22561,c_331]) ).
cnf(c_22664,plain,
( cyclic(sK2,sK7,A,sK2)
| ~ cyclic(sK2,sK2,sK7,A) ),
inference(resolve,[status(thm)],[c_22561,c_328]) ).
cnf(c_22688,plain,
cyclic(sK7,sK7,sK7,sK2),
inference(resolve,[status(thm)],[c_22619,c_331]) ).
cnf(c_22702,plain,
cyclic(sK2,sK2,sK7,sK7),
inference(resolve,[status(thm)],[c_22663,c_392]) ).
cnf(c_22704,plain,
( cyclic(sK2,sK2,sK7,A)
| ~ cyclic(sK2,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_22663,c_328]) ).
cnf(c_22719,plain,
cyclic(sK7,sK7,sK2,sK2),
inference(resolve,[status(thm)],[c_22688,c_392]) ).
cnf(c_22736,plain,
cyclic(sK2,sK7,sK2,sK7),
inference(resolve,[status(thm)],[c_22702,c_330]) ).
cnf(c_22738,plain,
( cyclic(sK2,sK7,sK7,A)
| ~ cyclic(sK2,sK2,sK7,A) ),
inference(resolve,[status(thm)],[c_22702,c_328]) ).
cnf(c_22751,plain,
( cyclic(sK7,sK2,A,sK2)
| ~ cyclic(sK7,sK7,sK2,A) ),
inference(resolve,[status(thm)],[c_22719,c_328]) ).
cnf(c_22763,plain,
cyclic(sK2,sK7,sK7,sK2),
inference(resolve,[status(thm)],[c_22736,c_331]) ).
cnf(c_22774,plain,
( cyclic(sK7,sK7,sK2,A)
| ~ cyclic(sK2,sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_22763,c_328]) ).
cnf(c_23001,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_8587,c_390]) ).
cnf(c_23003,plain,
eqangle(A,B,sK2,sK2,A,B,sK2,sK2),
inference(resolve,[status(thm)],[c_8587,c_326]) ).
cnf(c_23010,plain,
cyclic(A,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_23003,c_5062]) ).
cnf(c_23017,plain,
cyclic(sK2,A,sK2,sK2),
inference(resolve,[status(thm)],[c_23010,c_329]) ).
cnf(c_23020,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_23017,c_23001]) ).
cnf(c_23032,plain,
cyclic(sK2,sK2,A,sK2),
inference(resolve,[status(thm)],[c_23017,c_330]) ).
cnf(c_23044,plain,
cyclic(sK2,sK2,sK2,A),
inference(resolve,[status(thm)],[c_23032,c_331]) ).
cnf(c_23048,plain,
cyclic(sK2,sK2,sK7,A),
inference(resolve,[status(thm)],[c_23044,c_22704]) ).
cnf(c_23058,plain,
cyclic(sK2,sK7,sK7,A),
inference(resolve,[status(thm)],[c_23048,c_22738]) ).
cnf(c_23060,plain,
cyclic(sK2,sK7,A,sK2),
inference(resolve,[status(thm)],[c_23048,c_22664]) ).
cnf(c_23076,plain,
cyclic(sK7,sK7,sK2,A),
inference(resolve,[status(thm)],[c_23058,c_22774]) ).
cnf(c_23101,plain,
cyclic(sK7,sK2,A,sK2),
inference(resolve,[status(thm)],[c_23076,c_22751]) ).
cnf(c_30529,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK2,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_23044,c_328]) ).
cnf(c_23191,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_23044,c_30529]) ).
cnf(c_30530,plain,
( cyclic(sK2,sK7,A,B)
| ~ cyclic(sK2,sK2,sK7,A) ),
inference(resolve,[status(thm)],[c_23048,c_328]) ).
cnf(c_23204,plain,
cyclic(sK2,sK7,A,B),
inference(resolve,[status(thm)],[c_23191,c_30530]) ).
