%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO594+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 : n009.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 07:18:11 AM UTC 2026
% Result : Theorem 11.30s 1.98s
% Output : CNFRefutation 11.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 34
% Syntax : Number of formulae : 215 ( 99 unt; 0 def)
% Number of atoms : 420 ( 0 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 330 ( 125 ~; 125 |; 45 &)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 512 ( 66 sgn 178 !; 6 ?)
% 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(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(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(ruleD18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('theBenchmark.p',ruleD18) ).
fof(ruleD19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('theBenchmark.p',ruleD19) ).
fof(ruleD21,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('theBenchmark.p',ruleD21) ).
fof(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(ruleD29,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(A,B,P,Q,C,D,U,V) ),
file('theBenchmark.p',ruleD29) ).
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(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(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(ruleD57,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('theBenchmark.p',ruleD57) ).
fof(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(ruleD65,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('theBenchmark.p',ruleD65) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('theBenchmark.p',ruleD73) ).
fof(ruleD75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('theBenchmark.p',ruleD75) ).
fof(exemplo6GDDFULL416056,conjecture,
! [A,B,M,O,D,E] :
( ( para(A,O,E,M)
& perp(A,O,A,E)
& coll(D,A,B)
& coll(D,M,O)
& circle(O,A,B,M)
& ( cong(M,A,M,B)
| cong(M,A,A,B) ) )
=> cong(M,E,M,D) ),
file('theBenchmark.p',exemplo6GDDFULL416056) ).
fof(exemplo6GDDFULL416056_neg,negated_conjecture,
~ ! [A,B,M,O,D,E] :
( ( para(A,O,E,M)
& perp(A,O,A,E)
& coll(D,A,B)
& coll(D,M,O)
& circle(O,A,B,M)
& ( cong(M,A,M,B)
| cong(M,A,A,B) ) )
=> cong(M,E,M,D) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416056]) ).
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,M,O,D,E] :
( ~ cong(M,E,M,D)
& para(A,O,E,M)
& perp(A,O,A,E)
& coll(D,A,B)
& coll(D,M,O)
& circle(O,A,B,M)
& ( cong(M,A,M,B)
| cong(M,A,A,B) ) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL416056_neg]) ).
fof(sk_exemplo6GDDFULL416056_neg,plain,
( ~ cong(sK0,sK1,sK0,sK2)
& para(sK3,sK4,sK1,sK0)
& perp(sK3,sK4,sK3,sK1)
& coll(sK2,sK3,sK5)
& coll(sK2,sK0,sK4)
& circle(sK4,sK3,sK5,sK0)
& ( cong(sK0,sK3,sK0,sK5)
| cong(sK0,sK3,sK3,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK5,sK4,sK2,sK1]),skolemize(A,sK3),skolemize(B,sK5),skolemize(M,sK0),skolemize(O,sK4),skolemize(D,sK2),skolemize(E,sK1)],[nnf_95]) ).
cnf(c_162,negated_conjecture,
~ cong(sK0,sK1,sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416056_neg]) ).
cnf(c_163,negated_conjecture,
para(sK3,sK4,sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416056_neg]) ).
cnf(c_164,negated_conjecture,
perp(sK3,sK4,sK3,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416056_neg]) ).
cnf(c_165,negated_conjecture,
coll(sK2,sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416056_neg]) ).
cnf(c_166,negated_conjecture,
coll(sK2,sK0,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416056_neg]) ).
cnf(c_198,plain,
( cong(A,B,C,D)
| ~ cong(E,F,V6,V7)
| ~ eqratio(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD75]) ).
cnf(c_200,plain,
( para(A,B,C,D)
| ~ para(E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD73]) ).
cnf(c_206,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_207,plain,
( eqratio(E,A,A,C,E,B,B,D)
| ~ coll(E,B,D)
| ~ coll(E,A,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD65]) ).
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_215,plain,
( perp(B,A,A,D)
| ~ cyclic(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD57]) ).
cnf(c_216,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
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_228,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_239,plain,
( eqratio(A,B,E,F,C,D,V6,V7)
| ~ eqratio(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD29]) ).
