%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO616+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 07:18:14 AM UTC 2026
% Result : Theorem 117.07s 16.34s
% Output : CNFRefutation 117.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 27
% Syntax : Number of formulae : 176 ( 85 unt; 0 def)
% Number of atoms : 349 ( 0 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 270 ( 97 ~; 93 |; 52 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-7 aty)
% Number of variables : 351 ( 9 sgn 154 !; 14 ?)
% 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(ruleD6,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
file('theBenchmark.p',ruleD6) ).
fof(ruleD7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('theBenchmark.p',ruleD7) ).
fof(ruleD8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('theBenchmark.p',ruleD8) ).
fof(ruleD9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('theBenchmark.p',ruleD9) ).
fof(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(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('theBenchmark.p',ruleD23) ).
fof(ruleD24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('theBenchmark.p',ruleD24) ).
fof(ruleD25,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('theBenchmark.p',ruleD25) ).
fof(ruleD45,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('theBenchmark.p',ruleD45) ).
fof(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(ruleD63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('theBenchmark.p',ruleD63) ).
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(ruleX7,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( coll(D,A,B)
& coll(C,A,B)
& midp(N,C,D)
& midp(M,A,B) )
=> midp(P,A,Q) ),
file('theBenchmark.p',ruleX7) ).
fof(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(exemplo6GDDFULL618078,conjecture,
! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) )
=> perp(E,K,K,N) ),
file('theBenchmark.p',exemplo6GDDFULL618078) ).
fof(exemplo6GDDFULL618078_neg,negated_conjecture,
~ ! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) )
=> perp(E,K,K,N) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618078]) ).
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]) ).
fof(nnf_87,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[ruleX11]) ).
fof(sk_ruleX11,plain,
! [A,B,C,O] :
( perp(sK0(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0(A,B,C,O))],[nnf_87]) ).
cnf(c_102,plain,
( perp(sK0(B,C,D,A),B,B,A)
| ~ circle(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_ruleX11]) ).
fof(nnf_95,plain,
? [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ~ perp(E,K,K,N)
& circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618078_neg]) ).
fof(sk_exemplo6GDDFULL618078_neg,plain,
( ~ perp(sK5,sK6,sK6,sK7)
& circle(sK7,sK6,sK9,sK8)
& coll(sK8,sK1,sK9)
& perp(sK8,sK2,sK1,sK9)
& coll(sK6,sK2,sK3)
& perp(sK6,sK5,sK2,sK3)
& circle(sK1,sK2,sK5,sK11)
& coll(sK5,sK1,sK9)
& midp(sK9,sK4,sK3)
& circle(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK9,sK5,sK11,sK6,sK8,sK7]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4),skolemize(O,sK1),skolemize(G,sK9),skolemize(E,sK5),skolemize(K,sK6),skolemize(H,sK8),skolemize(N,sK7),skolemize(NWPNT1,sK11)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618078_neg]) ).
cnf(c_145,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
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]) ).
cnf(c_192,negated_conjecture,
~ perp(sK5,sK6,sK6,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618078_neg]) ).
cnf(c_194,negated_conjecture,
perp(sK8,sK2,sK1,sK9),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618078_neg]) ).
cnf(c_195,negated_conjecture,
coll(sK6,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618078_neg]) ).
cnf(c_196,negated_conjecture,
perp(sK6,sK5,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618078_neg]) ).
cnf(c_198,negated_conjecture,
midp(sK9,sK4,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618078_neg]) ).
fof(nnf_83,plain,
! [A,B,C,D,M,N,Q] :
? [P] :
( midp(P,A,Q)
| ~ coll(D,A,B)
| ~ coll(C,A,B)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(fof_nnf,[status(thm)],[ruleX7]) ).
fof(sk_ruleX7,plain,
! [A,B,C,D,M,N,Q] :
( midp(sK10(A,B,C,D,M,N,Q),A,Q)
| ~ coll(D,A,B)
| ~ coll(C,A,B)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(P,sK10(A,B,C,D,M,N,Q))],[nnf_83]) ).
cnf(c_215,plain,
( midp(sK10(B,C,E,F,A,D,V6),B,V6)
| ~ coll(F,B,C)
| ~ coll(E,B,C)
| ~ midp(D,E,F)
| ~ midp(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_ruleX7]) ).
cnf(c_234,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_235,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_236,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_239,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_240,plain,
( para(B,D,C,E)
| ~ midp(A,D,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD63]) ).
cnf(c_247,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_248,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_253,plain,
( midp(D,B,E)
| ~ coll(D,B,E)
| ~ para(A,D,C,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD45]) ).
cnf(c_274,plain,
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD25]) ).
