%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO647+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 : n015.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 07:18:18 AM UTC 2026
% Result : Theorem 12.40s 2.26s
% Output : CNFRefutation 12.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 17
% Syntax : Number of formulae : 106 ( 52 unt; 0 def)
% Number of atoms : 194 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 136 ( 48 ~; 44 |; 26 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 179 ( 1 sgn 79 !; 7 ?)
% 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(ruleD11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('theBenchmark.p',ruleD11) ).
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(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(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(exemplo6GDDFULLmoreE0156,conjecture,
! [A,B,C,D,E,F,G] :
( ( para(A,C,G,F)
& para(A,F,G,D)
& midp(F,C,B)
& midp(E,B,A)
& midp(D,A,C) )
=> para(C,E,G,B) ),
file('theBenchmark.p',exemplo6GDDFULLmoreE0156) ).
fof(exemplo6GDDFULLmoreE0156_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( para(A,C,G,F)
& para(A,F,G,D)
& midp(F,C,B)
& midp(E,B,A)
& midp(D,A,C) )
=> para(C,E,G,B) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULLmoreE0156]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G] :
( ~ para(C,E,G,B)
& para(A,C,G,F)
& para(A,F,G,D)
& midp(F,C,B)
& midp(E,B,A)
& midp(D,A,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULLmoreE0156_neg]) ).
fof(sk_exemplo6GDDFULLmoreE0156_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& para(sK4,sK0,sK2,sK5)
& para(sK4,sK5,sK2,sK6)
& midp(sK5,sK0,sK3)
& midp(sK1,sK3,sK4)
& midp(sK6,sK4,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK4,sK0,sK1,sK3,sK5,sK2]),skolemize(A,sK4),skolemize(B,sK3),skolemize(C,sK0),skolemize(D,sK6),skolemize(E,sK1),skolemize(F,sK5),skolemize(G,sK2)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0156_neg]) ).
cnf(c_148,negated_conjecture,
para(sK4,sK0,sK2,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0156_neg]) ).
cnf(c_149,negated_conjecture,
para(sK4,sK5,sK2,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0156_neg]) ).
cnf(c_150,negated_conjecture,
midp(sK5,sK0,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0156_neg]) ).
cnf(c_151,negated_conjecture,
midp(sK1,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0156_neg]) ).
cnf(c_152,negated_conjecture,
midp(sK6,sK4,sK0),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0156_neg]) ).
cnf(c_188,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_189,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_190,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_193,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_194,plain,
( para(B,D,C,E)
| ~ midp(A,D,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD63]) ).
cnf(c_208,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_228,plain,
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD25]) ).
cnf(c_229,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_230,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_241,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_246,plain,
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD6]) ).
cnf(c_247,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_248,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_249,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_250,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_251,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_291,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_193]) ).
cnf(c_305,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_249]) ).
cnf(c_360,plain,
coll(sK6,sK4,sK0),
inference(resolve,[status(thm)],[c_188,c_152]) ).
cnf(c_362,plain,
coll(sK5,sK0,sK3),
inference(resolve,[status(thm)],[c_188,c_150]) ).
cnf(c_363,plain,
cong(sK6,sK4,sK6,sK0),
inference(resolve,[status(thm)],[c_189,c_152]) ).
cnf(c_374,plain,
( para(sK0,A,sK3,B)
| ~ midp(sK5,A,B) ),
inference(resolve,[status(thm)],[c_194,c_150]) ).
cnf(c_375,plain,
( para(A,sK4,B,sK0)
| ~ midp(sK6,A,B) ),
inference(resolve,[status(thm)],[c_194,c_152]) ).
cnf(c_384,plain,
( para(A,sK1,B,sK4)
| ~ midp(A,sK3,B) ),
inference(resolve,[status(thm)],[c_208,c_151]) ).
cnf(c_388,plain,
midp(sK6,sK0,sK4),
inference(resolve,[status(thm)],[c_241,c_152]) ).
cnf(c_390,plain,
midp(sK5,sK3,sK0),
inference(resolve,[status(thm)],[c_241,c_150]) ).
cnf(c_393,plain,
( para(sK4,sK5,A,B)
| ~ para(sK2,sK6,A,B) ),
inference(resolve,[status(thm)],[c_246,c_149]) ).