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_247,plain,
( eqangle(A,B,E,F,C,D,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD21]) ).
cnf(c_249,plain,
( eqangle(C,D,A,B,V6,V7,E,F)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD19]) ).
cnf(c_250,plain,
( eqangle(B,A,C,D,E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD18]) ).
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_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_261,plain,
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD6]) ).
cnf(c_262,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
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_315,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_251]) ).
cnf(c_320,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_264]) ).
cnf(c_426,plain,
eqangle(sK3,sK4,A,B,sK1,sK0,A,B),
inference(resolve,[status(thm)],[c_228,c_163]) ).
cnf(c_444,plain,
( para(sK3,sK4,A,B)
| ~ perp(sK3,sK1,A,B) ),
inference(resolve,[status(thm)],[c_258,c_164]) ).
cnf(c_446,plain,
( para(A,B,sK3,sK1)
| ~ perp(A,B,sK3,sK4) ),
inference(resolve,[status(thm)],[c_258,c_164]) ).
cnf(c_448,plain,
perp(sK3,sK1,sK3,sK4),
inference(resolve,[status(thm)],[c_259,c_164]) ).
cnf(c_450,plain,
perp(sK3,sK4,sK1,sK3),
inference(resolve,[status(thm)],[c_260,c_164]) ).
cnf(c_453,plain,
( para(A,B,sK1,sK0)
| ~ para(A,B,sK3,sK4) ),
inference(resolve,[status(thm)],[c_261,c_163]) ).
cnf(c_454,plain,
para(sK1,sK0,sK3,sK4),
inference(resolve,[status(thm)],[c_262,c_163]) ).
cnf(c_455,plain,
para(sK3,sK4,sK0,sK1),
inference(resolve,[status(thm)],[c_263,c_163]) ).
cnf(c_460,plain,
coll(sK0,sK2,sK4),
inference(resolve,[status(thm)],[c_265,c_166]) ).
cnf(c_461,plain,
coll(sK3,sK2,sK5),
inference(resolve,[status(thm)],[c_265,c_165]) ).
cnf(c_463,plain,
coll(sK2,sK5,sK3),
inference(resolve,[status(thm)],[c_266,c_165]) ).
cnf(c_484,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_320,c_166]) ).
cnf(c_491,plain,
coll(sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_460,c_320]) ).
cnf(c_496,plain,
coll(sK3,sK5,sK2),
inference(resolve,[status(thm)],[c_461,c_266]) ).
cnf(c_497,plain,
( coll(A,sK5,sK3)
| ~ coll(sK3,sK2,A) ),
inference(resolve,[status(thm)],[c_461,c_264]) ).
cnf(c_503,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_463,c_320]) ).
cnf(c_507,plain,
coll(sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_484,c_320]) ).
cnf(c_517,plain,
( coll(A,sK0,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_491,c_264]) ).
cnf(c_527,plain,
coll(sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_496,c_320]) ).
cnf(c_536,plain,
coll(sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_503,c_266]) ).
cnf(c_542,plain,
( coll(A,sK4,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_507,c_264]) ).
cnf(c_581,plain,
coll(sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_536,c_320]) ).
cnf(c_637,plain,
perp(sK3,sK1,sK4,sK3),
inference(resolve,[status(thm)],[c_448,c_260]) ).
cnf(c_645,plain,
perp(sK1,sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_450,c_259]) ).
cnf(c_678,plain,
para(sK0,sK1,sK3,sK4),
inference(resolve,[status(thm)],[c_455,c_262]) ).
cnf(c_686,plain,
( eqratio(A,sK3,sK3,sK0,A,sK4,sK4,sK1)
| ~ coll(A,sK4,sK1)
| ~ coll(A,sK3,sK0) ),
inference(resolve,[status(thm)],[c_455,c_207]) ).
cnf(c_857,plain,
coll(sK3,sK4,sK2),
inference(resolve,[status(thm)],[c_542,c_527]) ).
cnf(c_859,plain,
coll(sK3,sK2,sK4),
inference(resolve,[status(thm)],[c_857,c_266]) ).
cnf(c_868,plain,
coll(sK4,sK5,sK3),
inference(resolve,[status(thm)],[c_859,c_497]) ).
