%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO653+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 : n020.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 11.84s 1.94s
% Output : CNFRefutation 11.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 94 ( 39 unt; 0 def)
% Number of atoms : 204 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 160 ( 50 ~; 46 |; 44 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 277 ( 27 sgn 108 !; 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(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(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(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(exemplo6GDDFULLmoreE0227,conjecture,
! [A,B,C,D,E,F,G,H] :
( ( coll(H,C,F)
& coll(H,B,E)
& coll(G,A,E)
& coll(G,D,F)
& coll(F,A,B)
& para(A,D,F,E)
& coll(E,C,D)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(G,H,A,B) ),
file('theBenchmark.p',exemplo6GDDFULLmoreE0227) ).
fof(exemplo6GDDFULLmoreE0227_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H] :
( ( coll(H,C,F)
& coll(H,B,E)
& coll(G,A,E)
& coll(G,D,F)
& coll(F,A,B)
& para(A,D,F,E)
& coll(E,C,D)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(G,H,A,B) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULLmoreE0227]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G,H] :
( ~ para(G,H,A,B)
& coll(H,C,F)
& coll(H,B,E)
& coll(G,A,E)
& coll(G,D,F)
& coll(F,A,B)
& para(A,D,F,E)
& coll(E,C,D)
& para(A,C,B,D)
& para(A,B,C,D) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULLmoreE0227_neg]) ).
fof(sk_exemplo6GDDFULLmoreE0227_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& coll(sK1,sK7,sK5)
& coll(sK1,sK3,sK6)
& coll(sK0,sK2,sK6)
& coll(sK0,sK4,sK5)
& coll(sK5,sK2,sK3)
& para(sK2,sK4,sK5,sK6)
& coll(sK6,sK7,sK4)
& para(sK2,sK7,sK3,sK4)
& para(sK2,sK3,sK7,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK7,sK4,sK6,sK5,sK0,sK1]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK7),skolemize(D,sK4),skolemize(E,sK6),skolemize(F,sK5),skolemize(G,sK0),skolemize(H,sK1)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0227_neg]) ).
cnf(c_153,negated_conjecture,
para(sK2,sK4,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0227_neg]) ).
cnf(c_156,negated_conjecture,
para(sK2,sK3,sK7,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0227_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_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_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_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_250,plain,
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD6]) ).
cnf(c_251,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_252,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_253,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_304,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_240]) ).
cnf(c_309,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_253]) ).
cnf(c_349,plain,
eqangle(sK2,sK3,A,B,sK7,sK4,A,B),
inference(resolve,[status(thm)],[c_217,c_156]) ).
cnf(c_357,plain,
( para(sK2,sK4,A,B)
| ~ para(sK5,sK6,A,B) ),
inference(resolve,[status(thm)],[c_250,c_153]) ).
cnf(c_358,plain,
( para(A,B,sK7,sK4)
| ~ para(A,B,sK2,sK3) ),
inference(resolve,[status(thm)],[c_250,c_156]) ).
cnf(c_361,plain,
para(sK7,sK4,sK2,sK3),
inference(resolve,[status(thm)],[c_251,c_156]) ).
cnf(c_363,plain,
para(sK5,sK6,sK2,sK4),
inference(resolve,[status(thm)],[c_251,c_153]) ).
cnf(c_364,plain,
para(sK2,sK3,sK4,sK7),
inference(resolve,[status(thm)],[c_252,c_156]) ).
cnf(c_716,plain,
eqangle(A,B,sK2,sK3,A,B,sK7,sK4),
inference(resolve,[status(thm)],[c_349,c_238]) ).
cnf(c_819,plain,
para(sK7,sK4,sK7,sK4),
inference(resolve,[status(thm)],[c_361,c_358]) ).
cnf(c_866,plain,
para(sK2,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_363,c_357]) ).
cnf(c_889,plain,
para(sK4,sK7,sK2,sK3),
inference(resolve,[status(thm)],[c_364,c_251]) ).
cnf(c_976,plain,
eqangle(sK7,sK4,A,B,sK7,sK4,A,B),
inference(resolve,[status(thm)],[c_819,c_217]) ).
cnf(c_1160,plain,
para(sK2,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_866,c_252]) ).
cnf(c_1211,plain,
para(sK4,sK7,sK7,sK4),
inference(resolve,[status(thm)],[c_889,c_358]) ).
cnf(c_1384,plain,
para(sK4,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_1160,c_251]) ).
cnf(c_1416,plain,
para(sK4,sK7,sK4,sK7),
inference(resolve,[status(thm)],[c_1211,c_252]) ).
cnf(c_1580,plain,
para(sK4,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_1384,c_252]) ).
cnf(c_1611,plain,
eqangle(sK4,sK7,A,B,sK4,sK7,A,B),
inference(resolve,[status(thm)],[c_1416,c_217]) ).
cnf(c_1671,plain,
eqangle(sK4,sK2,A,B,sK4,sK2,A,B),
inference(resolve,[status(thm)],[c_1580,c_217]) ).
cnf(c_2955,plain,
eqangle(A,B,A,B,sK2,sK3,sK7,sK4),
inference(resolve,[status(thm)],[c_716,c_236]) ).
cnf(c_3346,plain,
( cyclic(sK4,A,sK7,sK7)
| ~ coll(sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_976,c_214]) ).
