%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO657+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 07:18:19 AM UTC 2026
% Result : Theorem 6.48s 1.37s
% Output : CNFRefutation 6.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 94 ( 36 unt; 0 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 164 ( 59 ~; 55 |; 30 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 276 ( 27 sgn 106 !; 7 ?)
% 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(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(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(exemplo6GDDFULLmoreE02315,conjecture,
! [A,B,C,D,E,F,G] :
( ( coll(G,B,C)
& coll(F,C,D)
& para(A,D,F,E)
& para(A,B,G,E)
& coll(E,A,C) )
=> para(B,D,G,F) ),
file('theBenchmark.p',exemplo6GDDFULLmoreE02315) ).
fof(exemplo6GDDFULLmoreE02315_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( coll(G,B,C)
& coll(F,C,D)
& para(A,D,F,E)
& para(A,B,G,E)
& coll(E,A,C) )
=> para(B,D,G,F) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULLmoreE02315]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G] :
( ~ para(B,D,G,F)
& coll(G,B,C)
& coll(F,C,D)
& para(A,D,F,E)
& para(A,B,G,E)
& coll(E,A,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULLmoreE02315_neg]) ).
fof(sk_exemplo6GDDFULLmoreE02315_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& coll(sK2,sK0,sK6)
& coll(sK3,sK6,sK1)
& para(sK4,sK1,sK3,sK5)
& para(sK4,sK0,sK2,sK5)
& coll(sK5,sK4,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK4,sK6,sK0,sK2,sK1,sK3]),skolemize(A,sK4),skolemize(B,sK0),skolemize(C,sK6),skolemize(D,sK1),skolemize(E,sK5),skolemize(F,sK3),skolemize(G,sK2)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE02315_neg]) ).
cnf(c_150,negated_conjecture,
para(sK4,sK1,sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE02315_neg]) ).
cnf(c_151,negated_conjecture,
para(sK4,sK0,sK2,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE02315_neg]) ).
cnf(c_185,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_191,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_200,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_201,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_209,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_210,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_213,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_232,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_234,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_236,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_237,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_238,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_239,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_243,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
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_297,plain,
( cong(A,B,D,D)
| ~ eqangle(C,A,C,B,E,D,E,D)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_209]) ).
cnf(c_300,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_236]) ).
cnf(c_305,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_249]) ).
cnf(c_335,plain,
eqangle(sK4,sK0,A,B,sK2,sK5,A,B),
inference(resolve,[status(thm)],[c_213,c_151]) ).
cnf(c_340,plain,
( para(sK4,sK1,A,B)
| ~ para(sK3,sK5,A,B) ),
inference(resolve,[status(thm)],[c_246,c_150]) ).
cnf(c_344,plain,
para(sK3,sK5,sK4,sK1),
inference(resolve,[status(thm)],[c_247,c_150]) ).
cnf(c_551,plain,
eqangle(A,B,sK4,sK0,A,B,sK2,sK5),
inference(resolve,[status(thm)],[c_335,c_234]) ).
cnf(c_607,plain,
para(sK4,sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_344,c_340]) ).
cnf(c_733,plain,
para(sK4,sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_607,c_248]) ).
cnf(c_734,plain,
eqangle(sK4,sK1,A,B,sK4,sK1,A,B),
inference(resolve,[status(thm)],[c_607,c_213]) ).
cnf(c_930,plain,
para(sK1,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_733,c_247]) ).
cnf(c_1088,plain,
para(sK1,sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_930,c_248]) ).
cnf(c_1155,plain,
eqangle(sK1,sK4,A,B,sK1,sK4,A,B),
inference(resolve,[status(thm)],[c_1088,c_213]) ).
cnf(c_1857,plain,
eqangle(A,B,A,B,sK4,sK0,sK2,sK5),
inference(resolve,[status(thm)],[c_551,c_232]) ).
cnf(c_2383,plain,
( cong(sK1,sK1,sK1,sK1)
| ~ cyclic(sK1,sK1,sK4,sK4)
| ~ cyclic(sK1,sK1,sK4,sK1) ),
inference(resolve,[status(thm)],[c_734,c_297]) ).
cnf(c_2387,plain,
( cyclic(sK1,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_734,c_210]) ).
cnf(c_2388,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_734,c_209]) ).
cnf(c_2902,plain,
( cyclic(sK4,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1155,c_210]) ).
cnf(c_6260,plain,
( para(A,B,A,B)
| ~ para(sK4,sK0,sK2,sK5) ),
inference(resolve,[status(thm)],[c_1857,c_185]) ).
cnf(c_3052,negated_conjecture,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_151,c_6260]) ).
cnf(c_3066,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_3052,c_191]) ).
cnf(c_3154,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_3066,c_305]) ).
