%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO541+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 : n017.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 07:18:04 AM UTC 2026
% Result : Theorem 8.90s 1.56s
% Output : CNFRefutation 8.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 103 ( 39 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 198 ( 69 ~; 65 |; 43 &)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-6 aty)
% Number of variables : 257 ( 2 sgn 127 !; 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(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(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(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(ruleD44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('theBenchmark.p',ruleD44) ).
fof(ruleD53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('theBenchmark.p',ruleD53) ).
fof(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(ruleX6,axiom,
! [A,B,C,D,M,N] :
? [P] :
( ( midp(N,C,D)
& midp(M,A,B) )
=> ( para(P,N,A,C)
& para(P,M,B,D)
& midp(P,A,D) ) ),
file('theBenchmark.p',ruleX6) ).
fof(exemplo6GDDFULL012001,conjecture,
! [A,B,C,D,E,F,G] :
( ( midp(G,D,E)
& midp(F,C,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B) )
=> perp(F,G,D,E) ),
file('theBenchmark.p',exemplo6GDDFULL012001) ).
fof(exemplo6GDDFULL012001_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( midp(G,D,E)
& midp(F,C,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B) )
=> perp(F,G,D,E) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012001]) ).
cnf(c_97,plain,
( circle(A,B,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD12]) ).
cnf(c_101,plain,
( perp(B,C,C,D)
| ~ coll(A,B,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD53]) ).
cnf(c_142,plain,
( ~ cong(A,B,A,C)
| ~ cong(A,B,A,D)
| perp(B,D,D,C)
| ~ coll(A,B,C) ),
inference(resolve,[status(thm)],[c_101,c_97]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G] :
( ~ perp(F,G,D,E)
& midp(G,D,E)
& midp(F,C,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012001_neg]) ).
fof(sk_exemplo6GDDFULL012001_neg,plain,
( ~ perp(sK0,sK1,sK2,sK3)
& midp(sK1,sK2,sK3)
& midp(sK0,sK4,sK5)
& coll(sK3,sK6,sK4)
& perp(sK3,sK5,sK6,sK4)
& coll(sK2,sK6,sK5)
& perp(sK2,sK4,sK6,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK4,sK6,sK5,sK3,sK0,sK1]),skolemize(A,sK6),skolemize(B,sK5),skolemize(C,sK4),skolemize(D,sK2),skolemize(E,sK3),skolemize(F,sK0),skolemize(G,sK1)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ perp(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012001_neg]) ).
cnf(c_148,negated_conjecture,
midp(sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012001_neg]) ).
cnf(c_149,negated_conjecture,
midp(sK0,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012001_neg]) ).
cnf(c_153,negated_conjecture,
perp(sK2,sK4,sK6,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012001_neg]) ).
fof(nnf_82,plain,
! [A,B,C,D,M,N] :
? [P] :
( ( para(P,N,A,C)
& para(P,M,B,D)
& midp(P,A,D) )
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(fof_nnf,[status(thm)],[ruleX6]) ).
fof(sk_ruleX6_sk,plain,
! [A,B,C,D,M,N] :
( ( para(sK7(A,B,C,D,M,N),N,A,C)
& para(sK7(A,B,C,D,M,N),M,B,D)
& midp(sK7(A,B,C,D,M,N),A,D) )
| ~ 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))],[nnf_82]) ).
fof(sk_ruleX6,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( para(sK7(VAR_1,VAR_2,VAR_4,VAR_5,VAR_0,VAR_3),VAR_3,VAR_1,VAR_4)
| ~ midp(VAR_3,VAR_4,VAR_5)
| ~ midp(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( para(sK7(VAR_1,VAR_2,VAR_4,VAR_5,VAR_0,VAR_3),VAR_0,VAR_2,VAR_5)
| ~ midp(VAR_3,VAR_4,VAR_5)
| ~ midp(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( midp(sK7(VAR_1,VAR_2,VAR_4,VAR_5,VAR_0,VAR_3),VAR_1,VAR_5)
| ~ midp(VAR_3,VAR_4,VAR_5)
| ~ midp(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_ruleX6_sk]) ).
