%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO632+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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:18:16 AM UTC 2026
% Result : Theorem 23.57s 3.82s
% Output : CNFRefutation 23.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 27
% Syntax : Number of formulae : 192 ( 90 unt; 0 def)
% Number of atoms : 373 ( 0 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 291 ( 110 ~; 106 |; 47 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-7 aty)
% Number of variables : 407 ( 44 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(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(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(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(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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
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(exemplo6GDDFULL8110995,conjecture,
! [A,B,C,A1,S,F,P,Q,NWPNT1,NWPNT2] :
( ( coll(Q,A,S)
& circle(F,A,Q,NWPNT2)
& coll(P,A,A1)
& circle(F,A,P,NWPNT1)
& circle(F,A,B,C)
& coll(S,B,C)
& eqangle(S,A,A,B,C,A,A,A1)
& midp(A1,C,B) )
=> para(B,C,P,Q) ),
file('theBenchmark.p',exemplo6GDDFULL8110995) ).
fof(exemplo6GDDFULL8110995_neg,negated_conjecture,
~ ! [A,B,C,A1,S,F,P,Q,NWPNT1,NWPNT2] :
( ( coll(Q,A,S)
& circle(F,A,Q,NWPNT2)
& coll(P,A,A1)
& circle(F,A,P,NWPNT1)
& circle(F,A,B,C)
& coll(S,B,C)
& eqangle(S,A,A,B,C,A,A,A1)
& midp(A1,C,B) )
=> para(B,C,P,Q) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL8110995]) ).
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,A1,S,F,P,Q,NWPNT1,NWPNT2] :
( ~ para(B,C,P,Q)
& coll(Q,A,S)
& circle(F,A,Q,NWPNT2)
& coll(P,A,A1)
& circle(F,A,P,NWPNT1)
& circle(F,A,B,C)
& coll(S,B,C)
& eqangle(S,A,A,B,C,A,A,A1)
& midp(A1,C,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL8110995_neg]) ).
fof(sk_exemplo6GDDFULL8110995_neg,plain,
( ~ para(sK3,sK4,sK5,sK6)
& coll(sK6,sK2,sK7)
& circle(sK1,sK2,sK6,sK11)
& coll(sK5,sK2,sK8)
& circle(sK1,sK2,sK5,sK10)
& circle(sK1,sK2,sK3,sK4)
& coll(sK7,sK3,sK4)
& eqangle(sK7,sK2,sK2,sK3,sK4,sK2,sK2,sK8)
& midp(sK8,sK4,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK4,sK3,sK7,sK2,sK1,sK5,sK10,sK6,sK11]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4),skolemize(A1,sK8),skolemize(S,sK7),skolemize(F,sK1),skolemize(P,sK5),skolemize(Q,sK6),skolemize(NWPNT1,sK10),skolemize(NWPNT2,sK11)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110995_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,
~ para(sK3,sK4,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110995_neg]) ).
cnf(c_193,negated_conjecture,
coll(sK6,sK2,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110995_neg]) ).
cnf(c_195,negated_conjecture,
coll(sK7,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110995_neg]) ).
cnf(c_197,negated_conjecture,
midp(sK8,sK4,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110995_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(sK9(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,[sK9]),skolemize(P,sK9(A,B,C,D,M,N,Q))],[nnf_83]) ).
cnf(c_214,plain,
( midp(sK9(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_233,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_234,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_236,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_239,plain,
( para(B,D,C,E)
| ~ midp(A,D,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD63]) ).
cnf(c_246,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_254,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_255,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_258,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_281,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_282,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_283,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_284,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_285,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_286,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_287,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_288,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_289,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_292,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_293,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_294,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_295,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_296,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_311,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_187]) ).
cnf(c_329,plain,
( midp(sK9(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_214]) ).
cnf(c_337,plain,
( para(B,B,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_239]) ).
cnf(c_345,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_281]) ).
cnf(c_346,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_285]) ).
cnf(c_350,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_294]) ).
cnf(c_359,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_346]) ).
cnf(c_430,plain,
coll(sK8,sK4,sK3),
inference(resolve,[status(thm)],[c_233,c_197]) ).
cnf(c_431,plain,
cong(sK8,sK4,sK8,sK3),
inference(resolve,[status(thm)],[c_234,c_197]) ).
cnf(c_432,plain,
( para(sK4,A,sK3,B)
| ~ midp(sK8,A,B) ),
inference(resolve,[status(thm)],[c_239,c_197]) ).
