%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO609+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 07:18:13 AM UTC 2026
% Result : Theorem 12.04s 2.03s
% Output : CNFRefutation 12.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 20
% Syntax : Number of formulae : 94 ( 36 unt; 0 def)
% Number of atoms : 202 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 162 ( 54 ~; 50 |; 37 &)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 283 ( 33 sgn 110 !; 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(ruleD7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('theBenchmark.p',ruleD7) ).
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(exemplo6GDDFULL618071,conjecture,
! [A,B,C,O,E,F,G,NWPNT1] :
( ( coll(G,A,C)
& perp(G,E,A,C)
& coll(F,A,B)
& perp(F,E,A,B)
& circle(O,A,E,NWPNT1)
& para(B,C,E,A)
& circle(O,A,B,C) )
=> para(F,G,A,O) ),
file('theBenchmark.p',exemplo6GDDFULL618071) ).
fof(exemplo6GDDFULL618071_neg,negated_conjecture,
~ ! [A,B,C,O,E,F,G,NWPNT1] :
( ( coll(G,A,C)
& perp(G,E,A,C)
& coll(F,A,B)
& perp(F,E,A,B)
& circle(O,A,E,NWPNT1)
& para(B,C,E,A)
& circle(O,A,B,C) )
=> para(F,G,A,O) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618071]) ).
fof(nnf_95,plain,
? [A,B,C,O,E,F,G,NWPNT1] :
( ~ para(F,G,A,O)
& coll(G,A,C)
& perp(G,E,A,C)
& coll(F,A,B)
& perp(F,E,A,B)
& circle(O,A,E,NWPNT1)
& para(B,C,E,A)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618071_neg]) ).
fof(sk_exemplo6GDDFULL618071_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& coll(sK1,sK2,sK5)
& perp(sK1,sK4,sK2,sK5)
& coll(sK0,sK2,sK6)
& perp(sK0,sK4,sK2,sK6)
& circle(sK3,sK2,sK4,sK7)
& para(sK6,sK5,sK4,sK2)
& circle(sK3,sK2,sK6,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK6,sK5,sK4,sK7,sK0,sK1]),skolemize(A,sK2),skolemize(B,sK6),skolemize(C,sK5),skolemize(O,sK3),skolemize(E,sK4),skolemize(F,sK0),skolemize(G,sK1),skolemize(NWPNT1,sK7)],[nnf_95]) ).
cnf(c_177,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618071_neg]) ).
cnf(c_179,negated_conjecture,
perp(sK1,sK4,sK2,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618071_neg]) ).
cnf(c_182,negated_conjecture,
para(sK6,sK5,sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618071_neg]) ).
cnf(c_215,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_221,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_230,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_231,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_239,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_240,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_243,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_262,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_264,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_266,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_267,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_268,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_269,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_273,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_274,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_275,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_277,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_278,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_279,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_330,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_266]) ).
cnf(c_335,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_279]) ).
cnf(c_419,plain,
eqangle(sK6,sK5,A,B,sK4,sK2,A,B),
inference(resolve,[status(thm)],[c_243,c_182]) ).
cnf(c_422,plain,
( para(sK1,sK4,A,B)
| ~ perp(sK2,sK5,A,B) ),
inference(resolve,[status(thm)],[c_273,c_179]) ).
cnf(c_430,plain,
perp(sK2,sK5,sK1,sK4),
inference(resolve,[status(thm)],[c_274,c_179]) ).
cnf(c_615,plain,
perp(sK2,sK5,sK4,sK1),
inference(resolve,[status(thm)],[c_430,c_275]) ).
cnf(c_1085,plain,
eqangle(A,B,sK6,sK5,A,B,sK4,sK2),
inference(resolve,[status(thm)],[c_419,c_264]) ).
cnf(c_1109,plain,
para(sK1,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_422,c_615]) ).
cnf(c_1110,plain,
para(sK1,sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_422,c_430]) ).
cnf(c_1286,plain,
para(sK4,sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_1109,c_277]) ).
cnf(c_1301,plain,
eqangle(sK1,sK4,A,B,sK1,sK4,A,B),
inference(resolve,[status(thm)],[c_1110,c_243]) ).
cnf(c_2010,plain,
para(sK4,sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_1286,c_278]) ).
cnf(c_2176,plain,
eqangle(sK4,sK1,A,B,sK4,sK1,A,B),
inference(resolve,[status(thm)],[c_2010,c_243]) ).
cnf(c_3537,plain,
eqangle(A,B,A,B,sK6,sK5,sK4,sK2),
inference(resolve,[status(thm)],[c_1085,c_262]) ).
cnf(c_3809,plain,
( cyclic(sK4,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1301,c_240]) ).
cnf(c_4127,plain,
( cyclic(sK1,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_2176,c_240]) ).
cnf(c_4128,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_2176,c_239]) ).
cnf(c_12148,plain,
( para(A,B,A,B)
| ~ para(sK6,sK5,sK4,sK2) ),
inference(resolve,[status(thm)],[c_3537,c_215]) ).
cnf(c_4856,negated_conjecture,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_182,c_12148]) ).
cnf(c_4870,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_4856,c_221]) ).
cnf(c_4962,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_4870,c_335]) ).