cnf(c_275,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_276,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_287,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_288,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_289,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_290,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_291,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_292,plain,
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD6]) ).
cnf(c_293,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_294,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_295,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_296,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_297,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_312,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_187]) ).
cnf(c_330,plain,
( midp(sK10(B,C,B,C,A,A,D),B,D)
| ~ coll(C,B,C)
| ~ coll(B,B,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_215]) ).
cnf(c_337,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_239]) ).
cnf(c_338,plain,
( para(B,B,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_240]) ).
cnf(c_341,plain,
( perp(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_247]) ).
cnf(c_351,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_295]) ).
cnf(c_443,plain,
coll(sK9,sK4,sK3),
inference(resolve,[status(thm)],[c_234,c_198]) ).
cnf(c_444,plain,
cong(sK9,sK4,sK9,sK3),
inference(resolve,[status(thm)],[c_235,c_198]) ).
cnf(c_446,plain,
( para(A,sK4,B,sK3)
| ~ midp(sK9,A,B) ),
inference(resolve,[status(thm)],[c_240,c_198]) ).
cnf(c_457,plain,
midp(sK9,sK3,sK4),
inference(resolve,[status(thm)],[c_287,c_198]) ).
cnf(c_463,plain,
( para(A,B,sK2,sK3)
| ~ perp(A,B,sK6,sK5) ),
inference(resolve,[status(thm)],[c_289,c_196]) ).
cnf(c_464,plain,
( para(A,B,sK1,sK9)
| ~ perp(A,B,sK8,sK2) ),
inference(resolve,[status(thm)],[c_289,c_194]) ).
cnf(c_465,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_289,c_145]) ).
cnf(c_468,plain,
perp(sK2,sK3,sK6,sK5),
inference(resolve,[status(thm)],[c_290,c_196]) ).
cnf(c_470,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_290,c_145]) ).
cnf(c_473,plain,
perp(sK6,sK5,sK3,sK2),
inference(resolve,[status(thm)],[c_291,c_196]) ).
cnf(c_474,plain,
perp(sK8,sK2,sK9,sK1),
inference(resolve,[status(thm)],[c_291,c_194]) ).
cnf(c_485,plain,
coll(sK2,sK6,sK3),
inference(resolve,[status(thm)],[c_296,c_195]) ).
cnf(c_493,plain,
( midp(sK10(sK4,sK3,sK4,sK3,sK9,sK9,A),sK4,A)
| ~ coll(sK3,sK4,sK3)
| ~ coll(sK4,sK4,sK3) ),
inference(resolve,[status(thm)],[c_330,c_198]) ).
cnf(c_503,plain,
coll(sK3,sK3,sK9),
inference(resolve,[status(thm)],[c_443,c_351]) ).
cnf(c_504,plain,
coll(sK9,sK3,sK4),
inference(resolve,[status(thm)],[c_443,c_297]) ).
cnf(c_505,plain,
coll(sK4,sK9,sK3),
inference(resolve,[status(thm)],[c_443,c_296]) ).
cnf(c_509,plain,
para(sK3,sK3,sK4,sK4),
inference(resolve,[status(thm)],[c_457,c_338]) ).
cnf(c_520,plain,
cong(sK9,sK3,sK9,sK4),
inference(resolve,[status(thm)],[c_457,c_235]) ).
cnf(c_536,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_485,c_351]) ).
cnf(c_571,plain,
coll(sK9,sK9,sK3),
inference(resolve,[status(thm)],[c_503,c_351]) ).
cnf(c_575,plain,
coll(sK4,sK4,sK9),
inference(resolve,[status(thm)],[c_504,c_351]) ).
cnf(c_576,plain,
coll(sK3,sK9,sK4),
inference(resolve,[status(thm)],[c_504,c_296]) ).
cnf(c_579,plain,
coll(sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_505,c_351]) ).
cnf(c_600,plain,
coll(sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_536,c_351]) ).
cnf(c_659,plain,
coll(sK9,sK3,sK9),
inference(resolve,[status(thm)],[c_571,c_297]) ).
cnf(c_665,plain,
coll(sK9,sK9,sK4),
inference(resolve,[status(thm)],[c_575,c_351]) ).
cnf(c_669,plain,
coll(sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_576,c_351]) ).
cnf(c_673,plain,
( midp(sK10(sK4,sK3,sK4,sK3,sK9,sK9,A),sK4,A)
| ~ coll(sK3,sK4,sK3) ),
inference(resolve,[status(thm)],[c_669,c_493]) ).
cnf(c_674,plain,
coll(sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_579,c_297]) ).
