%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO637+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 : n020.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 101.69s 19.39s
% Output : CNFRefutation 101.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 32
% Syntax : Number of formulae : 203 ( 95 unt; 0 def)
% Number of atoms : 399 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 318 ( 122 ~; 118 |; 45 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-7 aty)
% Number of variables : 404 ( 20 sgn 162 !; 9 ?)
% 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(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(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(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(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(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(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(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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
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(exemplo6GDDFULL81109101,conjecture,
! [A,B,C,O,H,D,E] :
( ( perp(A,O,A,E)
& perp(C,O,C,E)
& coll(D,A,B)
& coll(D,O,H)
& midp(H,C,B)
& circle(O,A,B,C) )
=> cyclic(A,O,E,D) ),
file('theBenchmark.p',exemplo6GDDFULL81109101) ).
fof(exemplo6GDDFULL81109101_neg,negated_conjecture,
~ ! [A,B,C,O,H,D,E] :
( ( perp(A,O,A,E)
& perp(C,O,C,E)
& coll(D,A,B)
& coll(D,O,H)
& midp(H,C,B)
& circle(O,A,B,C) )
=> cyclic(A,O,E,D) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL81109101]) ).
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_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]) ).
cnf(c_158,plain,
( ~ cong(E,D,E,C)
| ~ cong(E,D,E,B)
| midp(A,B,C)
| ~ eqangle(D,B,D,C,E,B,E,A)
| ~ coll(A,B,C) ),
inference(resolve,[status(thm)],[c_100,c_97]) ).
fof(nnf_95,plain,
? [A,B,C,O,H,D,E] :
( ~ cyclic(A,O,E,D)
& perp(A,O,A,E)
& perp(C,O,C,E)
& coll(D,A,B)
& coll(D,O,H)
& midp(H,C,B)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL81109101_neg]) ).
fof(sk_exemplo6GDDFULL81109101_neg,plain,
( ~ cyclic(sK0,sK1,sK2,sK3)
& perp(sK0,sK1,sK0,sK2)
& perp(sK4,sK1,sK4,sK2)
& coll(sK3,sK0,sK5)
& coll(sK3,sK1,sK6)
& midp(sK6,sK4,sK5)
& circle(sK1,sK0,sK5,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK5,sK4,sK6,sK3,sK2]),skolemize(A,sK0),skolemize(B,sK5),skolemize(C,sK4),skolemize(O,sK1),skolemize(H,sK6),skolemize(D,sK3),skolemize(E,sK2)],[nnf_95]) ).
cnf(c_162,negated_conjecture,
~ cyclic(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109101_neg]) ).
cnf(c_163,negated_conjecture,
perp(sK0,sK1,sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109101_neg]) ).
cnf(c_164,negated_conjecture,
perp(sK4,sK1,sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109101_neg]) ).
cnf(c_165,negated_conjecture,
coll(sK3,sK0,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109101_neg]) ).
cnf(c_167,negated_conjecture,
midp(sK6,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109101_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(sK7(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,[sK7]),skolemize(P,sK7(A,B,C,D,M,N,Q))],[nnf_83]) ).
cnf(c_184,plain,
( midp(sK7(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_203,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_204,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_205,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_206,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_208,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_209,plain,
( para(B,D,C,E)
| ~ midp(A,D,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD63]) ).
cnf(c_217,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_222,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_224,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_225,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_227,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_228,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_243,plain,
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD25]) ).
cnf(c_244,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_245,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_251,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_252,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_253,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_254,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_255,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_256,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_258,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_259,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_260,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_263,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_264,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_265,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_266,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_282,plain,
( ~ cong(D,C,D,B)
| midp(A,B,B)
| ~ eqangle(C,B,C,B,D,B,D,A)
| ~ coll(A,B,B) ),
inference(factor,[status(thm)],[c_158]) ).
cnf(c_299,plain,
( midp(sK7(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_184]) ).
cnf(c_306,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_208]) ).
cnf(c_312,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_224]) ).
cnf(c_315,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_251]) ).
cnf(c_316,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_255]) ).
cnf(c_320,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_264]) ).
cnf(c_328,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_312]) ).
cnf(c_329,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_316]) ).
cnf(c_365,plain,
coll(sK6,sK4,sK5),
inference(resolve,[status(thm)],[c_203,c_167]) ).
cnf(c_366,plain,
cong(sK6,sK4,sK6,sK5),
inference(resolve,[status(thm)],[c_204,c_167]) ).
cnf(c_368,plain,
( para(A,sK4,B,sK5)
| ~ midp(sK6,A,B) ),
inference(resolve,[status(thm)],[c_209,c_167]) ).