cnf(c_433,plain,
( para(A,sK4,B,sK3)
| ~ midp(sK8,A,B) ),
inference(resolve,[status(thm)],[c_239,c_197]) ).
cnf(c_449,plain,
midp(sK8,sK3,sK4),
inference(resolve,[status(thm)],[c_286,c_197]) ).
cnf(c_453,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_288,c_145]) ).
cnf(c_456,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_289,c_145]) ).
cnf(c_468,plain,
coll(sK3,sK7,sK4),
inference(resolve,[status(thm)],[c_295,c_195]) ).
cnf(c_470,plain,
coll(sK2,sK6,sK7),
inference(resolve,[status(thm)],[c_295,c_193]) ).
cnf(c_471,plain,
coll(sK7,sK4,sK3),
inference(resolve,[status(thm)],[c_296,c_195]) ).
cnf(c_474,plain,
( midp(sK9(sK4,sK3,sK4,sK3,sK8,sK8,A),sK4,A)
| ~ coll(sK3,sK4,sK3)
| ~ coll(sK4,sK4,sK3) ),
inference(resolve,[status(thm)],[c_329,c_197]) ).
cnf(c_485,plain,
coll(sK8,sK3,sK4),
inference(resolve,[status(thm)],[c_430,c_296]) ).
cnf(c_486,plain,
coll(sK4,sK8,sK3),
inference(resolve,[status(thm)],[c_430,c_295]) ).
cnf(c_496,plain,
( midp(sK9(sK3,sK4,sK3,sK4,sK8,sK8,A),sK3,A)
| ~ coll(sK4,sK3,sK4)
| ~ coll(sK3,sK3,sK4) ),
inference(resolve,[status(thm)],[c_449,c_329]) ).
cnf(c_501,plain,
cong(sK8,sK3,sK8,sK4),
inference(resolve,[status(thm)],[c_449,c_234]) ).
cnf(c_513,plain,
coll(sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_468,c_350]) ).
cnf(c_514,plain,
coll(sK3,sK4,sK7),
inference(resolve,[status(thm)],[c_468,c_296]) ).
cnf(c_516,plain,
( coll(sK4,A,sK3)
| ~ coll(sK3,sK7,A) ),
inference(resolve,[status(thm)],[c_468,c_294]) ).
cnf(c_517,plain,
( midp(sK9(sK4,sK3,sK4,sK3,sK8,sK8,A),sK4,A)
| ~ coll(sK3,sK4,sK3) ),
inference(resolve,[status(thm)],[c_513,c_474]) ).
cnf(c_522,plain,
coll(sK7,sK7,sK2),
inference(resolve,[status(thm)],[c_470,c_350]) ).
cnf(c_526,plain,
coll(sK3,sK3,sK7),
inference(resolve,[status(thm)],[c_471,c_350]) ).
cnf(c_558,plain,
coll(sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_486,c_350]) ).
cnf(c_562,plain,
( midp(sK9(sK3,sK4,sK3,sK4,sK8,sK8,A),sK3,A)
| ~ coll(sK4,sK3,sK4) ),
inference(resolve,[status(thm)],[c_558,c_496]) ).
cnf(c_563,plain,
coll(sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_513,c_296]) ).
cnf(c_566,plain,
midp(sK9(sK3,sK4,sK3,sK4,sK8,sK8,A),sK3,A),
inference(resolve,[status(thm)],[c_563,c_562]) ).
cnf(c_567,plain,
coll(sK7,sK7,sK3),
inference(resolve,[status(thm)],[c_514,c_350]) ).
cnf(c_579,plain,
coll(sK2,sK2,sK7),
inference(resolve,[status(thm)],[c_522,c_350]) ).
cnf(c_587,plain,
coll(sK3,sK7,sK3),
inference(resolve,[status(thm)],[c_526,c_296]) ).
cnf(c_637,plain,
coll(sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_558,c_296]) ).
cnf(c_639,plain,
( coll(sK4,A,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_558,c_294]) ).
cnf(c_640,plain,
midp(sK9(sK4,sK3,sK4,sK3,sK8,sK8,A),sK4,A),
inference(resolve,[status(thm)],[c_637,c_517]) ).
cnf(c_647,plain,
( coll(A,sK3,sK7)
| ~ coll(sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_567,c_294]) ).
cnf(c_648,plain,
( coll(sK3,A,sK7)
| ~ coll(sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_567,c_294]) ).
cnf(c_663,plain,
( coll(A,sK7,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_579,c_294]) ).
cnf(c_674,plain,
( coll(A,sK3,sK3)
| ~ coll(sK3,sK7,A) ),
inference(resolve,[status(thm)],[c_587,c_294]) ).