cnf(c_869,plain,
coll(sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_859,c_320]) ).
cnf(c_888,plain,
coll(sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_868,c_320]) ).
cnf(c_892,plain,
coll(sK3,sK0,sK4),
inference(resolve,[status(thm)],[c_869,c_517]) ).
cnf(c_922,plain,
( coll(A,sK4,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_888,c_264]) ).
cnf(c_929,plain,
coll(sK3,sK4,sK0),
inference(resolve,[status(thm)],[c_892,c_266]) ).
cnf(c_967,plain,
coll(sK4,sK3,sK0),
inference(resolve,[status(thm)],[c_929,c_265]) ).
cnf(c_1330,plain,
eqangle(A,B,sK3,sK4,A,B,sK1,sK0),
inference(resolve,[status(thm)],[c_426,c_249]) ).
cnf(c_1618,plain,
para(sK3,sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_444,c_637]) ).
cnf(c_1628,plain,
para(sK4,sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_1618,c_262]) ).
cnf(c_1660,plain,
para(sK4,sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_1628,c_263]) ).
cnf(c_1675,plain,
eqangle(sK4,sK3,A,B,sK4,sK3,A,B),
inference(resolve,[status(thm)],[c_1660,c_228]) ).
cnf(c_1686,plain,
para(sK1,sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_446,c_645]) ).
cnf(c_1687,plain,
para(sK3,sK1,sK3,sK1),
inference(resolve,[status(thm)],[c_446,c_448]) ).
cnf(c_1692,plain,
para(sK1,sK3,sK1,sK3),
inference(resolve,[status(thm)],[c_1686,c_263]) ).
cnf(c_1708,plain,
eqangle(sK3,sK1,A,B,sK3,sK1,A,B),
inference(resolve,[status(thm)],[c_1687,c_228]) ).
cnf(c_1711,plain,
coll(sK3,sK1,sK1),
inference(resolve,[status(thm)],[c_1687,c_206]) ).
cnf(c_1718,plain,
coll(sK1,sK1,sK3),
inference(resolve,[status(thm)],[c_1711,c_320]) ).
cnf(c_1724,plain,
coll(sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_1718,c_320]) ).
cnf(c_1736,plain,
coll(sK1,sK4,sK3),
inference(resolve,[status(thm)],[c_1724,c_922]) ).
cnf(c_1784,plain,
coll(sK1,sK3,sK4),
inference(resolve,[status(thm)],[c_1736,c_266]) ).
cnf(c_1837,plain,
para(sK0,sK1,sK1,sK0),
inference(resolve,[status(thm)],[c_453,c_678]) ).
cnf(c_1838,plain,
para(sK1,sK0,sK1,sK0),
inference(resolve,[status(thm)],[c_453,c_454]) ).
cnf(c_1860,plain,
coll(sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_1784,c_320]) ).
cnf(c_2161,plain,
eqangle(sK1,sK3,A,B,sK1,sK3,A,B),
inference(resolve,[status(thm)],[c_1692,c_228]) ).
cnf(c_2189,plain,
para(sK0,sK1,sK0,sK1),
inference(resolve,[status(thm)],[c_1837,c_263]) ).
cnf(c_2220,plain,
eqangle(sK1,sK0,A,B,sK1,sK0,A,B),
inference(resolve,[status(thm)],[c_1838,c_228]) ).
cnf(c_2232,plain,
eqangle(sK0,sK1,A,B,sK0,sK1,A,B),
inference(resolve,[status(thm)],[c_2189,c_228]) ).
cnf(c_10587,plain,
( eqratio(sK4,sK3,sK3,sK0,sK4,sK4,sK4,sK1)
| ~ coll(sK4,sK3,sK0) ),
inference(resolve,[status(thm)],[c_686,c_1860]) ).
cnf(c_2440,plain,
eqratio(sK4,sK3,sK3,sK0,sK4,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_967,c_10587]) ).
cnf(c_2612,plain,
eqangle(A,B,sK3,sK4,B,A,sK1,sK0),
inference(resolve,[status(thm)],[c_1330,c_250]) ).