cnf(c_375,plain,
midp(sK6,sK5,sK4),
inference(resolve,[status(thm)],[c_256,c_167]) ).
cnf(c_379,plain,
( para(A,B,sK4,sK2)
| ~ perp(A,B,sK4,sK1) ),
inference(resolve,[status(thm)],[c_258,c_164]) ).
cnf(c_380,plain,
( para(A,B,sK0,sK2)
| ~ perp(A,B,sK0,sK1) ),
inference(resolve,[status(thm)],[c_258,c_163]) ).
cnf(c_382,plain,
perp(sK4,sK2,sK4,sK1),
inference(resolve,[status(thm)],[c_259,c_164]) ).
cnf(c_383,plain,
perp(sK0,sK2,sK0,sK1),
inference(resolve,[status(thm)],[c_259,c_163]) ).
cnf(c_385,plain,
perp(sK4,sK1,sK2,sK4),
inference(resolve,[status(thm)],[c_260,c_164]) ).
cnf(c_391,plain,
( coll(A,sK5,sK3)
| ~ coll(sK3,sK0,A) ),
inference(resolve,[status(thm)],[c_264,c_165]) ).
cnf(c_395,plain,
coll(sK3,sK5,sK0),
inference(resolve,[status(thm)],[c_266,c_165]) ).
cnf(c_397,plain,
( midp(sK7(sK4,sK5,sK4,sK5,sK6,sK6,A),sK4,A)
| ~ coll(sK5,sK4,sK5)
| ~ coll(sK4,sK4,sK5) ),
inference(resolve,[status(thm)],[c_299,c_167]) ).
cnf(c_405,plain,
coll(sK5,sK5,sK3),
inference(resolve,[status(thm)],[c_320,c_165]) ).
cnf(c_406,plain,
coll(sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_365,c_320]) ).
cnf(c_407,plain,
coll(sK6,sK5,sK4),
inference(resolve,[status(thm)],[c_365,c_266]) ).
cnf(c_408,plain,
coll(sK4,sK6,sK5),
inference(resolve,[status(thm)],[c_365,c_265]) ).
cnf(c_421,plain,
( para(A,sK5,B,sK4)
| ~ midp(sK6,A,B) ),
inference(resolve,[status(thm)],[c_375,c_209]) ).
cnf(c_422,plain,
( para(sK5,A,sK4,B)
| ~ midp(sK6,A,B) ),
inference(resolve,[status(thm)],[c_375,c_209]) ).
cnf(c_423,plain,
cong(sK6,sK5,sK6,sK4),
inference(resolve,[status(thm)],[c_375,c_204]) ).
cnf(c_447,plain,
coll(sK0,sK0,sK3),
inference(resolve,[status(thm)],[c_395,c_320]) ).
cnf(c_456,plain,
coll(sK5,sK3,sK5),
inference(resolve,[status(thm)],[c_405,c_266]) ).
cnf(c_460,plain,
coll(sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_406,c_266]) ).
cnf(c_464,plain,
coll(sK5,sK6,sK4),
inference(resolve,[status(thm)],[c_407,c_265]) ).
cnf(c_467,plain,
coll(sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_408,c_320]) ).
cnf(c_497,plain,
( coll(A,sK3,sK0)
| ~ coll(sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_447,c_264]) ).
cnf(c_529,plain,
coll(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_456,c_320]) ).
cnf(c_556,plain,
coll(sK6,sK5,sK5),
inference(resolve,[status(thm)],[c_460,c_265]) ).
cnf(c_563,plain,
coll(sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_464,c_320]) ).
cnf(c_567,plain,
( midp(sK7(sK4,sK5,sK4,sK5,sK6,sK6,A),sK4,A)
| ~ coll(sK5,sK4,sK5) ),
inference(resolve,[status(thm)],[c_563,c_397]) ).
cnf(c_568,plain,
coll(sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_467,c_266]) ).
cnf(c_571,plain,
midp(sK7(sK4,sK5,sK4,sK5,sK6,sK6,A),sK4,A),
inference(resolve,[status(thm)],[c_568,c_567]) ).
cnf(c_752,plain,
cyclic(sK4,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_366,c_329]) ).
cnf(c_810,plain,
( cong(A,B,sK6,sK5)
| ~ cong(A,B,sK6,sK4) ),
inference(resolve,[status(thm)],[c_366,c_243]) ).
cnf(c_825,plain,
perp(sK4,sK2,sK1,sK4),
inference(resolve,[status(thm)],[c_382,c_260]) ).
