%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO658+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 : n001.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 20.22s 3.40s
% Output : CNFRefutation 20.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 91 ( 35 unt; 0 def)
% Number of atoms : 213 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 175 ( 53 ~; 49 |; 53 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 278 ( 33 sgn 108 !; 9 ?)
% 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(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(exemplo6GDDFULLmoreE02316,conjecture,
! [A,B,C,D,E,F,G,H,I] :
( ( coll(I,A,B)
& coll(I,E,F)
& coll(H,A,D)
& coll(H,E,G)
& coll(G,B,C)
& perp(G,E,B,C)
& coll(F,C,D)
& perp(F,E,C,D)
& coll(E,A,C)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(G,F,H,I) ),
file('theBenchmark.p',exemplo6GDDFULLmoreE02316) ).
fof(exemplo6GDDFULLmoreE02316_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,I] :
( ( coll(I,A,B)
& coll(I,E,F)
& coll(H,A,D)
& coll(H,E,G)
& coll(G,B,C)
& perp(G,E,B,C)
& coll(F,C,D)
& perp(F,E,C,D)
& coll(E,A,C)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(G,F,H,I) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULLmoreE02316]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G,H,I] :
( ~ para(G,F,H,I)
& coll(I,A,B)
& coll(I,E,F)
& coll(H,A,D)
& coll(H,E,G)
& coll(G,B,C)
& perp(G,E,B,C)
& coll(F,C,D)
& perp(F,E,C,D)
& coll(E,A,C)
& para(A,C,B,D)
& para(A,B,C,D) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULLmoreE02316_neg]) ).
fof(sk_exemplo6GDDFULLmoreE02316_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& coll(sK3,sK7,sK8)
& coll(sK3,sK4,sK1)
& coll(sK2,sK7,sK6)
& coll(sK2,sK4,sK0)
& coll(sK0,sK8,sK5)
& perp(sK0,sK4,sK8,sK5)
& coll(sK1,sK5,sK6)
& perp(sK1,sK4,sK5,sK6)
& coll(sK4,sK7,sK5)
& para(sK7,sK5,sK8,sK6)
& para(sK7,sK8,sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK5,sK6,sK4,sK1,sK0,sK2,sK3]),skolemize(A,sK7),skolemize(B,sK8),skolemize(C,sK5),skolemize(D,sK6),skolemize(E,sK4),skolemize(F,sK1),skolemize(G,sK0),skolemize(H,sK2),skolemize(I,sK3)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE02316_neg]) ).
cnf(c_155,negated_conjecture,
perp(sK1,sK4,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE02316_neg]) ).
cnf(c_158,negated_conjecture,
para(sK7,sK8,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE02316_neg]) ).
cnf(c_191,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_197,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_206,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_207,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_215,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_216,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_219,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(A,B,E,F,C,D,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD21]) ).
cnf(c_240,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_242,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_243,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_244,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_245,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_249,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_250,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_253,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_254,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_255,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_306,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_242]) ).
cnf(c_311,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_255]) ).
cnf(c_363,plain,
eqangle(sK7,sK8,A,B,sK5,sK6,A,B),
inference(resolve,[status(thm)],[c_219,c_158]) ).
cnf(c_367,plain,
( para(sK1,sK4,A,B)
| ~ perp(sK5,sK6,A,B) ),
inference(resolve,[status(thm)],[c_249,c_155]) ).
cnf(c_371,plain,
perp(sK5,sK6,sK1,sK4),
inference(resolve,[status(thm)],[c_250,c_155]) ).
cnf(c_720,plain,
eqangle(A,B,sK7,sK8,A,B,sK5,sK6),
inference(resolve,[status(thm)],[c_363,c_240]) ).
cnf(c_772,plain,
para(sK1,sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_371,c_367]) ).
cnf(c_1094,plain,
para(sK1,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_772,c_254]) ).
cnf(c_1095,plain,
eqangle(sK1,sK4,A,B,sK1,sK4,A,B),
inference(resolve,[status(thm)],[c_772,c_219]) ).
cnf(c_1375,plain,
para(sK4,sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_1094,c_253]) ).
cnf(c_1667,plain,
para(sK4,sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_1375,c_254]) ).
cnf(c_1852,plain,
eqangle(sK4,sK1,A,B,sK4,sK1,A,B),
inference(resolve,[status(thm)],[c_1667,c_219]) ).
cnf(c_3131,plain,
eqangle(A,B,A,B,sK7,sK8,sK5,sK6),
inference(resolve,[status(thm)],[c_720,c_238]) ).
cnf(c_4118,plain,
( cyclic(sK4,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1095,c_216]) ).
cnf(c_5995,plain,
( cyclic(sK1,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_1852,c_216]) ).
cnf(c_5996,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_1852,c_215]) ).
cnf(c_11793,plain,
( para(A,B,A,B)
| ~ para(sK7,sK8,sK5,sK6) ),
inference(resolve,[status(thm)],[c_3131,c_191]) ).
cnf(c_6192,negated_conjecture,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_158,c_11793]) ).
cnf(c_6206,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_6192,c_197]) ).
cnf(c_6406,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_6206,c_311]) ).
cnf(c_6414,plain,
cyclic(sK1,A,sK4,sK4),
inference(resolve,[status(thm)],[c_6406,c_5995]) ).
cnf(c_6423,plain,
cyclic(sK4,A,sK1,sK1),
inference(resolve,[status(thm)],[c_6406,c_4118]) ).