cnf(c_173,plain,
( midp(sK7(B,C,E,F,A,D),B,F)
| ~ midp(D,E,F)
| ~ midp(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_ruleX6]) ).
cnf(c_189,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_190,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_191,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_194,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_195,plain,
( para(B,D,C,E)
| ~ midp(A,D,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD63]) ).
cnf(c_209,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_229,plain,
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD25]) ).
cnf(c_242,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_243,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_244,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_245,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_247,plain,
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD6]) ).
cnf(c_249,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_250,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_251,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_252,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_267,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_142]) ).
cnf(c_292,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_194]) ).
cnf(c_293,plain,
( para(B,B,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_195]) ).
cnf(c_306,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_250]) ).
cnf(c_16694,negated_conjecture,
( midp(sK7(sK4,sK5,B,C,sK0,A),sK4,C)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_173,c_149]) ).
cnf(c_359,negated_conjecture,
midp(sK7(sK4,sK5,sK2,sK3,sK0,sK1),sK4,sK3),
inference(resolve,[status(thm)],[c_16694,c_148]) ).
cnf(c_374,plain,
coll(sK0,sK4,sK5),
inference(resolve,[status(thm)],[c_189,c_149]) ).
cnf(c_375,plain,
coll(sK1,sK2,sK3),
inference(resolve,[status(thm)],[c_189,c_148]) ).
cnf(c_376,plain,
cong(sK0,sK4,sK0,sK5),
inference(resolve,[status(thm)],[c_190,c_149]) ).
cnf(c_377,plain,
cong(sK1,sK2,sK1,sK3),
inference(resolve,[status(thm)],[c_190,c_148]) ).
cnf(c_392,plain,
midp(sK0,sK5,sK4),
inference(resolve,[status(thm)],[c_242,c_149]) ).
cnf(c_393,plain,
midp(sK1,sK3,sK2),
inference(resolve,[status(thm)],[c_242,c_148]) ).
cnf(c_398,plain,
perp(sK6,sK5,sK2,sK4),
inference(resolve,[status(thm)],[c_245,c_153]) ).
cnf(c_414,plain,
coll(sK5,sK5,sK0),
inference(resolve,[status(thm)],[c_374,c_306]) ).
cnf(c_420,plain,
coll(sK1,sK3,sK2),
inference(resolve,[status(thm)],[c_375,c_252]) ).
cnf(c_425,plain,
para(sK5,sK5,sK4,sK4),
inference(resolve,[status(thm)],[c_392,c_293]) ).
cnf(c_436,plain,
cong(sK0,sK5,sK0,sK4),
inference(resolve,[status(thm)],[c_392,c_190]) ).
cnf(c_16695,negated_conjecture,
( para(sK4,A,sK5,B)
| ~ midp(sK0,A,B) ),
inference(resolve,[status(thm)],[c_195,c_149]) ).
cnf(c_447,negated_conjecture,
para(sK4,sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_16695,c_392]) ).
cnf(c_477,plain,
cong(sK1,sK3,sK1,sK2),
inference(resolve,[status(thm)],[c_393,c_190]) ).
cnf(c_539,plain,
coll(sK5,sK0,sK5),
inference(resolve,[status(thm)],[c_414,c_252]) ).
cnf(c_557,plain,
coll(sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_420,c_306]) ).
cnf(c_617,plain,
coll(sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_539,c_251]) ).
cnf(c_657,plain,
coll(sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_557,c_252]) ).
cnf(c_830,plain,
coll(sK1,sK2,sK2),
inference(resolve,[status(thm)],[c_657,c_251]) ).
cnf(c_1570,plain,
para(sK4,sK4,sK3,sK3),
inference(resolve,[status(thm)],[c_359,c_293]) ).
cnf(c_16696,plain,
( perp(sK2,sK3,sK3,sK3)
| ~ coll(sK1,sK2,sK3) ),
inference(resolve,[status(thm)],[c_377,c_267]) ).
cnf(c_2123,plain,
perp(sK2,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_375,c_16696]) ).
cnf(c_16697,negated_conjecture,
( para(sK2,sK4,A,B)
| ~ perp(sK6,sK5,A,B) ),
inference(resolve,[status(thm)],[c_244,c_153]) ).