cnf(c_2613,plain,
eqangle(A,B,A,B,sK3,sK4,sK1,sK0),
inference(resolve,[status(thm)],[c_1330,c_247]) ).
cnf(c_10588,plain,
( ~ cong(sK4,sK4,sK4,sK3)
| midp(sK3,sK3,sK3)
| ~ coll(sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_1675,c_282]) ).
cnf(c_2736,plain,
( ~ cong(sK4,sK4,sK4,sK3)
| midp(sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_581,c_10588]) ).
cnf(c_2760,plain,
( cyclic(sK1,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1708,c_225]) ).
cnf(c_2843,plain,
( cyclic(sK3,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_2161,c_225]) ).
cnf(c_2871,plain,
( cyclic(sK0,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_2220,c_225]) ).
cnf(c_2872,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK1,sK1)
| ~ cyclic(sK0,A,sK1,A)
| ~ cyclic(sK0,A,sK1,sK0) ),
inference(resolve,[status(thm)],[c_2220,c_224]) ).
cnf(c_2885,plain,
( cyclic(sK1,A,sK0,sK0)
| ~ coll(sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_2232,c_225]) ).
cnf(c_2886,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK0,sK0)
| ~ cyclic(sK1,A,sK0,A)
| ~ cyclic(sK1,A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_2232,c_224]) ).
cnf(c_3006,plain,
eqratio(sK4,sK3,sK4,sK4,sK3,sK0,sK4,sK1),
inference(resolve,[status(thm)],[c_2440,c_239]) ).
cnf(c_3581,plain,
( cong(sK1,sK4,sK3,sK0)
| ~ cyclic(sK1,sK4,sK3,sK1)
| ~ cyclic(sK1,sK4,sK3,sK0)
| ~ cyclic(sK1,sK4,sK3,sK3) ),
inference(resolve,[status(thm)],[c_2612,c_224]) ).
cnf(c_10589,plain,
( para(A,B,A,B)
| ~ para(sK3,sK4,sK1,sK0) ),
inference(resolve,[status(thm)],[c_2613,c_200]) ).
cnf(c_3586,negated_conjecture,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_163,c_10589]) ).
cnf(c_3600,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_3586,c_206]) ).
cnf(c_3654,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_3600,c_320]) ).
cnf(c_3670,plain,
cyclic(sK1,A,sK0,sK0),
inference(resolve,[status(thm)],[c_3654,c_2885]) ).
cnf(c_3671,plain,
cyclic(sK0,A,sK1,sK1),
inference(resolve,[status(thm)],[c_3654,c_2871]) ).
cnf(c_3672,plain,
cyclic(sK3,A,sK1,sK1),
inference(resolve,[status(thm)],[c_3654,c_2843]) ).
cnf(c_3673,plain,
cyclic(sK1,A,sK3,sK3),
inference(resolve,[status(thm)],[c_3654,c_2760]) ).
cnf(c_3758,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK0,A)
| ~ cyclic(sK1,A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_3670,c_2886]) ).
cnf(c_3761,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK1,A)
| ~ cyclic(sK0,A,sK1,sK0) ),
inference(resolve,[status(thm)],[c_3671,c_2872]) ).
cnf(c_3767,plain,
( cong(sK1,sK4,sK3,sK0)
| ~ cyclic(sK1,sK4,sK3,sK1)
| ~ cyclic(sK1,sK4,sK3,sK0) ),
inference(resolve,[status(thm)],[c_3673,c_3581]) ).
cnf(c_10590,plain,
( coll(B,C,A)
| ~ coll(A,A,B) ),
inference(resolve,[status(thm)],[c_3654,c_264]) ).
cnf(c_3931,plain,
coll(A,B,C),
inference(resolve,[status(thm)],[c_3654,c_10590]) ).
cnf(c_3954,plain,
( midp(D,B,E)
| ~ para(A,D,C,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_3931,c_222]) ).
cnf(c_4016,plain,
cyclic(sK1,sK0,A,sK0),
inference(resolve,[status(thm)],[c_3670,c_253]) ).
cnf(c_4033,plain,
cyclic(sK0,sK1,A,sK1),
inference(resolve,[status(thm)],[c_3671,c_253]) ).