cnf(c_777,plain,
cyclic(sK4,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_431,c_359]) ).
cnf(c_24681,plain,
( perp(sK3,sK4,sK4,sK4)
| ~ coll(sK8,sK3,sK4) ),
inference(resolve,[status(thm)],[c_501,c_311]) ).
cnf(c_930,plain,
perp(sK3,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_485,c_24681]) ).
cnf(c_999,plain,
cyclic(sK3,sK4,sK3,sK3),
inference(resolve,[status(thm)],[c_777,c_282]) ).
cnf(c_1094,plain,
( para(sK3,sK4,A,B)
| ~ perp(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_930,c_288]) ).
cnf(c_1138,plain,
cyclic(sK3,sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_999,c_283]) ).
cnf(c_1231,plain,
cyclic(sK3,sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_1138,c_284]) ).
cnf(c_1317,plain,
cyclic(sK3,sK3,sK4,sK4),
inference(resolve,[status(thm)],[c_1231,c_345]) ).
cnf(c_1410,plain,
cyclic(sK3,sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_1317,c_283]) ).
cnf(c_1475,plain,
cyclic(sK4,sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_1410,c_282]) ).
cnf(c_1533,plain,
( cyclic(sK3,sK3,sK4,A)
| ~ cyclic(sK4,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1475,c_281]) ).
cnf(c_1551,plain,
para(sK4,sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_432,c_449]) ).
cnf(c_1560,plain,
para(sK3,sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_433,c_449]) ).
cnf(c_1573,plain,
para(sK4,sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_1551,c_293]) ).
cnf(c_1597,plain,
para(sK3,sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_1560,c_293]) ).
cnf(c_1620,plain,
eqangle(sK4,sK3,A,B,sK4,sK3,A,B),
inference(resolve,[status(thm)],[c_1573,c_258]) ).
cnf(c_1632,plain,
eqangle(sK3,sK4,A,B,sK3,sK4,A,B),
inference(resolve,[status(thm)],[c_1597,c_258]) ).
cnf(c_1741,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_456,c_453]) ).
cnf(c_2296,plain,
midp(sK9(sK3,sK4,sK3,sK4,sK8,sK8,A),A,sK3),
inference(resolve,[status(thm)],[c_566,c_286]) ).
cnf(c_2299,plain,
( para(B,sK3,C,A)
| ~ midp(sK9(sK3,sK4,sK3,sK4,sK8,sK8,A),B,C) ),
inference(resolve,[status(thm)],[c_566,c_239]) ).
cnf(c_2622,plain,
para(sK4,sK4,A,A),
inference(resolve,[status(thm)],[c_640,c_337]) ).
cnf(c_2766,plain,
coll(sK2,sK1,sK1),
inference(resolve,[status(thm)],[c_1741,c_236]) ).
cnf(c_2773,plain,
coll(sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_2766,c_350]) ).
cnf(c_2785,plain,
coll(sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_2773,c_350]) ).
cnf(c_2798,plain,
coll(sK1,sK7,sK2),
inference(resolve,[status(thm)],[c_2785,c_663]) ).
cnf(c_2824,plain,
coll(sK1,sK2,sK7),
inference(resolve,[status(thm)],[c_2798,c_296]) ).
cnf(c_2880,plain,
coll(sK7,sK7,sK1),
inference(resolve,[status(thm)],[c_2824,c_350]) ).
cnf(c_2974,plain,
coll(sK3,sK1,sK7),
inference(resolve,[status(thm)],[c_2880,c_648]) ).
cnf(c_2975,plain,
coll(sK1,sK3,sK7),
inference(resolve,[status(thm)],[c_2880,c_647]) ).
cnf(c_3086,plain,
coll(sK3,sK7,sK1),
inference(resolve,[status(thm)],[c_2974,c_296]) ).
cnf(c_3095,plain,
coll(sK1,sK7,sK3),
inference(resolve,[status(thm)],[c_2975,c_296]) ).
cnf(c_3173,plain,
coll(sK1,sK3,sK3),
inference(resolve,[status(thm)],[c_3086,c_674]) ).
cnf(c_3174,plain,
coll(sK4,sK1,sK3),
inference(resolve,[status(thm)],[c_3086,c_516]) ).
cnf(c_3186,plain,
coll(sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_3095,c_350]) ).
cnf(c_3254,plain,
( coll(A,sK3,sK1)
| ~ coll(sK1,sK3,A) ),
inference(resolve,[status(thm)],[c_3173,c_294]) ).
