%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO660+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 : n012.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 07:18:20 AM UTC 2026
% Result : Theorem 17.36s 7.54s
% Output : CNFRefutation 17.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 15
% Syntax : Number of formulae : 79 ( 34 unt; 0 def)
% Number of atoms : 175 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 138 ( 42 ~; 38 |; 42 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 202 ( 28 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(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(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(exemplo7Book00EE02E02319,conjecture,
! [A,B,C,D,E,F,G] :
( ( coll(G,A,E)
& coll(G,B,C)
& eqangle(D,C,C,F,F,C,C,B)
& eqangle(B,A,A,E,E,A,A,C)
& coll(F,A,B)
& coll(E,C,D)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(C,A,C,B) )
=> para(E,F,C,B) ),
file('theBenchmark.p',exemplo7Book00EE02E02319) ).
fof(exemplo7Book00EE02E02319_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( coll(G,A,E)
& coll(G,B,C)
& eqangle(D,C,C,F,F,C,C,B)
& eqangle(B,A,A,E,E,A,A,C)
& coll(F,A,B)
& coll(E,C,D)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(C,A,C,B) )
=> para(E,F,C,B) ),
inference(assume_negation,[status(cth)],[exemplo7Book00EE02E02319]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G] :
( ~ para(E,F,C,B)
& coll(G,A,E)
& coll(G,B,C)
& eqangle(D,C,C,F,F,C,C,B)
& eqangle(B,A,A,E,E,A,A,C)
& coll(F,A,B)
& coll(E,C,D)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(C,A,C,B) ),
inference(fof_nnf,[status(thm)],[exemplo7Book00EE02E02319_neg]) ).
fof(sk_exemplo7Book00EE02E02319_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& coll(sK4,sK6,sK0)
& coll(sK4,sK3,sK2)
& eqangle(sK5,sK2,sK2,sK1,sK1,sK2,sK2,sK3)
& eqangle(sK3,sK6,sK6,sK0,sK0,sK6,sK6,sK2)
& coll(sK1,sK6,sK3)
& coll(sK0,sK2,sK5)
& coll(sK5,sK6,sK3)
& perp(sK5,sK2,sK6,sK3)
& perp(sK2,sK6,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK6,sK3,sK5,sK0,sK1,sK4]),skolemize(A,sK6),skolemize(B,sK3),skolemize(C,sK2),skolemize(D,sK5),skolemize(E,sK0),skolemize(F,sK1),skolemize(G,sK4)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo7Book00EE02E02319_neg]) ).
cnf(c_149,negated_conjecture,
coll(sK4,sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo7Book00EE02E02319_neg]) ).
cnf(c_154,negated_conjecture,
coll(sK5,sK6,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo7Book00EE02E02319_neg]) ).
cnf(c_156,negated_conjecture,
perp(sK2,sK6,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo7Book00EE02E02319_neg]) ).
cnf(c_205,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_213,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_214,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_217,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
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_240,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_241,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_242,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_243,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_247,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_248,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_253,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_254,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
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_505,plain,
( para(sK2,sK6,A,B)
| ~ perp(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_247,c_156]) ).
cnf(c_509,plain,
perp(sK2,sK3,sK2,sK6),
inference(resolve,[status(thm)],[c_248,c_156]) ).
cnf(c_526,plain,
coll(sK3,sK4,sK2),
inference(resolve,[status(thm)],[c_254,c_149]) ).
cnf(c_528,plain,
coll(sK5,sK3,sK6),
inference(resolve,[status(thm)],[c_255,c_154]) ).
cnf(c_563,plain,
coll(sK3,sK3,sK5),
inference(resolve,[status(thm)],[c_309,c_154]) ).
cnf(c_681,plain,
coll(sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_526,c_309]) ).
cnf(c_773,plain,
( coll(sK6,A,sK5)
| ~ coll(sK5,sK3,A) ),
inference(resolve,[status(thm)],[c_528,c_253]) ).
cnf(c_963,plain,
( coll(A,sK5,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_563,c_253]) ).
cnf(c_1334,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_681,c_309]) ).
cnf(c_5508,plain,
coll(sK2,sK5,sK3),
inference(resolve,[status(thm)],[c_963,c_1334]) ).
cnf(c_5525,plain,
coll(sK5,sK2,sK3),
inference(resolve,[status(thm)],[c_5508,c_254]) ).
cnf(c_5707,plain,
coll(sK5,sK3,sK2),
inference(resolve,[status(thm)],[c_5525,c_255]) ).
cnf(c_5968,plain,
coll(sK6,sK2,sK5),
inference(resolve,[status(thm)],[c_5707,c_773]) ).
cnf(c_6532,plain,
coll(sK6,sK5,sK2),
inference(resolve,[status(thm)],[c_5968,c_255]) ).
cnf(c_7227,plain,
coll(sK2,sK2,sK6),
inference(resolve,[status(thm)],[c_6532,c_309]) ).
cnf(c_8052,plain,
( cyclic(A,sK6,sK2,sK2)
| ~ eqangle(sK2,A,sK2,sK6,sK2,A,sK2,sK6) ),
inference(resolve,[status(thm)],[c_7227,c_214]) ).
cnf(c_16570,plain,
para(sK2,sK6,sK2,sK6),
inference(resolve,[status(thm)],[c_505,c_509]) ).