cnf(c_4049,plain,
cyclic(sK3,sK1,A,sK1),
inference(resolve,[status(thm)],[c_3672,c_253]) ).
cnf(c_4130,plain,
cyclic(sK1,sK0,sK0,A),
inference(resolve,[status(thm)],[c_4016,c_254]) ).
cnf(c_4131,plain,
cyclic(sK0,sK1,A,sK0),
inference(resolve,[status(thm)],[c_4016,c_252]) ).
cnf(c_4177,plain,
cyclic(sK0,sK1,sK1,A),
inference(resolve,[status(thm)],[c_4033,c_254]) ).
cnf(c_4178,plain,
cyclic(sK1,sK0,A,sK1),
inference(resolve,[status(thm)],[c_4033,c_252]) ).
cnf(c_4208,plain,
cyclic(sK1,sK3,A,sK1),
inference(resolve,[status(thm)],[c_4049,c_252]) ).
cnf(c_4375,plain,
cyclic(sK0,sK0,A,A),
inference(resolve,[status(thm)],[c_4130,c_315]) ).
cnf(c_10591,plain,
( cyclic(sK0,sK0,A,B)
| ~ cyclic(sK1,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_4130,c_251]) ).
cnf(c_4377,plain,
cyclic(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_4130,c_10591]) ).
cnf(c_4391,plain,
cyclic(sK0,A,sK1,sK0),
inference(resolve,[status(thm)],[c_4131,c_253]) ).
cnf(c_4392,plain,
( cyclic(sK1,A,B,sK0)
| ~ cyclic(sK0,sK1,A,B) ),
inference(resolve,[status(thm)],[c_4131,c_251]) ).
cnf(c_4393,plain,
( cyclic(sK1,A,sK0,B)
| ~ cyclic(sK0,sK1,A,B) ),
inference(resolve,[status(thm)],[c_4131,c_251]) ).
cnf(c_4407,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK1,A) ),
inference(resolve,[status(thm)],[c_4391,c_3761]) ).
cnf(c_10592,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK0,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_4177,c_251]) ).
cnf(c_4577,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_4177,c_10592]) ).
cnf(c_4591,plain,
cyclic(sK1,A,sK0,sK1),
inference(resolve,[status(thm)],[c_4178,c_253]) ).
cnf(c_4607,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK0,A) ),
inference(resolve,[status(thm)],[c_4591,c_3758]) ).
cnf(c_4681,plain,
cyclic(sK1,A,sK3,sK1),
inference(resolve,[status(thm)],[c_4208,c_253]) ).
cnf(c_4698,plain,
( cong(sK1,sK4,sK3,sK0)
| ~ cyclic(sK1,sK4,sK3,sK0) ),
inference(resolve,[status(thm)],[c_4681,c_3767]) ).
cnf(c_10593,plain,
( cyclic(sK0,A,B,A)
| ~ cyclic(sK0,sK0,A,B) ),
inference(resolve,[status(thm)],[c_4375,c_251]) ).
cnf(c_5264,plain,
cyclic(sK0,A,B,A),
inference(resolve,[status(thm)],[c_4377,c_10593]) ).
cnf(c_5277,plain,
cong(sK0,A,sK0,A),
inference(resolve,[status(thm)],[c_5264,c_4407]) ).
cnf(c_10594,plain,
( cyclic(sK0,A,B,C)
| ~ cyclic(sK0,sK0,A,B) ),
inference(resolve,[status(thm)],[c_4377,c_251]) ).
cnf(c_5349,plain,
cyclic(sK0,A,B,C),
inference(resolve,[status(thm)],[c_4377,c_10594]) ).
cnf(c_5361,plain,
cyclic(sK1,A,sK0,B),
inference(resolve,[status(thm)],[c_5349,c_4393]) ).
cnf(c_5362,plain,
cyclic(sK1,A,B,sK0),
inference(resolve,[status(thm)],[c_5349,c_4392]) ).
cnf(c_5390,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_5361,c_4607]) ).
cnf(c_5392,plain,
cong(sK1,sK4,sK3,sK0),
inference(resolve,[status(thm)],[c_5362,c_4698]) ).