cnf(c_677,plain,
midp(sK10(sK4,sK3,sK4,sK3,sK9,sK9,A),sK4,A),
inference(resolve,[status(thm)],[c_674,c_673]) ).
cnf(c_750,plain,
coll(sK3,sK9,sK9),
inference(resolve,[status(thm)],[c_659,c_296]) ).
cnf(c_755,plain,
coll(sK9,sK4,sK9),
inference(resolve,[status(thm)],[c_665,c_297]) ).
cnf(c_821,plain,
coll(sK4,sK9,sK9),
inference(resolve,[status(thm)],[c_755,c_296]) ).
cnf(c_911,plain,
cong(sK9,sK4,sK3,sK9),
inference(resolve,[status(thm)],[c_444,c_276]) ).
cnf(c_912,plain,
( cong(A,B,sK9,sK3)
| ~ cong(A,B,sK9,sK4) ),
inference(resolve,[status(thm)],[c_444,c_274]) ).
cnf(c_937,plain,
perp(sK2,sK3,sK5,sK6),
inference(resolve,[status(thm)],[c_468,c_291]) ).
cnf(c_965,plain,
perp(sK3,sK2,sK6,sK5),
inference(resolve,[status(thm)],[c_473,c_290]) ).
cnf(c_981,plain,
perp(sK9,sK1,sK8,sK2),
inference(resolve,[status(thm)],[c_474,c_290]) ).
cnf(c_1041,plain,
( para(A,B,sK4,sK4)
| ~ para(A,B,sK3,sK3) ),
inference(resolve,[status(thm)],[c_509,c_292]) ).
cnf(c_1108,plain,
cong(sK9,sK3,sK4,sK9),
inference(resolve,[status(thm)],[c_520,c_276]) ).
cnf(c_1168,plain,
cong(sK3,sK9,sK9,sK4),
inference(resolve,[status(thm)],[c_911,c_275]) ).
cnf(c_1171,plain,
perp(sK5,sK6,sK2,sK3),
inference(resolve,[status(thm)],[c_937,c_290]) ).
cnf(c_1291,plain,
cong(sK4,sK9,sK9,sK3),
inference(resolve,[status(thm)],[c_1108,c_275]) ).
cnf(c_1328,plain,
( para(sK5,sK6,A,B)
| ~ perp(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_1171,c_289]) ).
cnf(c_1409,plain,
cong(sK4,sK9,sK3,sK9),
inference(resolve,[status(thm)],[c_1291,c_276]) ).
cnf(c_1475,plain,
para(sK3,sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_446,c_457]) ).
cnf(c_1505,plain,
perp(sK4,sK3,sK9,sK9),
inference(resolve,[status(thm)],[c_1409,c_341]) ).
cnf(c_1567,plain,
para(sK3,sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_1475,c_294]) ).
cnf(c_1605,plain,
( cong(sK4,sK9,sK4,sK9)
| ~ midp(sK3,sK9,sK9) ),
inference(resolve,[status(thm)],[c_1505,c_248]) ).
cnf(c_1652,plain,
( midp(A,sK4,sK4)
| ~ midp(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_1567,c_337]) ).
cnf(c_1801,plain,
para(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_463,c_965]) ).
cnf(c_1802,plain,
para(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_463,c_468]) ).
cnf(c_1803,plain,
para(sK9,sK1,sK1,sK9),
inference(resolve,[status(thm)],[c_464,c_981]) ).
cnf(c_1834,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_470,c_465]) ).
cnf(c_1897,plain,
( midp(sK2,A,sK3)
| ~ coll(sK2,A,sK3)
| ~ midp(sK3,A,sK2) ),
inference(resolve,[status(thm)],[c_1801,c_253]) ).
cnf(c_1951,plain,
( midp(A,sK3,sK3)
| ~ midp(A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_1802,c_337]) ).
cnf(c_1967,plain,
para(sK9,sK1,sK9,sK1),
inference(resolve,[status(thm)],[c_1803,c_294]) ).
cnf(c_1995,plain,
para(sK2,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_1834,c_294]) ).
cnf(c_2168,plain,
( midp(A,sK1,sK1)
| ~ midp(A,sK9,sK9) ),
inference(resolve,[status(thm)],[c_1967,c_337]) ).
cnf(c_2199,plain,
para(sK1,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_1995,c_293]) ).
cnf(c_2278,plain,
para(sK1,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_2199,c_294]) ).
cnf(c_2306,plain,
( midp(A,sK2,sK2)
| ~ midp(A,sK1,sK1) ),
inference(resolve,[status(thm)],[c_2278,c_337]) ).