cnf(c_3162,plain,
cyclic(sK4,A,sK1,sK1),
inference(resolve,[status(thm)],[c_3154,c_2902]) ).
cnf(c_3168,plain,
cyclic(sK1,A,sK4,sK4),
inference(resolve,[status(thm)],[c_3154,c_2387]) ).
cnf(c_3290,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A)
| ~ cyclic(sK1,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_3168,c_2388]) ).
cnf(c_3291,plain,
( cong(sK1,sK1,sK1,sK1)
| ~ cyclic(sK1,sK1,sK4,sK1) ),
inference(resolve,[status(thm)],[c_3168,c_2383]) ).
cnf(c_3523,plain,
cyclic(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_3162,c_300]) ).
cnf(c_3525,plain,
cyclic(sK4,sK1,A,sK1),
inference(resolve,[status(thm)],[c_3162,c_238]) ).
cnf(c_3526,plain,
cyclic(A,sK4,sK1,sK1),
inference(resolve,[status(thm)],[c_3162,c_237]) ).
cnf(c_3660,plain,
cyclic(sK1,A,sK1,sK1),
inference(resolve,[status(thm)],[c_3523,c_237]) ).
cnf(c_3673,plain,
cyclic(sK4,sK1,sK1,A),
inference(resolve,[status(thm)],[c_3525,c_239]) ).
cnf(c_3674,plain,
cyclic(sK1,sK4,A,sK1),
inference(resolve,[status(thm)],[c_3525,c_237]) ).
cnf(c_3692,plain,
cyclic(A,sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_3526,c_238]) ).
cnf(c_3704,plain,
cong(sK1,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_3692,c_3291]) ).
cnf(c_3995,plain,
cyclic(sK1,sK1,A,sK1),
inference(resolve,[status(thm)],[c_3660,c_238]) ).
cnf(c_4008,plain,
cyclic(sK1,sK1,A,A),
inference(resolve,[status(thm)],[c_3673,c_300]) ).
cnf(c_6261,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK4,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3673,c_236]) ).
cnf(c_4010,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_3673,c_6261]) ).
cnf(c_4024,plain,
cyclic(sK1,A,sK4,sK1),
inference(resolve,[status(thm)],[c_3674,c_238]) ).
cnf(c_4040,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A) ),
inference(resolve,[status(thm)],[c_4024,c_3290]) ).
cnf(c_6262,plain,
( perp(A,sK1,sK1,sK1)
| ~ cong(sK1,sK1,sK1,sK1)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_3995,c_200]) ).
cnf(c_5079,plain,
( perp(A,sK1,sK1,sK1)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_3704,c_6262]) ).
cnf(c_6263,plain,
( cyclic(sK1,A,B,A)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_4008,c_236]) ).
cnf(c_5093,plain,
cyclic(sK1,A,B,A),
inference(resolve,[status(thm)],[c_4010,c_6263]) ).
cnf(c_5106,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_5093,c_4040]) ).
cnf(c_5108,plain,
perp(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_5106,c_5079]) ).
cnf(c_6264,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_5106,c_201]) ).
cnf(c_6204,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_5106,c_6264]) ).
cnf(c_6265,plain,
( para(C,sK1,A,B)
| ~ perp(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_5108,c_243]) ).
cnf(c_6258,plain,
para(A,sK1,B,C),
inference(resolve,[status(thm)],[c_6204,c_6265]) ).
cnf(c_6259,plain,
$false,
inference(resolve,[status(thm)],[c_6258,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO657+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n017.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 13:42:32 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 2412704 was started by sandbox on n017,
% 0.18/0.43 % Fri Sep 25 13:42:32 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.50
% 0.18/0.50 % From the command line: assign(max_seconds, 300).
% 6.48/1.37
% 6.48/1.37 % given #500 (T,wt=9): 1409 coll(c2,c5,c1). [resolve(427,a,692,a)].
% 6.48/1.37
% 6.48/1.37 % given #1000 (A,wt=25): 690 -midp(c2,c1,c1) | coll(f8(c1,c1,A,c2,c2,c1,c2),c2,c1). [back_unit_del(674),unit_del(b,686)].
% 6.48/1.37
% 6.48/1.37 % given #1500 (T,wt=14): 1041 eqangle(c5,c6,A,B,c4,c1,A,B). [resolve(871,a,213,a)].
% 6.48/1.37
% 6.48/1.37 % SZS status Theorem for theBenchmark
% 6.48/1.37
% 6.48/1.37 % Proof 1 at 0.61 (+ 0.22) seconds.
% 6.48/1.37 % Length of proof is 85.
% 6.48/1.37 % Level of proof is 17.
% 6.48/1.37 % Maximum clause weight is 34.000.
% 6.48/1.37 % Given clauses 1846.
% 6.48/1.37
% 6.48/1.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------