cnf(c_3256,plain,
coll(sK4,sK3,sK1),
inference(resolve,[status(thm)],[c_3174,c_296]) ).
cnf(c_3279,plain,
( coll(sK1,A,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_3186,c_294]) ).
cnf(c_3334,plain,
( coll(A,sK1,sK4)
| ~ coll(sK4,sK3,A) ),
inference(resolve,[status(thm)],[c_3256,c_294]) ).
cnf(c_3387,plain,
para(A,A,sK4,sK4),
inference(resolve,[status(thm)],[c_2622,c_292]) ).
cnf(c_3432,plain,
( perp(C,C,A,B)
| ~ perp(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_3387,c_287]) ).
cnf(c_13943,plain,
( cyclic(sK3,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_1620,c_255]) ).
cnf(c_14736,plain,
( cyclic(sK4,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1632,c_255]) ).
cnf(c_14737,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK3,sK3)
| ~ cyclic(sK4,A,sK3,A)
| ~ cyclic(sK4,A,sK3,sK4) ),
inference(resolve,[status(thm)],[c_1632,c_254]) ).
cnf(c_22398,plain,
para(A,sK3,sK3,A),
inference(resolve,[status(thm)],[c_2299,c_2296]) ).
cnf(c_22402,plain,
para(A,sK3,A,sK3),
inference(resolve,[status(thm)],[c_22398,c_293]) ).
cnf(c_22435,plain,
coll(A,sK3,sK3),
inference(resolve,[status(thm)],[c_22402,c_236]) ).
cnf(c_22499,plain,
coll(sK3,sK3,A),
inference(resolve,[status(thm)],[c_22435,c_350]) ).
cnf(c_22504,plain,
cyclic(sK4,A,sK3,sK3),
inference(resolve,[status(thm)],[c_22499,c_14736]) ).
cnf(c_22508,plain,
coll(sK1,A,sK3),
inference(resolve,[status(thm)],[c_22499,c_3279]) ).
cnf(c_22516,plain,
coll(sK4,A,sK3),
inference(resolve,[status(thm)],[c_22499,c_639]) ).
cnf(c_22537,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK3,A)
| ~ cyclic(sK4,A,sK3,sK4) ),
inference(resolve,[status(thm)],[c_22504,c_14737]) ).
cnf(c_24682,plain,
( coll(A,B,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_22499,c_294]) ).
cnf(c_22743,plain,
coll(A,B,sK3),
inference(resolve,[status(thm)],[c_22499,c_24682]) ).
cnf(c_22748,plain,
coll(sK1,sK3,A),
inference(resolve,[status(thm)],[c_22508,c_296]) ).
cnf(c_22766,plain,
coll(A,sK3,sK1),
inference(resolve,[status(thm)],[c_22748,c_3254]) ).
cnf(c_23074,plain,
coll(sK4,sK3,A),
inference(resolve,[status(thm)],[c_22516,c_296]) ).
cnf(c_23084,plain,
coll(A,sK1,sK4),
inference(resolve,[status(thm)],[c_23074,c_3334]) ).
cnf(c_23639,plain,
coll(A,sK3,B),
inference(resolve,[status(thm)],[c_22743,c_296]) ).
cnf(c_24683,plain,
( coll(B,sK1,A)
| ~ coll(A,sK3,B) ),
inference(resolve,[status(thm)],[c_22766,c_294]) ).
cnf(c_23705,plain,
coll(A,sK1,B),
inference(resolve,[status(thm)],[c_23639,c_24683]) ).
cnf(c_24684,plain,
( coll(B,sK4,A)
| ~ coll(A,sK1,B) ),
inference(resolve,[status(thm)],[c_23084,c_294]) ).
cnf(c_23783,plain,
coll(A,sK4,B),
inference(resolve,[status(thm)],[c_23705,c_24684]) ).
cnf(c_23787,plain,
cyclic(sK3,A,sK4,sK4),
inference(resolve,[status(thm)],[c_23783,c_13943]) ).
cnf(c_23875,plain,
cyclic(sK4,sK3,A,sK3),
inference(resolve,[status(thm)],[c_22504,c_283]) ).
cnf(c_23895,plain,
cyclic(sK3,sK4,A,sK4),
inference(resolve,[status(thm)],[c_23787,c_283]) ).
cnf(c_23944,plain,
cyclic(sK4,sK3,sK3,A),
inference(resolve,[status(thm)],[c_23875,c_284]) ).
cnf(c_23945,plain,
cyclic(sK3,sK4,A,sK3),
inference(resolve,[status(thm)],[c_23875,c_282]) ).
