%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO553+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 : n016.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 07:18:05 AM UTC 2026
% Result : Theorem 18.56s 10.48s
% Output : CNFRefutation 18.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 20
% Syntax : Number of formulae : 94 ( 36 unt; 0 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 174 ( 54 ~; 50 |; 49 &)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 283 ( 33 sgn 110 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(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(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(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(exemplo6GDDFULL012013,conjecture,
! [A,B,C,D,E,F,G,H] :
( ( coll(H,B,D)
& perp(H,C,B,D)
& coll(G,A,C)
& perp(G,D,A,C)
& coll(F,B,D)
& perp(F,A,B,D)
& coll(E,A,C)
& perp(E,B,A,C)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(E,F,G,H) ),
file('theBenchmark.p',exemplo6GDDFULL012013) ).
fof(exemplo6GDDFULL012013_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H] :
( ( coll(H,B,D)
& perp(H,C,B,D)
& coll(G,A,C)
& perp(G,D,A,C)
& coll(F,B,D)
& perp(F,A,B,D)
& coll(E,A,C)
& perp(E,B,A,C)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(E,F,G,H) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012013]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G,H] :
( ~ para(E,F,G,H)
& coll(H,B,D)
& perp(H,C,B,D)
& coll(G,A,C)
& perp(G,D,A,C)
& coll(F,B,D)
& perp(F,A,B,D)
& coll(E,A,C)
& perp(E,B,A,C)
& para(A,C,B,D)
& para(A,B,C,D) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012013_neg]) ).
fof(sk_exemplo6GDDFULL012013_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& coll(sK3,sK5,sK6)
& perp(sK3,sK7,sK5,sK6)
& coll(sK2,sK4,sK7)
& perp(sK2,sK6,sK4,sK7)
& coll(sK1,sK5,sK6)
& perp(sK1,sK4,sK5,sK6)
& coll(sK0,sK4,sK7)
& perp(sK0,sK5,sK4,sK7)
& para(sK4,sK7,sK5,sK6)
& para(sK4,sK5,sK7,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK7,sK6,sK0,sK1,sK2,sK3]),skolemize(A,sK4),skolemize(B,sK5),skolemize(C,sK7),skolemize(D,sK6),skolemize(E,sK0),skolemize(F,sK1),skolemize(G,sK2),skolemize(H,sK3)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012013_neg]) ).
cnf(c_153,negated_conjecture,
perp(sK1,sK4,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012013_neg]) ).
cnf(c_157,negated_conjecture,
para(sK4,sK5,sK7,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012013_neg]) ).
cnf(c_190,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_196,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_205,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_206,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_214,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_215,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_218,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_237,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_239,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_241,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_242,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_243,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_244,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_248,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_249,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_250,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_252,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_253,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_254,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_305,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_241]) ).
cnf(c_310,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_254]) ).
cnf(c_384,plain,
eqangle(sK4,sK5,A,B,sK7,sK6,A,B),
inference(resolve,[status(thm)],[c_218,c_157]) ).
cnf(c_389,plain,
( para(sK1,sK4,A,B)
| ~ perp(sK5,sK6,A,B) ),
inference(resolve,[status(thm)],[c_248,c_153]) ).
cnf(c_397,plain,
perp(sK5,sK6,sK1,sK4),
inference(resolve,[status(thm)],[c_249,c_153]) ).
cnf(c_710,plain,
perp(sK5,sK6,sK4,sK1),
inference(resolve,[status(thm)],[c_397,c_250]) ).
cnf(c_1262,plain,
eqangle(A,B,sK4,sK5,A,B,sK7,sK6),
inference(resolve,[status(thm)],[c_384,c_239]) ).
cnf(c_1438,plain,
para(sK1,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_389,c_710]) ).
cnf(c_1440,plain,
para(sK1,sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_389,c_397]) ).
cnf(c_1690,plain,
para(sK4,sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_1438,c_252]) ).
cnf(c_1721,plain,
eqangle(sK1,sK4,A,B,sK1,sK4,A,B),
inference(resolve,[status(thm)],[c_1440,c_218]) ).
cnf(c_2387,plain,
para(sK4,sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_1690,c_253]) ).
cnf(c_4077,plain,
eqangle(sK4,sK1,A,B,sK4,sK1,A,B),
inference(resolve,[status(thm)],[c_2387,c_218]) ).
cnf(c_5383,plain,
eqangle(A,B,A,B,sK4,sK5,sK7,sK6),
inference(resolve,[status(thm)],[c_1262,c_237]) ).
cnf(c_5490,plain,
( cyclic(sK4,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1721,c_215]) ).
cnf(c_6013,plain,
( cyclic(sK1,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_4077,c_215]) ).
cnf(c_6014,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,sK4)
| ~ cyclic(sK1,A,sK4,A)
| ~ cyclic(sK1,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_4077,c_214]) ).
cnf(c_14747,plain,
( para(A,B,A,B)
| ~ para(sK4,sK5,sK7,sK6) ),
inference(resolve,[status(thm)],[c_5383,c_190]) ).
cnf(c_7225,negated_conjecture,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_157,c_14747]) ).
cnf(c_7239,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_7225,c_196]) ).
cnf(c_7288,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_7239,c_310]) ).
cnf(c_7299,plain,
cyclic(sK1,A,sK4,sK4),
inference(resolve,[status(thm)],[c_7288,c_6013]) ).
cnf(c_7310,plain,
cyclic(sK4,A,sK1,sK1),
inference(resolve,[status(thm)],[c_7288,c_5490]) ).
