%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO548+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 : n003.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 07:18:05 AM UTC 2026
% Result : Theorem 132.59s 18.36s
% Output : CNFRefutation 132.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 26
% Syntax : Number of formulae : 132 ( 51 unt; 0 def)
% Number of atoms : 297 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 244 ( 79 ~; 75 |; 63 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 13 con; 0-4 aty)
% Number of variables : 471 ( 71 sgn 162 !; 15 ?)
% 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(ruleD18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('theBenchmark.p',ruleD18) ).
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(ruleD22,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('theBenchmark.p',ruleD22) ).
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(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(ruleD41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('theBenchmark.p',ruleD41) ).
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(ruleD46,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
file('theBenchmark.p',ruleD46) ).
fof(ruleD48,axiom,
! [A,B,C,O,X] :
( ( perp(O,A,A,X)
& circle(O,A,B,C) )
=> eqangle(A,X,A,B,C,A,C,B) ),
file('theBenchmark.p',ruleD48) ).
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(ruleX14,axiom,
! [A,B,C,D] :
? [O] :
( ( cyclic(A,B,C,D)
& perp(A,C,C,B) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleX14) ).
fof(exemplo6GDDFULL012008,conjecture,
! [A,B,C,O,P,G,F,P1,G1,F1,K,NWPNT1,NWPNT2] :
( ( coll(K,G,F)
& coll(K,G1,F1)
& coll(F1,A,C)
& perp(F1,P1,A,C)
& coll(G1,A,B)
& perp(G1,P1,A,B)
& circle(O,A,P1,NWPNT2)
& coll(F,A,C)
& perp(F,P,A,C)
& coll(G,A,B)
& perp(G,P,A,B)
& circle(O,A,P,NWPNT1)
& circle(O,A,B,C) )
=> eqangle(P,A,A,P1,F1,K,K,F) ),
file('theBenchmark.p',exemplo6GDDFULL012008) ).
fof(exemplo6GDDFULL012008_neg,negated_conjecture,
~ ! [A,B,C,O,P,G,F,P1,G1,F1,K,NWPNT1,NWPNT2] :
( ( coll(K,G,F)
& coll(K,G1,F1)
& coll(F1,A,C)
& perp(F1,P1,A,C)
& coll(G1,A,B)
& perp(G1,P1,A,B)
& circle(O,A,P1,NWPNT2)
& coll(F,A,C)
& perp(F,P,A,C)
& coll(G,A,B)
& perp(G,P,A,B)
& circle(O,A,P,NWPNT1)
& circle(O,A,B,C) )
=> eqangle(P,A,A,P1,F1,K,K,F) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012008]) ).
cnf(c_96,plain,
( eqangle(B,E,B,C,D,B,D,C)
| ~ perp(A,B,B,E)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD48]) ).
fof(nnf_90,plain,
! [A,B,C,D] :
? [O] :
( circle(O,A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(fof_nnf,[status(thm)],[ruleX14]) ).
fof(sk_ruleX14,plain,
! [A,B,C,D] :
( circle(sK0(A,B,C,D),A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(O,sK0(A,B,C,D))],[nnf_90]) ).
cnf(c_108,plain,
( circle(sK0(A,C,B,D),A,C,B)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(split_conjunct,[status(thm)],[sk_ruleX14]) ).
cnf(c_154,plain,
( eqangle(A,E,A,C,B,A,B,C)
| ~ perp(sK0(A,C,B,D),A,A,E)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(resolve,[status(thm)],[c_108,c_96]) ).
fof(nnf_95,plain,
? [A,B,C,O,P,G,F,P1,G1,F1,K,NWPNT1,NWPNT2] :
( ~ eqangle(P,A,A,P1,F1,K,K,F)
& coll(K,G,F)
& coll(K,G1,F1)
& coll(F1,A,C)
& perp(F1,P1,A,C)
& coll(G1,A,B)
& perp(G1,P1,A,B)
& circle(O,A,P1,NWPNT2)
& coll(F,A,C)
& perp(F,P,A,C)
& coll(G,A,B)
& perp(G,P,A,B)
& circle(O,A,P,NWPNT1)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012008_neg]) ).