cnf(c_16586,plain,
eqangle(sK2,sK6,A,B,sK2,sK6,A,B),
inference(resolve,[status(thm)],[c_16570,c_217]) ).
cnf(c_17846,plain,
eqangle(A,B,sK2,sK6,A,B,sK2,sK6),
inference(resolve,[status(thm)],[c_16586,c_238]) ).
cnf(c_17849,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK2,sK2)
| ~ cyclic(sK6,A,sK2,A)
| ~ cyclic(sK6,A,sK2,sK6) ),
inference(resolve,[status(thm)],[c_16586,c_213]) ).
cnf(c_17856,plain,
cyclic(A,sK6,sK2,sK2),
inference(resolve,[status(thm)],[c_17846,c_8052]) ).
cnf(c_17867,plain,
cyclic(A,sK2,sK6,sK2),
inference(resolve,[status(thm)],[c_17856,c_242]) ).
cnf(c_17868,plain,
cyclic(sK6,A,sK2,sK2),
inference(resolve,[status(thm)],[c_17856,c_241]) ).
cnf(c_17874,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK2,A)
| ~ cyclic(sK6,A,sK2,sK6) ),
inference(resolve,[status(thm)],[c_17868,c_17849]) ).
cnf(c_17894,plain,
cyclic(sK2,A,sK6,sK2),
inference(resolve,[status(thm)],[c_17867,c_241]) ).
cnf(c_18467,plain,
cyclic(sK6,sK2,A,sK2),
inference(resolve,[status(thm)],[c_17868,c_242]) ).
cnf(c_18803,plain,
cyclic(sK2,sK6,A,sK2),
inference(resolve,[status(thm)],[c_17894,c_242]) ).
cnf(c_19485,plain,
cyclic(sK6,sK2,sK2,A),
inference(resolve,[status(thm)],[c_18467,c_243]) ).
cnf(c_20032,plain,
( cyclic(sK6,A,sK2,B)
| ~ cyclic(sK2,sK6,A,B) ),
inference(resolve,[status(thm)],[c_18803,c_240]) ).
cnf(c_30354,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK6,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_19485,c_240]) ).
cnf(c_21346,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_19485,c_30354]) ).
cnf(c_30355,plain,
( cyclic(sK2,A,B,C)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_21346,c_240]) ).
cnf(c_23066,plain,
cyclic(sK2,A,B,C),
inference(resolve,[status(thm)],[c_21346,c_30355]) ).
cnf(c_23072,plain,
cyclic(sK6,A,sK2,B),
inference(resolve,[status(thm)],[c_23066,c_20032]) ).
cnf(c_30356,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK2,A) ),
inference(resolve,[status(thm)],[c_23072,c_17874]) ).
cnf(c_23087,plain,
cong(sK6,A,sK6,A),
inference(resolve,[status(thm)],[c_23072,c_30356]) ).
cnf(c_30357,plain,
( perp(sK6,sK6,A,B)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_23087,c_205]) ).
cnf(c_24827,plain,
perp(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_23087,c_30357]) ).
cnf(c_30351,plain,
perp(A,B,sK6,sK6),
inference(resolve,[status(thm)],[c_24827,c_248]) ).
cnf(c_30358,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK6,sK6) ),
inference(resolve,[status(thm)],[c_24827,c_247]) ).
cnf(c_30352,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_30351,c_30358]) ).
cnf(c_30353,plain,
$false,
inference(resolve,[status(thm)],[c_30352,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO660+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/5.30 % Computer : n012.cluster.edu
% 0.03/5.30 % Model : x86_64 x86_64
% 0.03/5.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.30 % Memory : 8046.5625MB
% 0.03/5.30 % OS : Linux 6.8.0-71-generic
% 0.03/5.30 % CPULimit : 300
% 0.03/5.30 % WCLimit : 300
% 0.03/5.30 % DateTime : Fri Sep 25 13:46:55 UTC 2026
% 0.03/5.31 % CPUTime :
% 0.03/5.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/5.31 % Process 2226497 was started by sandbox2 on n012,
% 0.03/5.31 % Fri Sep 25 13:46:55 2026
% 0.03/5.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/5.32
% 0.03/5.32 % From the command line: assign(max_seconds, 300).
% 17.36/7.54
% 17.36/7.54 % given #500 (T,wt=9): 8981 coll(c1,c2,c3). [resolve(7965,a,254,a)].
% 17.36/7.54
% 17.36/7.54 % given #1000 (W,wt=13): 7747 -coll(c7,c4,A) | coll(A,c1,c7). [resolve(6885,a,253,b)].
% 17.36/7.54
% 17.36/7.54 % given #1500 (T,wt=14): 2720 -cong(c3,c2,c3,c3) | midp(c3,c2,c3). [resolve(1349,a,194,b)].
% 17.36/7.54
% 17.36/7.54 % given #2000 (W,wt=9): 21061 midp(c5,c1,c1). [resolve(21059,a,17683,a)].
% 17.36/7.54
% 17.36/7.54 % SZS status Theorem for theBenchmark
% 17.36/7.54
% 17.36/7.54 % Proof 1 at 1.68 (+ 0.51) seconds.
% 17.36/7.54 % Length of proof is 71.
% 17.36/7.54 % Level of proof is 23.
% 17.36/7.54 % Maximum clause weight is 34.000.
% 17.36/7.54 % Given clauses 2321.
% 17.36/7.54
% 17.36/7.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------