cnf(c_845,plain,
perp(sK2,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_385,c_259]) ).
cnf(c_995,plain,
cyclic(sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_752,c_315]) ).
cnf(c_1030,plain,
perp(sK1,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_825,c_259]) ).
cnf(c_1168,plain,
eqangle(sK5,sK5,sK5,sK5,sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_995,c_227]) ).
cnf(c_1198,plain,
perp(sK1,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_1030,c_260]) ).
cnf(c_1277,plain,
para(sK5,sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_368,c_375]) ).
cnf(c_1350,plain,
( cong(sK1,sK2,sK1,sK4)
| ~ midp(sK4,sK2,sK4) ),
inference(resolve,[status(thm)],[c_1198,c_217]) ).
cnf(c_1362,plain,
para(sK5,sK4,sK5,sK4),
inference(resolve,[status(thm)],[c_1277,c_263]) ).
cnf(c_1452,plain,
( midp(A,sK4,sK4)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1362,c_306]) ).
cnf(c_1578,plain,
para(sK2,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_379,c_845]) ).
cnf(c_1579,plain,
para(sK4,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_379,c_382]) ).
cnf(c_1581,plain,
para(sK0,sK2,sK0,sK2),
inference(resolve,[status(thm)],[c_380,c_383]) ).
cnf(c_1721,plain,
( midp(sK4,A,sK2)
| ~ coll(sK4,A,sK2)
| ~ midp(sK2,A,sK4) ),
inference(resolve,[status(thm)],[c_1578,c_222]) ).
cnf(c_1729,plain,
( midp(A,sK2,sK2)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_1579,c_306]) ).
cnf(c_1732,plain,
eqangle(sK4,sK2,A,B,sK4,sK2,A,B),
inference(resolve,[status(thm)],[c_1579,c_228]) ).
cnf(c_1735,plain,
coll(sK4,sK2,sK2),
inference(resolve,[status(thm)],[c_1579,c_206]) ).
cnf(c_1742,plain,
coll(sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_1735,c_320]) ).
cnf(c_1748,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_1742,c_320]) ).
cnf(c_1788,plain,
coll(sK0,sK2,sK2),
inference(resolve,[status(thm)],[c_1581,c_206]) ).
cnf(c_1795,plain,
coll(sK2,sK2,sK0),
inference(resolve,[status(thm)],[c_1788,c_320]) ).
cnf(c_1801,plain,
coll(sK0,sK0,sK2),
inference(resolve,[status(thm)],[c_1795,c_320]) ).
cnf(c_2472,plain,
coll(sK2,sK3,sK0),
inference(resolve,[status(thm)],[c_497,c_1801]) ).
cnf(c_2474,plain,
coll(sK3,sK2,sK0),
inference(resolve,[status(thm)],[c_2472,c_265]) ).
cnf(c_2484,plain,
coll(sK3,sK0,sK2),
inference(resolve,[status(thm)],[c_2474,c_266]) ).
cnf(c_2494,plain,
coll(sK2,sK5,sK3),
inference(resolve,[status(thm)],[c_2484,c_391]) ).
cnf(c_2514,plain,
coll(sK2,sK3,sK5),
inference(resolve,[status(thm)],[c_2494,c_266]) ).
cnf(c_2553,plain,
coll(sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_2514,c_320]) ).
cnf(c_2574,plain,
coll(sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_2553,c_266]) ).
cnf(c_2594,plain,
coll(sK2,sK5,sK5),
inference(resolve,[status(thm)],[c_2574,c_265]) ).
cnf(c_2816,plain,
midp(sK7(sK4,sK5,sK4,sK5,sK6,sK6,A),A,sK4),
inference(resolve,[status(thm)],[c_571,c_256]) ).
cnf(c_2819,plain,
( para(B,sK4,C,A)
| ~ midp(sK7(sK4,sK5,sK4,sK5,sK6,sK6,A),B,C) ),
inference(resolve,[status(thm)],[c_571,c_209]) ).
cnf(c_3465,plain,
cong(sK6,sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_810,c_423]) ).
cnf(c_34654,plain,
( midp(sK6,sK5,sK5)
| ~ coll(sK6,sK5,sK5) ),
inference(resolve,[status(thm)],[c_3465,c_205]) ).
cnf(c_3531,plain,
midp(sK6,sK5,sK5),
inference(resolve,[status(thm)],[c_556,c_34654]) ).
cnf(c_3544,plain,
midp(sK6,sK4,sK4),
inference(resolve,[status(thm)],[c_3531,c_1452]) ).
cnf(c_3557,plain,
para(sK5,sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_3531,c_421]) ).