cnf(c_395,plain,
( para(A,B,sK2,sK6)
| ~ para(A,B,sK4,sK5) ),
inference(resolve,[status(thm)],[c_246,c_149]) ).
cnf(c_396,plain,
( para(A,B,sK2,sK5)
| ~ para(A,B,sK4,sK0) ),
inference(resolve,[status(thm)],[c_246,c_148]) ).
cnf(c_397,plain,
para(sK2,sK6,sK4,sK5),
inference(resolve,[status(thm)],[c_247,c_149]) ).
cnf(c_398,plain,
para(sK2,sK5,sK4,sK0),
inference(resolve,[status(thm)],[c_247,c_148]) ).
cnf(c_399,plain,
para(sK4,sK5,sK6,sK2),
inference(resolve,[status(thm)],[c_248,c_149]) ).
cnf(c_427,plain,
coll(sK0,sK0,sK6),
inference(resolve,[status(thm)],[c_360,c_305]) ).
cnf(c_438,plain,
coll(sK5,sK3,sK0),
inference(resolve,[status(thm)],[c_362,c_251]) ).
cnf(c_454,plain,
cong(sK6,sK0,sK6,sK4),
inference(resolve,[status(thm)],[c_388,c_189]) ).
cnf(c_513,plain,
coll(sK0,sK6,sK0),
inference(resolve,[status(thm)],[c_427,c_251]) ).
cnf(c_514,plain,
( coll(A,sK6,sK0)
| ~ coll(sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_427,c_249]) ).
cnf(c_542,plain,
coll(sK0,sK0,sK5),
inference(resolve,[status(thm)],[c_438,c_305]) ).
cnf(c_555,plain,
coll(sK6,sK0,sK0),
inference(resolve,[status(thm)],[c_513,c_250]) ).
cnf(c_857,plain,
( cong(A,B,sK6,sK0)
| ~ cong(A,B,sK6,sK4) ),
inference(resolve,[status(thm)],[c_363,c_228]) ).
cnf(c_1098,plain,
para(sK6,sK2,sK4,sK5),
inference(resolve,[status(thm)],[c_399,c_247]) ).
cnf(c_2452,plain,
para(sK0,sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_375,c_388]) ).
cnf(c_2810,plain,
para(sK0,sK4,sK0,sK4),
inference(resolve,[status(thm)],[c_2452,c_248]) ).
cnf(c_2823,plain,
para(sK5,sK1,sK0,sK4),
inference(resolve,[status(thm)],[c_384,c_390]) ).
cnf(c_3108,plain,
para(sK4,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_393,c_397]) ).
cnf(c_3207,plain,
para(sK6,sK2,sK2,sK6),
inference(resolve,[status(thm)],[c_395,c_1098]) ).
cnf(c_3209,plain,
( midp(A,sK4,sK4)
| ~ midp(A,sK0,sK0) ),
inference(resolve,[status(thm)],[c_2810,c_291]) ).
cnf(c_3241,plain,
para(sK5,sK1,sK4,sK0),
inference(resolve,[status(thm)],[c_2823,c_248]) ).
cnf(c_3302,plain,
para(sK2,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_396,c_398]) ).
cnf(c_3484,plain,
( midp(A,sK5,sK5)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_3108,c_291]) ).
cnf(c_3725,plain,
para(sK6,sK2,sK6,sK2),
inference(resolve,[status(thm)],[c_3207,c_248]) ).
cnf(c_3878,plain,
para(sK5,sK1,sK2,sK5),
inference(resolve,[status(thm)],[c_3241,c_396]) ).
cnf(c_4076,plain,
( midp(A,sK5,sK5)
| ~ midp(A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_3302,c_291]) ).
cnf(c_4405,plain,
( midp(A,sK2,sK2)
| ~ midp(A,sK6,sK6) ),
inference(resolve,[status(thm)],[c_3725,c_291]) ).
cnf(c_4434,plain,
para(sK5,sK1,sK5,sK2),
inference(resolve,[status(thm)],[c_3878,c_248]) ).
cnf(c_4620,plain,
para(sK5,sK2,sK5,sK1),
inference(resolve,[status(thm)],[c_4434,c_247]) ).
cnf(c_21145,plain,
( midp(A,sK1,sK2)
| ~ para(sK5,sK2,sK5,sK1)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_4434,c_193]) ).
cnf(c_4627,plain,
( midp(A,sK1,sK2)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_4620,c_21145]) ).