fof(sk_exemplo6GDDFULL012008_neg,plain,
( ~ eqangle(sK1,sK2,sK2,sK3,sK4,sK5,sK5,sK6)
& coll(sK5,sK7,sK6)
& coll(sK5,sK13,sK4)
& coll(sK4,sK2,sK10)
& perp(sK4,sK3,sK2,sK10)
& coll(sK13,sK2,sK8)
& perp(sK13,sK3,sK2,sK8)
& circle(sK9,sK2,sK3,sK12)
& coll(sK6,sK2,sK10)
& perp(sK6,sK1,sK2,sK10)
& coll(sK7,sK2,sK8)
& perp(sK7,sK1,sK2,sK8)
& circle(sK9,sK2,sK1,sK11)
& circle(sK9,sK2,sK8,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK2,sK8,sK10,sK1,sK11,sK7,sK6,sK3,sK12,sK13,sK4,sK5]),skolemize(A,sK2),skolemize(B,sK8),skolemize(C,sK10),skolemize(O,sK9),skolemize(P,sK1),skolemize(G,sK7),skolemize(F,sK6),skolemize(P1,sK3),skolemize(G1,sK13),skolemize(F1,sK4),skolemize(K,sK5),skolemize(NWPNT1,sK11),skolemize(NWPNT2,sK12)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ eqangle(sK1,sK2,sK2,sK3,sK4,sK5,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012008_neg]) ).
cnf(c_202,negated_conjecture,
perp(sK7,sK1,sK2,sK8),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012008_neg]) ).
cnf(c_241,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_250,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_251,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_256,plain,
( eqangle(A,B,B,C,B,C,A,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD46]) ).
cnf(c_259,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_260,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_262,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_263,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_264,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_281,plain,
( eqangle(A,B,C,D,V8,V9,V10,V11)
| ~ eqangle(E,F,V6,V7,V8,V9,V10,V11)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD22]) ).
cnf(c_282,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_284,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_285,plain,
( eqangle(B,A,C,D,E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD18]) ).
cnf(c_286,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_287,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_288,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_289,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_293,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_294,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_295,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_297,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_298,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_299,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_344,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_250]) ).
cnf(c_350,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_286]) ).
cnf(c_355,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_299]) ).
cnf(c_472,plain,
( para(sK7,sK1,A,B)
| ~ perp(sK2,sK8,A,B) ),
inference(resolve,[status(thm)],[c_293,c_202]) ).
cnf(c_486,plain,
perp(sK2,sK8,sK7,sK1),
inference(resolve,[status(thm)],[c_294,c_202]) ).
cnf(c_906,plain,
perp(sK2,sK8,sK1,sK7),
inference(resolve,[status(thm)],[c_486,c_295]) ).
cnf(c_2407,plain,
para(sK7,sK1,sK1,sK7),
inference(resolve,[status(thm)],[c_472,c_906]) ).
cnf(c_2409,plain,
para(sK7,sK1,sK7,sK1),
inference(resolve,[status(thm)],[c_472,c_486]) ).
cnf(c_2431,plain,
para(sK1,sK7,sK7,sK1),
inference(resolve,[status(thm)],[c_2407,c_297]) ).
cnf(c_2463,plain,
eqangle(sK7,sK1,A,B,sK7,sK1,A,B),
inference(resolve,[status(thm)],[c_2409,c_263]) ).
cnf(c_3147,plain,
para(sK1,sK7,sK1,sK7),
inference(resolve,[status(thm)],[c_2431,c_298]) ).
cnf(c_3196,plain,
eqangle(sK1,sK7,A,B,sK1,sK7,A,B),
inference(resolve,[status(thm)],[c_3147,c_263]) ).
cnf(c_3272,plain,
eqangle(A,B,sK7,sK1,A,B,sK7,sK1),
inference(resolve,[status(thm)],[c_2463,c_284]) ).
cnf(c_3274,plain,
( cyclic(sK1,A,sK7,sK7)
| ~ coll(sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_2463,c_260]) ).
cnf(c_3275,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK7,sK7)
| ~ cyclic(sK1,A,sK7,A)
| ~ cyclic(sK1,A,sK7,sK1) ),
inference(resolve,[status(thm)],[c_2463,c_259]) ).
cnf(c_3307,plain,
( cyclic(sK7,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3196,c_260]) ).
cnf(c_3354,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_3272,c_264]) ).
cnf(c_3379,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_3354,c_241]) ).
cnf(c_3399,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_3379,c_355]) ).
cnf(c_3407,plain,
cyclic(sK7,A,sK1,sK1),
inference(resolve,[status(thm)],[c_3399,c_3307]) ).
cnf(c_3408,plain,
cyclic(sK1,A,sK7,sK7),
inference(resolve,[status(thm)],[c_3399,c_3274]) ).
cnf(c_3563,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK7,A)
| ~ cyclic(sK1,A,sK7,sK1) ),
inference(resolve,[status(thm)],[c_3408,c_3275]) ).
cnf(c_3663,plain,
cyclic(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_3407,c_350]) ).