cnf(c_23955,plain,
cyclic(sK3,sK3,sK4,A),
inference(resolve,[status(thm)],[c_23944,c_1533]) ).
cnf(c_24076,plain,
( cyclic(sK4,A,B,sK4)
| ~ cyclic(sK3,sK4,A,B) ),
inference(resolve,[status(thm)],[c_23895,c_281]) ).
cnf(c_24685,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK4,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_23944,c_281]) ).
cnf(c_24120,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_23944,c_24685]) ).
cnf(c_24126,plain,
( cyclic(sK4,A,sK3,B)
| ~ cyclic(sK3,sK4,A,B) ),
inference(resolve,[status(thm)],[c_23945,c_281]) ).
cnf(c_24686,plain,
( cyclic(sK3,sK4,A,B)
| ~ cyclic(sK3,sK3,sK4,A) ),
inference(resolve,[status(thm)],[c_23955,c_281]) ).
cnf(c_24156,plain,
cyclic(sK3,sK4,A,B),
inference(resolve,[status(thm)],[c_24120,c_24686]) ).
cnf(c_24159,plain,
cyclic(sK4,A,sK3,B),
inference(resolve,[status(thm)],[c_24156,c_24126]) ).
cnf(c_24162,plain,
cyclic(sK4,A,B,sK4),
inference(resolve,[status(thm)],[c_24156,c_24076]) ).
cnf(c_24687,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK3,A) ),
inference(resolve,[status(thm)],[c_24162,c_22537]) ).
cnf(c_24165,plain,
cong(sK4,A,sK4,A),
inference(resolve,[status(thm)],[c_24159,c_24687]) ).
cnf(c_24688,plain,
( perp(sK4,sK4,A,B)
| ~ cong(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_24165,c_246]) ).
cnf(c_24645,plain,
perp(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_24165,c_24688]) ).
cnf(c_24677,plain,
perp(A,A,B,C),
inference(resolve,[status(thm)],[c_24645,c_3432]) ).
cnf(c_24679,plain,
para(sK3,sK4,A,B),
inference(resolve,[status(thm)],[c_24677,c_1094]) ).
cnf(c_24680,plain,
$false,
inference(resolve,[status(thm)],[c_24679,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO632+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:45:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2221166 was started by sandbox2 on n012,
% 0.08/0.35 % Fri Sep 25 13:45:35 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 23.57/3.82
% 23.57/3.82 % given #500 (A,wt=24): 454 -perp(A,B,f12(c1,c7,c9,c6),c1) | para(A,B,c1,c6). [resolve(288,b,131,a)].
% 23.57/3.82
% 23.57/3.82 % given #1000 (T,wt=10): 3400 para(c6,c1,c1,c6). [resolve(2762,a,292,a)].
% 23.57/3.82
% 23.57/3.82 % given #1500 (A,wt=33): 939 -cong(A,c2,A,c3) | c4 = A | coll(f13(c2,c3,B,c3,A,c4),c2,B) | -cong(A,c2,A,B). [resolve(501,a,307,b)].
% 23.57/3.82
% 23.57/3.82 % given #2000 (W,wt=10): 7297 para(c3,c2,c4,c3). [resolve(6897,a,292,a)].
% 23.57/3.82
% 23.57/3.82 % given #2500 (T,wt=10): 9426 para(c4,c2,c4,c4). [resolve(8464,a,1050,a)].
% 23.57/3.82
% 23.57/3.82 % given #3000 (W,wt=10): 16002 para(c3,c1,c1,c4). [resolve(14938,a,293,a)].
% 23.57/3.82
% 23.57/3.82 % given #3500 (T,wt=10): 20547 para(c3,c4,c3,c4). [resolve(20015,a,293,a)].
% 23.57/3.82
% 23.57/3.82 % given #4000 (A,wt=36): 2639 -midp(A,B,C) | midp(f6(B,C,c3,D,A,f7(c3,c2,c3,c2,c4,c4,D)),B,D). [resolve(640,a,217,b)].
% 23.57/3.82
% 23.57/3.82 % SZS status Theorem for theBenchmark
% 23.57/3.82
% 23.57/3.82 % Proof 1 at 2.38 (+ 0.85) seconds.
% 23.57/3.82 % Length of proof is 177.
% 23.57/3.82 % Level of proof is 28.
% 23.57/3.82 % Maximum clause weight is 37.000.
% 23.57/3.82 % Given clauses 4358.
% 23.57/3.82
% 23.57/3.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------