cnf(c_3160,plain,
para(sK4,sK4,A,A),
inference(resolve,[status(thm)],[c_677,c_338]) ).
cnf(c_3170,plain,
cong(sK10(sK4,sK3,sK4,sK3,sK9,sK9,A),sK4,sK10(sK4,sK3,sK4,sK3,sK9,sK9,A),A),
inference(resolve,[status(thm)],[c_677,c_235]) ).
cnf(c_3171,plain,
coll(sK10(sK4,sK3,sK4,sK3,sK9,sK9,A),sK4,A),
inference(resolve,[status(thm)],[c_677,c_234]) ).
cnf(c_4418,plain,
( perp(sK4,sK4,B,C)
| ~ perp(A,A,B,C) ),
inference(resolve,[status(thm)],[c_3160,c_288]) ).
cnf(c_4617,plain,
cong(sK3,sK9,sK9,sK3),
inference(resolve,[status(thm)],[c_912,c_1168]) ).
cnf(c_4639,plain,
cong(sK3,sK9,sK3,sK9),
inference(resolve,[status(thm)],[c_4617,c_276]) ).
cnf(c_32980,plain,
( midp(sK3,sK9,sK9)
| ~ coll(sK3,sK9,sK9) ),
inference(resolve,[status(thm)],[c_4639,c_236]) ).
cnf(c_5038,plain,
midp(sK3,sK9,sK9),
inference(resolve,[status(thm)],[c_750,c_32980]) ).
cnf(c_5061,plain,
cong(sK4,sK9,sK4,sK9),
inference(resolve,[status(thm)],[c_5038,c_1605]) ).
cnf(c_32981,plain,
( midp(sK4,sK9,sK9)
| ~ coll(sK4,sK9,sK9) ),
inference(resolve,[status(thm)],[c_5061,c_236]) ).
cnf(c_5482,plain,
midp(sK4,sK9,sK9),
inference(resolve,[status(thm)],[c_821,c_32981]) ).
cnf(c_8996,plain,
midp(sK4,sK1,sK1),
inference(resolve,[status(thm)],[c_2168,c_5482]) ).
cnf(c_8997,plain,
midp(sK3,sK1,sK1),
inference(resolve,[status(thm)],[c_2168,c_5038]) ).
cnf(c_12083,plain,
midp(sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_2306,c_8997]) ).
cnf(c_12084,plain,
midp(sK4,sK2,sK2),
inference(resolve,[status(thm)],[c_2306,c_8996]) ).
cnf(c_12197,plain,
midp(sK4,sK3,sK3),
inference(resolve,[status(thm)],[c_12084,c_1951]) ).
cnf(c_12654,plain,
midp(sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_12197,c_1652]) ).
cnf(c_32982,plain,
( midp(sK2,sK2,sK3)
| ~ coll(sK2,sK2,sK3) ),
inference(resolve,[status(thm)],[c_1897,c_12083]) ).
cnf(c_20150,plain,
midp(sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_600,c_32982]) ).
cnf(c_20185,plain,
cong(sK2,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_20150,c_235]) ).
cnf(c_32983,plain,
( perp(sK2,sK3,sK3,sK3)
| ~ coll(sK2,sK2,sK3) ),
inference(resolve,[status(thm)],[c_20185,c_312]) ).
cnf(c_20232,plain,
perp(sK2,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_600,c_32983]) ).
cnf(c_20301,plain,
para(sK5,sK6,sK3,sK3),
inference(resolve,[status(thm)],[c_20232,c_1328]) ).
cnf(c_20418,plain,
para(sK5,sK6,sK4,sK4),
inference(resolve,[status(thm)],[c_20301,c_1041]) ).
cnf(c_20587,plain,
( perp(sK5,sK6,A,B)
| ~ perp(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_20418,c_288]) ).
cnf(c_32984,plain,
( perp(sK4,A,A,A)
| ~ coll(sK10(sK4,sK3,sK4,sK3,sK9,sK9,A),sK4,A) ),
inference(resolve,[status(thm)],[c_3170,c_312]) ).
cnf(c_30943,plain,
perp(sK4,A,A,A),
inference(resolve,[status(thm)],[c_3171,c_32984]) ).
cnf(c_31690,plain,
perp(A,A,sK4,A),
inference(resolve,[status(thm)],[c_30943,c_290]) ).
cnf(c_31826,plain,
perp(A,A,A,sK4),
inference(resolve,[status(thm)],[c_31690,c_291]) ).
cnf(c_32493,plain,
perp(sK4,sK4,A,sK4),
inference(resolve,[status(thm)],[c_4418,c_31826]) ).
cnf(c_32611,plain,
perp(A,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_32493,c_290]) ).