cnf(c_3665,plain,
cyclic(sK7,sK1,A,sK1),
inference(resolve,[status(thm)],[c_3407,c_288]) ).
cnf(c_3814,plain,
cyclic(sK1,A,sK1,sK1),
inference(resolve,[status(thm)],[c_3663,c_287]) ).
cnf(c_3827,plain,
cyclic(sK7,sK1,sK1,A),
inference(resolve,[status(thm)],[c_3665,c_289]) ).
cnf(c_3828,plain,
cyclic(sK1,sK7,A,sK1),
inference(resolve,[status(thm)],[c_3665,c_287]) ).
cnf(c_4089,plain,
cyclic(sK1,sK1,A,sK1),
inference(resolve,[status(thm)],[c_3814,c_288]) ).
cnf(c_4090,plain,
( cyclic(A,sK1,B,sK1)
| ~ cyclic(sK1,A,sK1,B) ),
inference(resolve,[status(thm)],[c_3814,c_286]) ).
cnf(c_4102,plain,
cyclic(sK1,sK1,A,A),
inference(resolve,[status(thm)],[c_3827,c_350]) ).
cnf(c_7046,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK7,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3827,c_286]) ).
cnf(c_4104,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_3827,c_7046]) ).
cnf(c_4118,plain,
cyclic(sK1,A,sK7,sK1),
inference(resolve,[status(thm)],[c_3828,c_288]) ).
cnf(c_4134,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK7,A) ),
inference(resolve,[status(thm)],[c_4118,c_3563]) ).
cnf(c_7047,plain,
( cyclic(sK1,A,sK1,B)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_4089,c_286]) ).
cnf(c_4317,plain,
cyclic(sK1,A,sK1,B),
inference(resolve,[status(thm)],[c_4104,c_7047]) ).
cnf(c_4330,plain,
cyclic(A,sK1,B,sK1),
inference(resolve,[status(thm)],[c_4317,c_4090]) ).
cnf(c_4332,plain,
( perp(A,sK1,sK1,A)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_4102,c_344]) ).
cnf(c_7048,plain,
( cyclic(sK1,A,B,A)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_4102,c_286]) ).
cnf(c_4333,plain,
cyclic(sK1,A,B,A),
inference(resolve,[status(thm)],[c_4104,c_7048]) ).
cnf(c_4346,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_4333,c_4134]) ).
cnf(c_4347,plain,
perp(A,sK1,sK1,A),
inference(resolve,[status(thm)],[c_4346,c_4332]) ).
cnf(c_7049,plain,
( perp(A,sK1,sK1,B)
| ~ cong(sK1,B,sK1,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_4104,c_250]) ).
cnf(c_7050,plain,
( perp(B,sK1,sK1,A)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_4346,c_7049]) ).
cnf(c_4395,plain,
perp(A,sK1,sK1,B),
inference(resolve,[status(thm)],[c_4346,c_7050]) ).
cnf(c_7051,plain,
( eqangle(sK1,C,sK1,sK1,A,sK1,A,sK1)
| ~ perp(sK0(sK1,sK1,A,B),sK1,sK1,C)
| ~ perp(sK1,A,A,sK1) ),
inference(resolve,[status(thm)],[c_4104,c_154]) ).
cnf(c_4403,plain,
( eqangle(sK1,B,sK1,sK1,A,sK1,A,sK1)
| ~ perp(sK1,A,A,sK1) ),
inference(resolve,[status(thm)],[c_4395,c_7051]) ).
cnf(c_4735,plain,
eqangle(A,B,A,sK1,sK1,B,sK1,sK1),
inference(resolve,[status(thm)],[c_4330,c_262]) ).
cnf(c_4761,plain,
eqangle(A,sK1,A,B,B,sK1,B,B),
inference(resolve,[status(thm)],[c_4333,c_262]) ).
cnf(c_4806,plain,
eqangle(sK1,A,A,A,A,A,sK1,A),
inference(resolve,[status(thm)],[c_4346,c_256]) ).
cnf(c_7052,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_4346,c_251]) ).
cnf(c_4807,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_4346,c_7052]) ).
cnf(c_4844,plain,
perp(sK1,A,A,sK1),
inference(resolve,[status(thm)],[c_4347,c_294]) ).
cnf(c_4860,plain,
eqangle(sK1,A,sK1,sK1,B,sK1,B,sK1),
inference(resolve,[status(thm)],[c_4844,c_4403]) ).
cnf(c_5284,plain,
perp(A,B,sK1,sK1),
inference(resolve,[status(thm)],[c_4807,c_294]) ).
cnf(c_7053,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK1,sK1) ),
inference(resolve,[status(thm)],[c_4807,c_293]) ).
