%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO547+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 : Fri Sep 25 01:18:07 PM UTC 2026
% Result : Theorem 11.28s 6.95s
% Output : Proof 11.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 31 unt; 0 def)
% Number of atoms : 95 ( 26 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 66 ( 18 ~; 12 |; 31 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 77 ( 0 sgn 48 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f94,conjecture,
! [A,B,C,O,D,E,F,G,NWPNT1] :
( ( coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(E,B,C)
& perp(E,D,B,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> coll(E,F,G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012007) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,F,G,NWPNT1] :
( ( coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(E,B,C)
& perp(E,D,B,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> coll(E,F,G) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,D,E,F,G,NWPNT1] :
( ~ coll(E,F,G)
& coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(E,B,C)
& perp(E,D,B,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ coll(sk25,sk26,sk27)
& coll(sk27,sk20,sk21)
& perp(sk27,sk24,sk20,sk21)
& coll(sk26,sk20,sk22)
& perp(sk26,sk24,sk20,sk22)
& coll(sk25,sk21,sk22)
& perp(sk25,sk24,sk21,sk22)
& circle(sk23,sk20,sk24,sk28)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28])],[f94_nnf]) ).
cnf(c118,plain,
coll(sk26,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
coll(sk26,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h5,plain,
coll(sk26,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi118]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h21,plain,
coll(sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h5,h5]) ).
cnf(c120,plain,
coll(sk27,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
coll(sk27,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h8,plain,
coll(sk27,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi120]) ).
cnf(h27,plain,
coll(sk20,sk20,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,h8,h8]) ).
cnf(h66,plain,
coll(sk27,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h27,h21]) ).
cnf(h120,plain,
coll(sk27,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h66]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h7,plain,
coll(sk20,sk27,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi120]) ).
cnf(h25,plain,
coll(sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h7,h7]) ).
cnf(c116,plain,
coll(sk25,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk25,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h2,plain,
coll(sk25,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi116]) ).
cnf(h13,plain,
coll(sk21,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h2]) ).
cnf(h60,plain,
coll(sk25,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h13,h25]) ).
cnf(h117,plain,
coll(sk25,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h60]) ).
cnf(h6,plain,
coll(sk21,sk21,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi120,hi120]) ).
cnf(h39,plain,
coll(sk25,sk27,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h13,h6]) ).
cnf(h81,plain,
coll(sk25,sk21,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi0,h39]) ).
cnf(h169,plain,
coll(sk27,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h81,h117]) ).
cnf(t76,plain,
coll(sk25,sk26,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,h169,h120]) ).
cnf(t627,plain,
coll(sk25,sk26,sk27) = true,
inference(orient,[status(thm)],[t76]) ).
cnf(c121,plain,
~ coll(sk25,sk26,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
coll(sk25,sk26,sk27) != true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t627]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO547+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/5.40 % Computer : n019.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Wed Sep 23 12:22:11 UTC 2026
% 0.12/5.40 % CPUTime :
% 0.12/5.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.28/6.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.28/6.95 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------