%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO579+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 : n004.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 07:18:09 AM UTC 2026
% Result : Theorem 1.87s 0.75s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 24 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 79 ( 19 ~; 15 |; 36 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 108 ( 1 sgn 54 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('theBenchmark.p',ruleD3) ).
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(ruleD39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('theBenchmark.p',ruleD39) ).
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(exemplo6GDDFULL416041,conjecture,
! [A,B,C,I,Y,L,X] :
( ( coll(X,A,I)
& perp(X,B,A,I)
& coll(L,B,C)
& perp(L,I,B,C)
& coll(Y,A,C)
& perp(Y,I,A,C)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) )
=> coll(X,Y,L) ),
file('theBenchmark.p',exemplo6GDDFULL416041) ).
fof(exemplo6GDDFULL416041_neg,negated_conjecture,
~ ! [A,B,C,I,Y,L,X] :
( ( coll(X,A,I)
& perp(X,B,A,I)
& coll(L,B,C)
& perp(L,I,B,C)
& coll(Y,A,C)
& perp(Y,I,A,C)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) )
=> coll(X,Y,L) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416041]) ).
fof(nnf_95,plain,
? [A,B,C,I,Y,L,X] :
( ~ coll(X,Y,L)
& coll(X,A,I)
& perp(X,B,A,I)
& coll(L,B,C)
& perp(L,I,B,C)
& coll(Y,A,C)
& perp(Y,I,A,C)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL416041_neg]) ).
fof(sk_exemplo6GDDFULL416041_neg,plain,
( ~ coll(sK0,sK1,sK2)
& coll(sK0,sK3,sK4)
& perp(sK0,sK5,sK3,sK4)
& coll(sK2,sK5,sK6)
& perp(sK2,sK4,sK5,sK6)
& coll(sK1,sK3,sK6)
& perp(sK1,sK4,sK3,sK6)
& eqangle(sK4,sK6,sK6,sK3,sK4,sK6,sK6,sK5)
& eqangle(sK4,sK5,sK5,sK6,sK4,sK5,sK5,sK3)
& eqangle(sK4,sK3,sK3,sK5,sK4,sK3,sK3,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK3,sK5,sK6,sK1,sK2,sK0]),skolemize(A,sK3),skolemize(B,sK5),skolemize(C,sK6),skolemize(I,sK4),skolemize(Y,sK1),skolemize(L,sK2),skolemize(X,sK0)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ coll(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416041_neg]) ).
cnf(c_148,negated_conjecture,
coll(sK0,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416041_neg]) ).
cnf(c_150,negated_conjecture,
coll(sK2,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416041_neg]) ).
cnf(c_152,negated_conjecture,
coll(sK1,sK3,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416041_neg]) ).
cnf(c_154,negated_conjecture,
eqangle(sK4,sK6,sK6,sK3,sK4,sK6,sK6,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416041_neg]) ).
cnf(c_189,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_195,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_218,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_236,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_238,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_253,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_255,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_309,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_253]) ).
cnf(c_369,plain,
eqangle(sK4,sK6,sK4,sK6,sK6,sK3,sK6,sK5),
inference(resolve,[status(thm)],[c_236,c_154]) ).
cnf(c_375,plain,
eqangle(sK6,sK3,sK4,sK6,sK6,sK5,sK4,sK6),
inference(resolve,[status(thm)],[c_238,c_154]) ).
cnf(c_403,plain,
coll(sK6,sK6,sK1),
inference(resolve,[status(thm)],[c_309,c_152]) ).
cnf(c_404,plain,
coll(sK6,sK6,sK2),
inference(resolve,[status(thm)],[c_309,c_150]) ).
cnf(c_405,plain,
coll(sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_309,c_148]) ).
cnf(c_432,plain,
( coll(A,sK1,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_403,c_253]) ).
cnf(c_437,plain,
( coll(sK2,A,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_404,c_253]) ).
cnf(c_441,plain,
( coll(sK0,A,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_405,c_253]) ).
cnf(c_915,plain,
( para(sK4,sK6,sK4,sK6)
| ~ para(sK6,sK3,sK6,sK5) ),
inference(resolve,[status(thm)],[c_369,c_189]) ).
cnf(c_974,plain,
para(sK6,sK3,sK6,sK5),
inference(resolve,[status(thm)],[c_375,c_218]) ).
cnf(c_977,plain,
para(sK4,sK6,sK4,sK6),
inference(resolve,[status(thm)],[c_974,c_915]) ).
cnf(c_1152,plain,
coll(sK4,sK6,sK6),
inference(resolve,[status(thm)],[c_977,c_195]) ).
cnf(c_1159,plain,
coll(sK6,sK6,sK4),
inference(resolve,[status(thm)],[c_1152,c_309]) ).
cnf(c_1165,plain,
coll(sK4,sK4,sK6),
inference(resolve,[status(thm)],[c_1159,c_309]) ).
cnf(c_1252,plain,
coll(sK2,sK1,sK6),
inference(resolve,[status(thm)],[c_432,c_404]) ).
cnf(c_1267,plain,
coll(sK2,sK6,sK1),
inference(resolve,[status(thm)],[c_1252,c_255]) ).
cnf(c_1300,plain,
( coll(A,sK1,sK2)
| ~ coll(sK2,sK6,A) ),
inference(resolve,[status(thm)],[c_1267,c_253]) ).
cnf(c_1303,plain,
coll(sK0,sK6,sK4),
inference(resolve,[status(thm)],[c_441,c_1165]) ).
cnf(c_1381,plain,
coll(sK0,sK4,sK6),
inference(resolve,[status(thm)],[c_1303,c_255]) ).
cnf(c_1514,plain,
coll(sK6,sK6,sK0),
inference(resolve,[status(thm)],[c_1381,c_309]) ).
cnf(c_1665,plain,
coll(sK2,sK0,sK6),
inference(resolve,[status(thm)],[c_1514,c_437]) ).
cnf(c_1780,plain,
coll(sK2,sK6,sK0),
inference(resolve,[status(thm)],[c_1665,c_255]) ).
cnf(c_2647,plain,
coll(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_1300,c_1780]) ).
cnf(c_2646,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_147,c_2647]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO579+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n004.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 13:42:50 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3294407 was started by sandbox2 on n004,
% 0.18/0.45 % Fri Sep 25 13:42:50 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.49
% 0.18/0.49 % From the command line: assign(max_seconds, 300).
% 1.87/0.75
% 1.87/0.75 % given #500 (A,wt=13): 477 -coll(c1,c1,A) | coll(A,c7,c1). [resolve(426,a,253,b)].
% 1.87/0.75
% 1.87/0.75 % SZS status Theorem for theBenchmark
% 1.87/0.75
% 1.87/0.75 % Proof 1 at 0.18 (+ 0.06) seconds.
% 1.87/0.75 % Length of proof is 44.
% 1.87/0.75 % Level of proof is 13.
% 1.87/0.75 % Maximum clause weight is 24.000.
% 1.87/0.75 % Given clauses 966.
% 1.87/0.75
% 1.87/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------