cnf(c_5285,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_5284,c_7053]) ).
cnf(c_5319,plain,
eqangle(A,B,C,D,E,F,C,D),
inference(resolve,[status(thm)],[c_5285,c_263]) ).
cnf(c_6308,plain,
eqangle(A,B,sK1,B,A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_4735,c_282]) ).
cnf(c_6311,plain,
eqangle(sK1,A,A,B,B,sK1,B,B),
inference(resolve,[status(thm)],[c_4761,c_285]) ).
cnf(c_6319,plain,
eqangle(A,sK1,A,A,A,A,sK1,A),
inference(resolve,[status(thm)],[c_4806,c_285]) ).
cnf(c_6333,plain,
eqangle(A,sK1,sK1,sK1,B,sK1,B,sK1),
inference(resolve,[status(thm)],[c_4860,c_285]) ).
cnf(c_6449,plain,
eqangle(A,B,C,D,A,B,E,F),
inference(resolve,[status(thm)],[c_5319,c_284]) ).
cnf(c_6847,plain,
( eqangle(A,F,sK1,F,B,C,D,E)
| ~ eqangle(A,sK1,sK1,sK1,B,C,D,E) ),
inference(resolve,[status(thm)],[c_6308,c_281]) ).
cnf(c_6851,plain,
( eqangle(sK1,F,F,A,B,C,D,E)
| ~ eqangle(A,sK1,A,A,B,C,D,E) ),
inference(resolve,[status(thm)],[c_6311,c_281]) ).
cnf(c_6861,plain,
( eqangle(A,sK1,A,A,B,C,D,E)
| ~ eqangle(A,A,sK1,A,B,C,D,E) ),
inference(resolve,[status(thm)],[c_6319,c_281]) ).
cnf(c_6881,plain,
( eqangle(F,sK1,sK1,sK1,B,C,D,E)
| ~ eqangle(A,sK1,A,sK1,B,C,D,E) ),
inference(resolve,[status(thm)],[c_6333,c_281]) ).
cnf(c_6997,plain,
eqangle(A,B,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_6449,c_282]) ).
cnf(c_7003,plain,
eqangle(A,sK1,sK1,sK1,B,C,D,E),
inference(resolve,[status(thm)],[c_6997,c_6881]) ).
cnf(c_7026,plain,
eqangle(A,B,sK1,B,C,D,E,F),
inference(resolve,[status(thm)],[c_7003,c_6847]) ).
cnf(c_7038,plain,
eqangle(A,sK1,A,A,B,C,D,E),
inference(resolve,[status(thm)],[c_7026,c_6861]) ).
cnf(c_7044,plain,
eqangle(sK1,A,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_7038,c_6851]) ).
cnf(c_7045,plain,
$false,
inference(resolve,[status(thm)],[c_7044,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO548+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n003.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 13:42:52 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 289089 was started by sandbox2 on n003,
% 0.17/0.44 % Fri Sep 25 13:42:52 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.48
% 0.17/0.48 % From the command line: assign(max_seconds, 300).
% 132.59/18.36
% 132.59/18.36 % given #500 (T,wt=9): 1443 coll(c10,c11,c6). [resolve(1417,a,301,a)].
% 132.59/18.36
% 132.59/18.36 % given #1000 (T,wt=13): 884 -coll(c7,c11,A) | coll(A,c11,c7). [resolve(814,a,299,b)].
% 132.59/18.36
% 132.59/18.36 % given #1500 (T,wt=13): 2023 -coll(c1,c6,A) | coll(A,c7,c1). [resolve(1904,a,299,b)].
% 132.59/18.36
% 132.59/18.36 % given #2000 (T,wt=9): 2814 coll(c1,c9,c5). [resolve(2605,a,301,a)].
% 132.59/18.36
% 132.59/18.36 % given #2500 (T,wt=14): 3272 eqangle(A,B,c6,c5,A,B,c6,c5). [resolve(2463,a,284,a)].
% 132.59/18.36
% 132.59/18.36 % given #3000 (T,wt=10): 5970 cong(A,B,c6,A). [resolve(5737,a,280,a)].
% 132.59/18.36
% 132.59/18.36 % SZS status Theorem for theBenchmark
% 132.59/18.36
% 132.59/18.36 % Proof 1 at 1.30 (+ 0.42) seconds.
% 132.59/18.36 % Length of proof is 119.
% 132.59/18.36 % Level of proof is 25.
% 132.59/18.36 % Maximum clause weight is 38.000.
% 132.59/18.36 % Given clauses 3327.
% 132.59/18.36
% 132.59/18.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------