cnf(c_6596,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A)
| ~ cyclic(sK1,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_6414,c_5996]) ).
cnf(c_7131,plain,
cyclic(sK1,sK4,A,sK4),
inference(resolve,[status(thm)],[c_6414,c_244]) ).
cnf(c_7279,plain,
cyclic(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_6423,c_306]) ).
cnf(c_7281,plain,
cyclic(sK4,sK1,A,sK1),
inference(resolve,[status(thm)],[c_6423,c_244]) ).
cnf(c_7327,plain,
cyclic(sK1,sK4,sK4,A),
inference(resolve,[status(thm)],[c_7131,c_245]) ).
cnf(c_7328,plain,
cyclic(sK4,sK1,A,sK4),
inference(resolve,[status(thm)],[c_7131,c_243]) ).
cnf(c_7681,plain,
cyclic(sK1,A,sK1,sK1),
inference(resolve,[status(thm)],[c_7279,c_243]) ).
cnf(c_7695,plain,
cyclic(sK1,sK4,A,sK1),
inference(resolve,[status(thm)],[c_7281,c_243]) ).
cnf(c_11794,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK1,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_7327,c_242]) ).
cnf(c_7769,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_7327,c_11794]) ).
cnf(c_7785,plain,
( cyclic(sK1,A,sK4,B)
| ~ cyclic(sK4,sK1,A,B) ),
inference(resolve,[status(thm)],[c_7328,c_242]) ).
cnf(c_8924,plain,
cyclic(sK1,sK1,A,sK1),
inference(resolve,[status(thm)],[c_7681,c_244]) ).
cnf(c_8953,plain,
cyclic(sK1,A,sK4,sK1),
inference(resolve,[status(thm)],[c_7695,c_244]) ).
cnf(c_8969,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A) ),
inference(resolve,[status(thm)],[c_8953,c_6596]) ).
cnf(c_11795,plain,
( cyclic(sK4,A,B,C)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_7769,c_242]) ).
cnf(c_9145,plain,
cyclic(sK4,A,B,C),
inference(resolve,[status(thm)],[c_7769,c_11795]) ).
cnf(c_9157,plain,
cyclic(sK1,A,sK4,B),
inference(resolve,[status(thm)],[c_9145,c_7785]) ).
cnf(c_9200,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_9157,c_8969]) ).
cnf(c_11796,plain,
( perp(A,sK1,sK1,sK1)
| ~ cong(sK1,sK1,sK1,sK1)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_8924,c_206]) ).
cnf(c_11797,plain,
( perp(A,sK1,sK1,sK1)
| ~ cong(sK1,sK1,sK1,sK1) ),
inference(resolve,[status(thm)],[c_9200,c_11796]) ).
cnf(c_10175,plain,
perp(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_9200,c_11797]) ).
cnf(c_11798,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_9200,c_207]) ).
cnf(c_10876,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_9200,c_11798]) ).
cnf(c_11799,plain,
( para(C,sK1,A,B)
| ~ perp(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_10175,c_249]) ).
cnf(c_11791,plain,
para(A,sK1,B,C),
inference(resolve,[status(thm)],[c_10876,c_11799]) ).
cnf(c_11792,plain,
$false,
inference(resolve,[status(thm)],[c_11791,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO658+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n001.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 13:52:55 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3439024 was started by sandbox2 on n001,
% 0.19/0.45 % Fri Sep 25 13:52:55 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.49
% 0.19/0.49 % From the command line: assign(max_seconds, 300).
% 20.22/3.40
% 20.22/3.40 % given #500 (W,wt=10): 1119 perp(c5,c6,c3,c4). [resolve(774,a,250,a)].
% 20.22/3.40
% 20.22/3.40 % given #1000 (T,wt=9): 2596 coll(c9,c9,c3). [resolve(2190,a,311,a)].
% 20.22/3.40
% 20.22/3.40 % given #1500 (W,wt=13): 1133 -midp(A,c2,c2) | midp(A,c3,c3). [resolve(803,a,297,b)].
% 20.22/3.40
% 20.22/3.40 % given #2000 (T,wt=13): 2616 -coll(c2,c1,A) | coll(c4,A,c2). [resolve(2200,a,255,a)].
% 20.22/3.40
% 20.22/3.40 % given #2500 (A,wt=24): 1498 -perp(c5,c3,c4,c6) | perp(c4,f10(c4,c5,c6,c3),c6,c5). [resolve(1174,a,168,a)].
% 20.22/3.40
% 20.22/3.40 % given #3000 (T,wt=13): 3644 -coll(c6,c7,A) | coll(A,c9,c6). [resolve(3365,a,255,b)].
% 20.22/3.40
% 20.22/3.40 % given #3500 (A,wt=20): 2289 coll(f20(c1,c3,c2,c4,c7,c5),c2,c4). [back_unit_del(2242),unit_del(a,2269)].
% 20.22/3.40
% 20.22/3.40 % given #4000 (T,wt=10): 10152 cyclic(A,c3,c2,B). [resolve(8893,a,242,a),unit_del(a,9878)].
% 20.22/3.40
% 20.22/3.40 % SZS status Theorem for theBenchmark
% 20.22/3.40
% 20.22/3.40 % Proof 1 at 2.13 (+ 0.74) seconds.
% 20.22/3.40 % Length of proof is 81.
% 20.22/3.40 % Level of proof is 18.
% 20.22/3.40 % Maximum clause weight is 34.000.
% 20.22/3.40 % Given clauses 4001.
% 20.22/3.40
% 20.22/3.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
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