cnf(c_2676,negated_conjecture,
para(sK2,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_16697,c_398]) ).
cnf(c_16698,plain,
( cong(sK0,sK5,A,B)
| ~ cong(sK0,sK4,A,B) ),
inference(resolve,[status(thm)],[c_229,c_436]) ).
cnf(c_3048,plain,
cong(sK0,sK5,sK0,sK5),
inference(resolve,[status(thm)],[c_16698,c_376]) ).
cnf(c_3053,plain,
para(sK4,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_447,c_249]) ).
cnf(c_16699,plain,
( cong(sK1,sK2,A,B)
| ~ cong(sK1,sK3,A,B) ),
inference(resolve,[status(thm)],[c_229,c_377]) ).
cnf(c_3610,plain,
cong(sK1,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_16699,c_477]) ).
cnf(c_16700,plain,
( para(sK5,sK5,A,B)
| ~ para(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_247,c_425]) ).
cnf(c_3971,plain,
para(sK5,sK5,sK3,sK3),
inference(resolve,[status(thm)],[c_16700,c_1570]) ).
cnf(c_4267,plain,
perp(sK3,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_2123,c_245]) ).
cnf(c_16701,plain,
( midp(sK0,sK5,sK5)
| ~ coll(sK0,sK5,sK5) ),
inference(resolve,[status(thm)],[c_3048,c_191]) ).
cnf(c_6184,plain,
midp(sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_617,c_16701]) ).
cnf(c_16702,plain,
( midp(sK1,sK2,sK2)
| ~ coll(sK1,sK2,sK2) ),
inference(resolve,[status(thm)],[c_3610,c_191]) ).
cnf(c_7134,plain,
midp(sK1,sK2,sK2),
inference(resolve,[status(thm)],[c_830,c_16702]) ).
cnf(c_16703,plain,
( midp(sK1,A,A)
| ~ para(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_292,c_7134]) ).
cnf(c_7211,plain,
midp(sK1,sK4,sK4),
inference(resolve,[status(thm)],[c_16703,c_2676]) ).
cnf(c_16704,plain,
( midp(sK1,A,A)
| ~ para(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_292,c_7211]) ).
cnf(c_7354,plain,
midp(sK1,sK5,sK5),
inference(resolve,[status(thm)],[c_16704,c_3053]) ).
cnf(c_16705,plain,
( para(sK0,A,sK5,B)
| ~ midp(A,sK5,B) ),
inference(resolve,[status(thm)],[c_209,c_6184]) ).
cnf(c_7511,plain,
para(sK0,sK1,sK5,sK5),
inference(resolve,[status(thm)],[c_16705,c_7354]) ).
cnf(c_16706,plain,
( perp(sK5,sK5,A,B)
| ~ perp(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_243,c_3971]) ).
cnf(c_9145,plain,
perp(sK5,sK5,sK2,sK3),
inference(resolve,[status(thm)],[c_16706,c_4267]) ).
cnf(c_16707,plain,
( perp(sK0,sK1,A,B)
| ~ perp(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_243,c_7511]) ).
cnf(c_16708,plain,
perp(sK0,sK1,sK2,sK3),
inference(resolve,[status(thm)],[c_16707,c_9145]) ).
cnf(c_16693,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_147,c_16708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO541+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.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 13:35:33 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 2392525 was started by sandbox on n017,
% 0.12/0.36 % Fri Sep 25 13:35:33 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 8.90/1.56
% 8.90/1.56 % given #500 (W,wt=9): 1153 coll(c5,c3,c4). [resolve(854,a,251,a)].
% 8.90/1.56
% 8.90/1.56 % SZS status Theorem for theBenchmark
% 8.90/1.56
% 8.90/1.56 % Proof 1 at 0.81 (+ 0.34) seconds.
% 8.90/1.56 % Length of proof is 82.
% 8.90/1.56 % Level of proof is 11.
% 8.90/1.56 % Maximum clause weight is 28.000.
% 8.90/1.56 % Given clauses 861.
% 8.90/1.56
% 8.90/1.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------