cnf(c_3347,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK7,sK7)
| ~ cyclic(sK4,A,sK7,A)
| ~ cyclic(sK4,A,sK7,sK4) ),
inference(resolve,[status(thm)],[c_976,c_213]) ).
cnf(c_4292,plain,
( cyclic(sK7,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_1611,c_214]) ).
cnf(c_4378,plain,
( cyclic(sK2,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_1671,c_214]) ).
cnf(c_10258,plain,
( para(A,B,A,B)
| ~ para(sK2,sK3,sK7,sK4) ),
inference(resolve,[status(thm)],[c_2955,c_189]) ).
cnf(c_4641,negated_conjecture,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_156,c_10258]) ).
cnf(c_4655,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_4641,c_195]) ).
cnf(c_4791,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_4655,c_309]) ).
cnf(c_4799,plain,
cyclic(sK2,A,sK4,sK4),
inference(resolve,[status(thm)],[c_4791,c_4378]) ).
cnf(c_4804,plain,
cyclic(sK7,A,sK4,sK4),
inference(resolve,[status(thm)],[c_4791,c_4292]) ).
cnf(c_4810,plain,
cyclic(sK4,A,sK7,sK7),
inference(resolve,[status(thm)],[c_4791,c_3346]) ).
cnf(c_4983,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK7,A)
| ~ cyclic(sK4,A,sK7,sK4) ),
inference(resolve,[status(thm)],[c_4810,c_3347]) ).
cnf(c_5343,plain,
cyclic(sK2,sK4,A,sK4),
inference(resolve,[status(thm)],[c_4799,c_242]) ).
cnf(c_5426,plain,
cyclic(sK7,sK4,A,sK4),
inference(resolve,[status(thm)],[c_4804,c_242]) ).
cnf(c_5554,plain,
cyclic(sK2,sK4,sK4,A),
inference(resolve,[status(thm)],[c_5343,c_243]) ).
cnf(c_5759,plain,
cyclic(sK4,sK7,A,sK4),
inference(resolve,[status(thm)],[c_5426,c_241]) ).
cnf(c_6009,plain,
cyclic(sK4,sK4,A,A),
inference(resolve,[status(thm)],[c_5554,c_304]) ).
cnf(c_10259,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK2,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_5554,c_240]) ).
cnf(c_6011,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_5554,c_10259]) ).
cnf(c_6933,plain,
cyclic(sK4,A,sK7,sK4),
inference(resolve,[status(thm)],[c_5759,c_242]) ).
cnf(c_6949,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK7,A) ),
inference(resolve,[status(thm)],[c_6933,c_4983]) ).
cnf(c_10260,plain,
( cyclic(sK4,A,B,A)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_6009,c_240]) ).
cnf(c_7453,plain,
cyclic(sK4,A,B,A),
inference(resolve,[status(thm)],[c_6011,c_10260]) ).
cnf(c_7466,plain,
cong(sK4,A,sK4,A),
inference(resolve,[status(thm)],[c_7453,c_6949]) ).
cnf(c_10261,plain,
( perp(sK4,sK4,A,B)
| ~ cong(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_7466,c_205]) ).
cnf(c_8834,plain,
perp(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_7466,c_10261]) ).
cnf(c_10255,plain,
perp(A,B,sK4,sK4),
inference(resolve,[status(thm)],[c_8834,c_248]) ).
cnf(c_10262,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK4,sK4) ),
inference(resolve,[status(thm)],[c_8834,c_247]) ).
cnf(c_10256,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_10255,c_10262]) ).
cnf(c_10257,plain,
$false,
inference(resolve,[status(thm)],[c_10256,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO653+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:47:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3062320 was started by sandbox on n020,
% 0.08/0.36 % Fri Sep 25 13:47:34 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 11.84/1.94
% 11.84/1.94 % given #500 (A,wt=13): 445 -coll(c7,c5,A) | coll(c1,A,c7). [resolve(388,a,253,a)].
% 11.84/1.94
% 11.84/1.94 % given #1000 (T,wt=13): 736 -coll(c7,c5,A) | coll(c7,A,c7). [resolve(582,a,253,a)].
% 11.84/1.94
% 11.84/1.94 % given #1500 (A,wt=15): 1005 -para(A,B,c3,c4) | para(A,B,c2,c1). [resolve(823,a,250,b)].
% 11.84/1.94
% 11.84/1.94 % given #2000 (T,wt=13): 2817 -coll(c4,c7,A) | coll(A,c2,c4). [resolve(2561,a,253,b)].
% 11.84/1.94
% 11.84/1.94 % given #2500 (A,wt=15): 1581 -para(c1,c4,A,B) | para(c4,c1,A,B). [resolve(1384,a,250,a)].
% 11.84/1.94
% 11.84/1.94 % SZS status Theorem for theBenchmark
% 11.84/1.94
% 11.84/1.94 % Proof 1 at 1.18 (+ 0.34) seconds.
% 11.84/1.94 % Length of proof is 86.
% 11.84/1.94 % Level of proof is 18.
% 11.84/1.94 % Maximum clause weight is 34.000.
% 11.84/1.94 % Given clauses 2855.
% 11.84/1.94
% 11.84/1.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
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