cnf(c_32985,plain,
( cong(A,sK4,A,sK4)
| ~ midp(sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_32611,c_248]) ).
cnf(c_32748,plain,
cong(A,sK4,A,sK4),
inference(resolve,[status(thm)],[c_12654,c_32985]) ).
cnf(c_32861,plain,
cong(A,sK4,sK4,A),
inference(resolve,[status(thm)],[c_32748,c_276]) ).
cnf(c_32908,plain,
cong(sK4,A,A,sK4),
inference(resolve,[status(thm)],[c_32861,c_275]) ).
cnf(c_32923,plain,
cong(sK4,A,sK4,A),
inference(resolve,[status(thm)],[c_32908,c_276]) ).
cnf(c_32986,plain,
( perp(sK4,sK4,A,B)
| ~ cong(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_32923,c_247]) ).
cnf(c_32963,plain,
perp(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_32923,c_32986]) ).
cnf(c_32978,plain,
perp(sK5,sK6,A,B),
inference(resolve,[status(thm)],[c_32963,c_20587]) ).
cnf(c_32979,plain,
$false,
inference(resolve,[status(thm)],[c_32978,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO616+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 13:43:08 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 1134915 was started by sandbox2 on n007,
% 0.10/0.38 % Fri Sep 25 13:43:08 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.42
% 0.15/0.42 % From the command line: assign(max_seconds, 300).
% 117.07/16.34
% 117.07/16.34 % given #500 (T,wt=4): 1819 coll(c1,c8,c1). [resolve(1811,a,296,a)].
% 117.07/16.34
% 117.07/16.34 % given #1000 (A,wt=8): 766 -coll(c2,c3,A) | coll(A,c5,c2). [resolve(670,a,295,b)].
% 117.07/16.34
% 117.07/16.34 % given #1500 (T,wt=4): 5713 coll(c9,c1,c4). [resolve(2045,a,4216,a)].
% 117.07/16.34
% 117.07/16.34 % given #2000 (A,wt=10): 1173 -perp(c6,c7,A,B) | para(c1,c2,A,B). [resolve(937,a,289,a)].
% 117.07/16.34
% 117.07/16.34 % given #2500 (T,wt=7): 14752 coll(c5,c2,f19(c2,c2,c2)). [resolve(14630,a,297,a)].
% 117.07/16.34
% 117.07/16.34 % given #3000 (A,wt=13): 1683 -perp(c3,c5,c5,c2) | coll(f11(c3,c5,c2,c5),c2,c3). [resolve(1602,a,207,b)].
% 117.07/16.34
% 117.07/16.34 % given #3500 (T,wt=5): 20666 para(c2,c1,c7,c6). [resolve(20478,a,1203,a)].
% 117.07/16.34
% 117.07/16.34 % given #4000 (A,wt=15): 2196 -midp(c1,c1,c4) | coll(f8(c1,c4,A,c4,c1,c4,c1),c1,c4). [resolve(1995,a,328,b),unit_del(b,2007)].
% 117.07/16.34
% 117.07/16.34 % given #4500 (T,wt=5): 25818 cyclic(c2,c2,c5,c5). [resolve(24528,a,346,a)].
% 117.07/16.34
% 117.07/16.34 % given #5000 (A,wt=13): 2681 coll(c5,f17(f12(c1,c6,c10,c4),c4,c1,c5,c6),c6). [resolve(592,a,296,a)].
% 117.07/16.34
% 117.07/16.34 % given #5500 (T,wt=5): 30218 perp(c5,c2,c4,c4). [resolve(30154,a,341,a)].
% 117.07/16.34
% 117.07/16.34 % given #6000 (A,wt=8): 3256 -coll(c6,c2,A) | coll(A,c1,c6). [resolve(2931,a,295,b)].
% 117.07/16.34
% 117.07/16.34 % given #6500 (T,wt=5): 31886 cyclic(A,c6,c7,c6). [resolve(31726,a,284,a)].
% 117.07/16.34
% 117.07/16.34 % given #7000 (A,wt=8): 4504 coll(c3,f10(c2,c2,c3,c2),c2). [resolve(1421,a,296,a)].
% 117.07/16.34
% 117.07/16.34 % SZS status Theorem for theBenchmark
% 117.07/16.34
% 117.07/16.34 % Proof 1 at 6.45 (+ 1.25) seconds.
% 117.07/16.34 % Length of proof is 162.
% 117.07/16.34 % Level of proof is 21.
% 117.07/16.34 % Maximum clause weight is 27.000.
% 117.07/16.34 % Given clauses 7267.
% 117.07/16.34
% 117.07/16.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------