cnf(c_4781,plain,
coll(sK5,sK6,sK0),
inference(resolve,[status(thm)],[c_514,c_542]) ).
cnf(c_4794,plain,
coll(sK5,sK0,sK6),
inference(resolve,[status(thm)],[c_4781,c_251]) ).
cnf(c_4809,plain,
coll(sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_4794,c_305]) ).
cnf(c_4848,plain,
coll(sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_4809,c_251]) ).
cnf(c_4915,plain,
coll(sK5,sK6,sK6),
inference(resolve,[status(thm)],[c_4848,c_250]) ).
cnf(c_8033,plain,
cong(sK6,sK0,sK6,sK0),
inference(resolve,[status(thm)],[c_857,c_454]) ).
cnf(c_21146,plain,
( midp(sK6,sK0,sK0)
| ~ coll(sK6,sK0,sK0) ),
inference(resolve,[status(thm)],[c_8033,c_190]) ).
cnf(c_8101,plain,
midp(sK6,sK0,sK0),
inference(resolve,[status(thm)],[c_555,c_21146]) ).
cnf(c_8145,plain,
midp(sK6,sK4,sK4),
inference(resolve,[status(thm)],[c_8101,c_3209]) ).
cnf(c_8269,plain,
midp(sK6,sK5,sK5),
inference(resolve,[status(thm)],[c_8145,c_3484]) ).
cnf(c_8555,plain,
cong(sK6,sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_8269,c_189]) ).
cnf(c_10586,plain,
cong(sK6,sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_8555,c_230]) ).
cnf(c_15000,plain,
cong(sK5,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_10586,c_229]) ).
cnf(c_17025,plain,
cong(sK5,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_15000,c_230]) ).
cnf(c_21147,plain,
( midp(sK5,sK6,sK6)
| ~ coll(sK5,sK6,sK6) ),
inference(resolve,[status(thm)],[c_17025,c_190]) ).
cnf(c_18767,plain,
midp(sK5,sK6,sK6),
inference(resolve,[status(thm)],[c_4915,c_21147]) ).
cnf(c_18774,plain,
midp(sK5,sK2,sK2),
inference(resolve,[status(thm)],[c_18767,c_4405]) ).
cnf(c_18853,plain,
midp(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_18774,c_4076]) ).
cnf(c_18937,plain,
midp(sK5,sK1,sK2),
inference(resolve,[status(thm)],[c_18853,c_4627]) ).
cnf(c_19066,plain,
para(sK0,sK1,sK3,sK2),
inference(resolve,[status(thm)],[c_18937,c_374]) ).
cnf(c_21148,plain,
para(sK0,sK1,sK2,sK3),
inference(resolve,[status(thm)],[c_19066,c_248]) ).
cnf(c_21144,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_147,c_21148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO647+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n015.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 13:49:42 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 1512821 was started by sandbox2 on n015,
% 0.16/0.44 % Fri Sep 25 13:49:42 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.48
% 0.16/0.48 % From the command line: assign(max_seconds, 300).
% 12.40/2.26
% 12.40/2.26 % given #500 (T,wt=10): 3069 perp(c6,c6,c3,c2). [resolve(2675,a,244,a)].
% 12.40/2.26
% 12.40/2.26 % given #1000 (A,wt=21): 741 para(f6(c2,c1,c2,c3,c5,c6),c6,c2,c2). [resolve(337,a,390,a)].
% 12.40/2.26
% 12.40/2.26 % given #1500 (T,wt=10): 9719 para(c3,c6,c2,c3). [resolve(9577,a,496,a)].
% 12.40/2.26
% 12.40/2.26 % given #2000 (A,wt=38): 1032 -cong(c6,c3,c6,A) | -cong(B,c3,B,C) | c6 = B | coll(f13(c3,C,c2,A,c6,B),c3,c2) | -cong(c6,c3,c6,C). [resolve(365,a,140,f),flip(c)].
% 12.40/2.26
% 12.40/2.26 % SZS status Theorem for theBenchmark
% 12.40/2.26
% 12.40/2.26 % Proof 1 at 1.35 (+ 0.39) seconds.
% 12.40/2.26 % Length of proof is 99.
% 12.40/2.26 % Level of proof is 18.
% 12.40/2.26 % Maximum clause weight is 23.000.
% 12.40/2.26 % Given clauses 2107.
% 12.40/2.26
% 12.40/2.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
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