cnf(c_3560,plain,
para(sK5,sK4,sK5,sK5),
inference(resolve,[status(thm)],[c_3531,c_368]) ).
cnf(c_3594,plain,
midp(sK6,sK2,sK2),
inference(resolve,[status(thm)],[c_3544,c_1729]) ).
cnf(c_3655,plain,
para(sK5,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_3594,c_422]) ).
cnf(c_34655,plain,
( midp(A,sK5,sK4)
| ~ para(sK5,sK4,sK5,sK5)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_3557,c_208]) ).
cnf(c_3962,plain,
( midp(A,sK5,sK4)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_3560,c_34655]) ).
cnf(c_4210,plain,
( midp(A,sK2,sK2)
| ~ midp(A,sK5,sK4) ),
inference(resolve,[status(thm)],[c_3655,c_306]) ).
cnf(c_34656,plain,
( cong(sK5,sK5,sK5,sK5)
| ~ cyclic(sK5,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1168,c_328]) ).
cnf(c_6297,plain,
cong(sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_995,c_34656]) ).
cnf(c_34657,plain,
( ~ cong(sK5,sK5,sK5,sK5)
| midp(sK5,sK5,sK5)
| ~ coll(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1168,c_282]) ).
cnf(c_34658,plain,
( ~ cong(sK5,sK5,sK5,sK5)
| midp(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_529,c_34657]) ).
cnf(c_6299,plain,
midp(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_6297,c_34658]) ).
cnf(c_6321,plain,
midp(sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_6299,c_3962]) ).
cnf(c_6419,plain,
midp(sK5,sK2,sK2),
inference(resolve,[status(thm)],[c_6321,c_4210]) ).
cnf(c_6688,plain,
cong(sK5,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_6419,c_204]) ).
cnf(c_8574,plain,
cong(sK5,sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_6688,c_245]) ).
cnf(c_9718,plain,
cong(sK2,sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_8574,c_244]) ).
cnf(c_10265,plain,
cong(sK2,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_9718,c_245]) ).
cnf(c_34659,plain,
( midp(sK2,sK5,sK5)
| ~ coll(sK2,sK5,sK5) ),
inference(resolve,[status(thm)],[c_10265,c_205]) ).
cnf(c_11166,plain,
midp(sK2,sK5,sK5),
inference(resolve,[status(thm)],[c_2594,c_34659]) ).
cnf(c_11175,plain,
midp(sK2,sK4,sK4),
inference(resolve,[status(thm)],[c_11166,c_1452]) ).
cnf(c_34660,plain,
( midp(sK4,sK4,sK2)
| ~ coll(sK4,sK4,sK2) ),
inference(resolve,[status(thm)],[c_1721,c_11175]) ).
cnf(c_27119,plain,
midp(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_1748,c_34660]) ).
cnf(c_27176,plain,
midp(sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_27119,c_256]) ).
cnf(c_27186,plain,
cong(sK1,sK2,sK1,sK4),
inference(resolve,[status(thm)],[c_27176,c_1350]) ).
cnf(c_27410,plain,
( cyclic(sK2,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_1732,c_225]) ).
cnf(c_28131,plain,
cyclic(sK2,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_27186,c_329]) ).
cnf(c_29364,plain,
cyclic(sK4,sK2,sK4,sK4),
inference(resolve,[status(thm)],[c_28131,c_252]) ).
cnf(c_30086,plain,
cyclic(sK4,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_29364,c_253]) ).
cnf(c_30557,plain,
cyclic(sK4,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_30086,c_254]) ).
cnf(c_30955,plain,
cyclic(sK4,sK4,sK2,sK2),
inference(resolve,[status(thm)],[c_30557,c_315]) ).
cnf(c_31222,plain,
cyclic(sK4,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_30955,c_253]) ).
cnf(c_31481,plain,
cyclic(sK2,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_31222,c_252]) ).
cnf(c_31712,plain,
( cyclic(sK4,sK4,A,sK2)
| ~ cyclic(sK2,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_31481,c_251]) ).
cnf(c_33067,plain,
para(A,sK4,sK4,A),
inference(resolve,[status(thm)],[c_2819,c_2816]) ).
cnf(c_33069,plain,
para(A,sK4,A,sK4),
inference(resolve,[status(thm)],[c_33067,c_263]) ).
cnf(c_33079,plain,
coll(A,sK4,sK4),
inference(resolve,[status(thm)],[c_33069,c_206]) ).
cnf(c_33080,plain,
coll(sK4,sK4,A),
inference(resolve,[status(thm)],[c_33079,c_320]) ).