cnf(c_4972,plain,
cyclic(sK1,A,sK4,sK4),
inference(resolve,[status(thm)],[c_4962,c_4127]) ).
cnf(c_4982,plain,
cyclic(sK4,A,sK1,sK1),
inference(resolve,[status(thm)],[c_4962,c_3809]) ).
cnf(c_5122,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A)
| ~ cyclic(sK1,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_4972,c_4128]) ).
cnf(c_5619,plain,
cyclic(sK1,sK4,A,sK4),
inference(resolve,[status(thm)],[c_4972,c_268]) ).
cnf(c_5808,plain,
cyclic(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_4982,c_330]) ).
cnf(c_5810,plain,
cyclic(sK4,sK1,A,sK1),
inference(resolve,[status(thm)],[c_4982,c_268]) ).
cnf(c_5996,plain,
cyclic(sK1,sK4,sK4,A),
inference(resolve,[status(thm)],[c_5619,c_269]) ).
cnf(c_5997,plain,
cyclic(sK4,sK1,A,sK4),
inference(resolve,[status(thm)],[c_5619,c_267]) ).
cnf(c_6383,plain,
cyclic(sK1,A,sK1,sK1),
inference(resolve,[status(thm)],[c_5808,c_267]) ).
cnf(c_6406,plain,
cyclic(sK1,sK4,A,sK1),
inference(resolve,[status(thm)],[c_5810,c_267]) ).
cnf(c_12149,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK1,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_5996,c_266]) ).
cnf(c_6998,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_5996,c_12149]) ).
cnf(c_7014,plain,
( cyclic(sK1,A,sK4,B)
| ~ cyclic(sK4,sK1,A,B) ),
inference(resolve,[status(thm)],[c_5997,c_266]) ).
cnf(c_8189,plain,
cyclic(sK1,sK1,A,sK1),
inference(resolve,[status(thm)],[c_6383,c_268]) ).
cnf(c_8218,plain,
cyclic(sK1,A,sK4,sK1),
inference(resolve,[status(thm)],[c_6406,c_268]) ).
cnf(c_8234,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A) ),
inference(resolve,[status(thm)],[c_8218,c_5122]) ).
cnf(c_12150,plain,
( cyclic(sK4,A,B,C)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_6998,c_266]) ).
cnf(c_9031,plain,
cyclic(sK4,A,B,C),
inference(resolve,[status(thm)],[c_6998,c_12150]) ).
cnf(c_9048,plain,
cyclic(sK1,A,sK4,B),
inference(resolve,[status(thm)],[c_9031,c_7014]) ).
cnf(c_9127,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_9048,c_8234]) ).
cnf(c_12151,plain,
( perp(A,sK1,sK1,sK1)
| ~ cong(sK1,sK1,sK1,sK1)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_8189,c_230]) ).
cnf(c_12152,plain,
( perp(A,sK1,sK1,sK1)
| ~ cong(sK1,sK1,sK1,sK1) ),
inference(resolve,[status(thm)],[c_9127,c_12151]) ).
cnf(c_9881,plain,
perp(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_9127,c_12152]) ).
cnf(c_12153,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_9127,c_231]) ).
cnf(c_11635,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_9127,c_12153]) ).
cnf(c_12154,plain,
( para(C,sK1,A,B)
| ~ perp(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_9881,c_273]) ).
cnf(c_12146,plain,
para(A,sK1,B,C),
inference(resolve,[status(thm)],[c_11635,c_12154]) ).
cnf(c_12147,plain,
$false,
inference(resolve,[status(thm)],[c_12146,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO609+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 13:44:09 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 3297815 was started by sandbox2 on n004,
% 0.08/0.36 % Fri Sep 25 13:44:09 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 12.04/2.03
% 12.04/2.03 % given #500 (A,wt=28): 488 -coll(c3,c2,c5) | -coll(A,c2,c3) | coll(f20(c2,c3,c5,c1,c3,A),c5,c1). [resolve(457,a,349,b)].
% 12.04/2.03
% 12.04/2.03 % given #1000 (W,wt=13): 1116 -coll(c1,c2,A) | coll(c3,A,c1). [resolve(1059,a,279,a)].
% 12.04/2.03
% 12.04/2.03 % given #1500 (T,wt=13): 1914 -coll(c7,c1,A) | coll(A,c5,c7). [resolve(1869,a,279,b)].
% 12.04/2.03
% 12.04/2.03 % given #2000 (W,wt=9): 5000 coll(c1,A,c5). [back_unit_del(1886),unit_del(a,4962)].
% 12.04/2.03
% 12.04/2.03 % given #2500 (T,wt=10): 8496 cyclic(c4,A,c4,B). [resolve(6526,a,266,a),unit_del(a,6541)].
% 12.04/2.03
% 12.04/2.03 % SZS status Theorem for theBenchmark
% 12.04/2.03
% 12.04/2.03 % Proof 1 at 1.19 (+ 0.42) seconds.
% 12.04/2.03 % Length of proof is 84.
% 12.04/2.03 % Level of proof is 18.
% 12.04/2.03 % Maximum clause weight is 34.000.
% 12.04/2.03 % Given clauses 2789.
% 12.04/2.03
% 12.04/2.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
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