cnf(c_7467,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A)
| ~ cyclic(sK1,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_7299,c_6014]) ).
cnf(c_8080,plain,
cyclic(sK1,sK4,A,sK4),
inference(resolve,[status(thm)],[c_7299,c_243]) ).
cnf(c_8257,plain,
cyclic(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_7310,c_305]) ).
cnf(c_8259,plain,
cyclic(sK4,sK1,A,sK1),
inference(resolve,[status(thm)],[c_7310,c_243]) ).
cnf(c_8447,plain,
cyclic(sK1,sK4,sK4,A),
inference(resolve,[status(thm)],[c_8080,c_244]) ).
cnf(c_8448,plain,
cyclic(sK4,sK1,A,sK4),
inference(resolve,[status(thm)],[c_8080,c_242]) ).
cnf(c_8811,plain,
cyclic(sK1,A,sK1,sK1),
inference(resolve,[status(thm)],[c_8257,c_242]) ).
cnf(c_8825,plain,
cyclic(sK1,sK4,A,sK1),
inference(resolve,[status(thm)],[c_8259,c_242]) ).
cnf(c_14748,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK1,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_8447,c_241]) ).
cnf(c_9516,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_8447,c_14748]) ).
cnf(c_9532,plain,
( cyclic(sK1,A,sK4,B)
| ~ cyclic(sK4,sK1,A,B) ),
inference(resolve,[status(thm)],[c_8448,c_241]) ).
cnf(c_10641,plain,
cyclic(sK1,sK1,A,sK1),
inference(resolve,[status(thm)],[c_8811,c_243]) ).
cnf(c_10670,plain,
cyclic(sK1,A,sK4,sK1),
inference(resolve,[status(thm)],[c_8825,c_243]) ).
cnf(c_10686,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A) ),
inference(resolve,[status(thm)],[c_10670,c_7467]) ).
cnf(c_14749,plain,
( cyclic(sK4,A,B,C)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_9516,c_241]) ).
cnf(c_11655,plain,
cyclic(sK4,A,B,C),
inference(resolve,[status(thm)],[c_9516,c_14749]) ).
cnf(c_11667,plain,
cyclic(sK1,A,sK4,B),
inference(resolve,[status(thm)],[c_11655,c_9532]) ).
cnf(c_11734,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_11667,c_10686]) ).
cnf(c_14750,plain,
( perp(A,sK1,sK1,sK1)
| ~ cong(sK1,sK1,sK1,sK1)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_10641,c_205]) ).
cnf(c_14751,plain,
( perp(A,sK1,sK1,sK1)
| ~ cong(sK1,sK1,sK1,sK1) ),
inference(resolve,[status(thm)],[c_11734,c_14750]) ).
cnf(c_12404,plain,
perp(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_11734,c_14751]) ).
cnf(c_14752,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_11734,c_206]) ).
cnf(c_14498,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_11734,c_14752]) ).
cnf(c_14753,plain,
( para(C,sK1,A,B)
| ~ perp(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_12404,c_248]) ).
cnf(c_14745,plain,
para(A,sK1,B,C),
inference(resolve,[status(thm)],[c_14498,c_14753]) ).
cnf(c_14746,plain,
$false,
inference(resolve,[status(thm)],[c_14745,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO553+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n016.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 13:46:04 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 2504126 was started by sandbox on n016,
% 0.10/5.37 % Fri Sep 25 13:46:04 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.41
% 0.14/5.41 % From the command line: assign(max_seconds, 300).
% 18.56/10.48
% 18.56/10.48 % given #500 (W,wt=10): 1559 perp(c1,c6,c3,c1). [resolve(1366,a,250,a)].
% 18.56/10.48
% 18.56/10.48 % given #1000 (T,wt=9): 3475 coll(c7,c8,c8). [resolve(636,a,2684,a)].
% 18.56/10.48
% 18.56/10.48 % given #1500 (A,wt=14): 885 -midp(c3,c2,c5) | cong(c1,c2,c1,c5). [resolve(696,a,207,b)].
% 18.56/10.48
% 18.56/10.48 % given #2000 (T,wt=13): 3522 -coll(c1,c7,A) | coll(c4,A,c1). [resolve(3164,a,254,a)].
% 18.56/10.48
% 18.56/10.48 % given #2500 (A,wt=23): 1265 -eqangle(c3,c4,A,B,C,D,E,F) | eqangle(c1,c2,A,B,C,D,E,F). [resolve(384,a,236,a)].
% 18.56/10.48
% 18.56/10.48 % given #3000 (T,wt=9): 7379 coll(A,c6,c1). [back_unit_del(1740),unit_del(a,7288)].
% 18.56/10.48
% 18.56/10.48 % given #3500 (A,wt=25): 2182 -midp(c1,c1,c3) | coll(f8(c1,c3,A,c3,c1,c3,c1),c1,c3). [resolve(1569,a,287,b),unit_del(b,491)].
% 18.56/10.48
% 18.56/10.48 % SZS status Theorem for theBenchmark
% 18.56/10.48
% 18.56/10.48 % Proof 1 at 1.87 (+ 0.48) seconds.
% 18.56/10.48 % Length of proof is 84.
% 18.56/10.48 % Level of proof is 18.
% 18.56/10.48 % Maximum clause weight is 34.000.
% 18.56/10.48 % Given clauses 3767.
% 18.56/10.48
% 18.56/10.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------