cnf(c_30531,plain,
( cyclic(sK7,A,sK2,B)
| ~ cyclic(sK2,sK7,A,B) ),
inference(resolve,[status(thm)],[c_23060,c_328]) ).
cnf(c_23315,plain,
cyclic(sK7,A,sK2,B),
inference(resolve,[status(thm)],[c_23204,c_30531]) ).
cnf(c_30532,plain,
( cyclic(sK7,sK2,A,B)
| ~ cyclic(sK7,sK7,sK2,A) ),
inference(resolve,[status(thm)],[c_23076,c_328]) ).
cnf(c_23366,plain,
cyclic(sK7,sK2,A,B),
inference(resolve,[status(thm)],[c_23315,c_30532]) ).
cnf(c_30533,plain,
( cyclic(sK2,A,sK2,B)
| ~ cyclic(sK7,sK2,A,B) ),
inference(resolve,[status(thm)],[c_23101,c_328]) ).
cnf(c_23451,plain,
cyclic(sK2,A,sK2,B),
inference(resolve,[status(thm)],[c_23366,c_30533]) ).
cnf(c_23457,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_23451,c_23020]) ).
cnf(c_30534,plain,
( perp(sK2,sK2,A,B)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_23457,c_293]) ).
cnf(c_26018,plain,
perp(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_23457,c_30534]) ).
cnf(c_30520,plain,
perp(A,B,sK2,sK2),
inference(resolve,[status(thm)],[c_26018,c_336]) ).
cnf(c_30535,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK2,sK2) ),
inference(resolve,[status(thm)],[c_26018,c_335]) ).
cnf(c_30521,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_30520,c_30535]) ).
cnf(c_30536,plain,
( perp(A,B,C,D)
| ~ para(A,B,sK2,sK2) ),
inference(resolve,[status(thm)],[c_26018,c_334]) ).
cnf(c_30522,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_30521,c_30536]) ).
cnf(c_30523,plain,
$false,
inference(resolve,[status(thm)],[c_30522,c_237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO642+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 13:50:43 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 2518679 was started by sandbox2 on n016,
% 0.14/0.36 % Fri Sep 25 13:50:43 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.39
% 0.14/0.39 % From the command line: assign(max_seconds, 300).
% 104.81/14.60
% 104.81/14.60 % given #500 (W,wt=13): 939 -coll(c3,c2,A) | coll(c1,A,c3). [resolve(766,a,341,a)].
% 104.81/14.60
% 104.81/14.60 % given #1000 (T,wt=9): 18686 coll(c5,c8,c3). [resolve(18400,a,342,a)].
% 104.81/14.60
% 104.81/14.60 % given #1500 (T,wt=13): 12157 -coll(c9,c2,A) | coll(A,c5,c9). [resolve(11819,a,341,b)].
% 104.81/14.60
% 104.81/14.60 % given #2000 (W,wt=13): 16798 -coll(c4,c6,A) | coll(A,c5,c4). [resolve(16638,a,341,b)].
% 104.81/14.60
% 104.81/14.60 % given #2500 (T,wt=13): 20105 -coll(c5,c6,A) | coll(A,c3,c5). [resolve(20082,a,341,b)].
% 104.81/14.60
% 104.81/14.60 % given #3000 (T,wt=10): 23059 cyclic(c1,c3,A,c3). [back_unit_del(22737),unit_del(a,23048)].
% 104.81/14.60
% 104.81/14.60 % given #3500 (W,wt=10): 24773 para(c1,c7,c2,c2). [resolve(23974,a,8223,a)].
% 104.81/14.60
% 104.81/14.60 % SZS status Theorem for theBenchmark
% 104.81/14.60
% 104.81/14.60 % Proof 1 at 4.64 (+ 1.44) seconds.
% 104.81/14.60 % Length of proof is 183.
% 104.81/14.60 % Level of proof is 39.
% 104.81/14.60 % Maximum clause weight is 34.000.
% 104.81/14.60 % Given clauses 3665.
% 104.81/14.60
% 104.81/14.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------