cnf(c_10595,plain,
( perp(A,sK1,sK1,B)
| ~ cong(sK1,B,sK1,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_4577,c_215]) ).
cnf(c_10596,plain,
( perp(B,sK1,sK1,A)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_5390,c_10595]) ).
cnf(c_5527,plain,
perp(A,sK1,sK1,B),
inference(resolve,[status(thm)],[c_5390,c_10596]) ).
cnf(c_10597,plain,
( perp(sK0,sK0,A,B)
| ~ cong(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_5277,c_216]) ).
cnf(c_6179,plain,
perp(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_5277,c_10597]) ).
cnf(c_6550,plain,
cong(sK3,sK0,sK1,sK4),
inference(resolve,[status(thm)],[c_5392,c_244]) ).
cnf(c_6735,plain,
( cong(B,sK1,B,A)
| ~ midp(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_5527,c_217]) ).
cnf(c_7199,plain,
perp(A,B,sK0,sK0),
inference(resolve,[status(thm)],[c_6179,c_259]) ).
cnf(c_10598,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK0,sK0) ),
inference(resolve,[status(thm)],[c_6179,c_258]) ).
cnf(c_7200,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_7199,c_10598]) ).
cnf(c_7214,plain,
( midp(D,B,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7200,c_3954]) ).
cnf(c_10599,plain,
( midp(A,E,D)
| ~ para(B,D,C,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7200,c_208]) ).
cnf(c_7218,plain,
( midp(A,D,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7200,c_10599]) ).
cnf(c_7303,plain,
cong(sK3,sK0,sK4,sK1),
inference(resolve,[status(thm)],[c_6550,c_245]) ).
cnf(c_10600,plain,
( cong(sK4,sK3,sK4,sK4)
| ~ cong(sK3,sK0,sK4,sK1) ),
inference(resolve,[status(thm)],[c_3006,c_198]) ).
cnf(c_9600,plain,
cong(sK4,sK3,sK4,sK4),
inference(resolve,[status(thm)],[c_7303,c_10600]) ).
cnf(c_9651,plain,
cong(sK4,sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_9600,c_244]) ).
cnf(c_9668,plain,
midp(sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_9651,c_2736]) ).
cnf(c_9669,plain,
midp(sK3,A,B),
inference(resolve,[status(thm)],[c_9668,c_7218]) ).
cnf(c_10453,plain,
midp(A,B,C),
inference(resolve,[status(thm)],[c_9669,c_7214]) ).
cnf(c_10585,plain,
cong(A,sK1,A,B),
inference(resolve,[status(thm)],[c_10453,c_6735]) ).
cnf(c_10586,plain,
$false,
inference(resolve,[status(thm)],[c_10585,c_162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO594+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 13:43:43 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 1722106 was started by sandbox2 on n009,
% 0.19/0.44 % Fri Sep 25 13:43:43 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.49
% 0.19/0.49 % From the command line: assign(max_seconds, 300).
% 11.30/1.98
% 11.30/1.98 % given #500 (T,wt=13): 601 -coll(c3,c4,A) | coll(A,c4,c3). [resolve(558,a,264,b)].
% 11.30/1.98
% 11.30/1.98 % given #1000 (W,wt=13): 1964 -coll(c6,c5,A) | coll(A,c2,c6). [resolve(1869,a,264,b)].
% 11.30/1.98
% 11.30/1.98 % given #1500 (T,wt=10): 4971 cyclic(c4,c4,A,B). [resolve(4300,a,251,b),unit_del(a,4300)].
% 11.30/1.98
% 11.30/1.98 % given #2000 (W,wt=14): 2717 eqangle(c1,c4,c1,c4,A,B,A,B). [resolve(1647,a,247,a)].
% 11.30/1.98
% 11.30/1.98 % SZS status Theorem for theBenchmark
% 11.30/1.98
% 11.30/1.98 % Proof 1 at 1.18 (+ 0.28) seconds.
% 11.30/1.98 % Length of proof is 198.
% 11.30/1.98 % Level of proof is 23.
% 11.30/1.98 % Maximum clause weight is 34.000.
% 11.30/1.98 % Given clauses 2205.
% 11.30/1.98
% 11.30/1.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------