cnf(c_33084,plain,
cyclic(sK2,A,sK4,sK4),
inference(resolve,[status(thm)],[c_33080,c_27410]) ).
cnf(c_33875,plain,
cyclic(sK2,sK4,A,sK4),
inference(resolve,[status(thm)],[c_33084,c_253]) ).
cnf(c_34027,plain,
cyclic(sK2,sK4,sK4,A),
inference(resolve,[status(thm)],[c_33875,c_254]) ).
cnf(c_34031,plain,
cyclic(sK4,sK4,A,sK2),
inference(resolve,[status(thm)],[c_34027,c_31712]) ).
cnf(c_34661,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK2,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_34027,c_251]) ).
cnf(c_34290,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_34027,c_34661]) ).
cnf(c_34662,plain,
( cyclic(sK4,A,B,sK2)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_34031,c_251]) ).
cnf(c_34300,plain,
cyclic(sK4,A,B,sK2),
inference(resolve,[status(thm)],[c_34290,c_34662]) ).
cnf(c_34663,plain,
( cyclic(sK4,A,B,C)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_34290,c_251]) ).
cnf(c_34632,plain,
cyclic(sK4,A,B,C),
inference(resolve,[status(thm)],[c_34290,c_34663]) ).
cnf(c_34664,plain,
( cyclic(A,B,sK2,C)
| ~ cyclic(sK4,A,B,C) ),
inference(resolve,[status(thm)],[c_34300,c_251]) ).
cnf(c_34652,plain,
cyclic(A,B,sK2,C),
inference(resolve,[status(thm)],[c_34632,c_34664]) ).
cnf(c_34653,plain,
$false,
inference(resolve,[status(thm)],[c_34652,c_162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO637+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n020.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Fri Sep 25 13:47:09 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 3061547 was started by sandbox on n020,
% 0.16/5.45 % Fri Sep 25 13:47:09 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.48
% 0.16/5.48 % From the command line: assign(max_seconds, 300).
% 101.69/19.39
% 101.69/19.39 % given #500 (T,wt=6): 2103 coll(c5,c2,c1). [resolve(2072,a,441,a)].
% 101.69/19.39
% 101.69/19.39 % given #1000 (W,wt=10): 1888 -midp(A,c7,c7) | midp(A,c3,c3). [resolve(1716,a,306,b)].
% 101.69/19.39
% 101.69/19.39 % given #1500 (T,wt=10): 2522 -coll(c7,c6,A) | coll(c7,A,c7). [resolve(2498,a,264,a)].
% 101.69/19.39
% 101.69/19.39 % given #2000 (W,wt=7): 9370 cong(c1,c3,c3,c1). [resolve(7602,a,245,a)].
% 101.69/19.39
% 101.69/19.39 % given #2500 (T,wt=7): 16935 perp(c3,c2,c3,c5). [resolve(16180,a,260,a)].
% 101.69/19.39
% 101.69/19.39 % given #3000 (W,wt=7): 21481 cong(c5,c1,c2,c5). [resolve(21023,a,245,a)].
% 101.69/19.39
% 101.69/19.39 % given #3500 (T,wt=6): 24979 midp(c4,c4,c1). [resolve(24961,a,256,a)].
% 101.69/19.39
% 101.69/19.39 % given #4000 (W,wt=6): 27794 midp(c1,c7,c3). [resolve(27771,a,256,a)].
% 101.69/19.39
% 101.69/19.39 % given #4500 (T,wt=7): 30138 para(c4,c3,c1,c5). [resolve(29598,a,262,a)].
% 101.69/19.39
% 101.69/19.39 % given #5000 (W,wt=6): 32742 midp(c5,c7,c3). [resolve(32740,a,13225,a)].
% 101.69/19.39
% 101.69/19.39 % given #5500 (T,wt=6): 33574 coll(A,c6,c5). [back_unit_del(2062),unit_del(a,33564)].
% 101.69/19.39
% 101.69/19.39 % given #6000 (W,wt=7): 34190 para(c7,c4,c2,c3). [resolve(33931,a,262,a)].
% 101.69/19.39
% 101.69/19.39 % SZS status Theorem for theBenchmark
% 101.69/19.39
% 101.69/19.39 % Proof 1 at 4.50 (+ 1.25) seconds.
% 101.69/19.39 % Length of proof is 187.
% 101.69/19.39 % Level of proof is 32.
% 101.69/19.39 % Maximum clause weight is 31.000.
% 101.69/19.39 % Given clauses 6046.
% 101.69/19.39
% 101.69/19.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------