%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO620+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 : n015.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 01:18:18 PM UTC 2026
% Result : Theorem 8.99s 6.62s
% Output : Proof 8.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 29 unt; 0 def)
% Number of atoms : 101 ( 24 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 74 ( 18 ~; 12 |; 39 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-4 aty)
% Number of variables : 74 ( 0 sgn 46 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
fof(f94,conjecture,
! [A,B,C,O,I,E,J,L] :
( ( coll(L,B,O)
& perp(L,C,B,O)
& coll(J,A,E)
& perp(J,C,A,E)
& perp(A,O,A,E)
& coll(I,A,O)
& perp(I,C,A,O)
& eqangle(O,C,C,A,O,C,C,B)
& eqangle(O,B,B,C,O,B,B,A)
& eqangle(O,A,A,B,O,A,A,C) )
=> coll(I,L,J) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL8110982) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,I,E,J,L] :
( ( coll(L,B,O)
& perp(L,C,B,O)
& coll(J,A,E)
& perp(J,C,A,E)
& perp(A,O,A,E)
& coll(I,A,O)
& perp(I,C,A,O)
& eqangle(O,C,C,A,O,C,C,B)
& eqangle(O,B,B,C,O,B,B,A)
& eqangle(O,A,A,B,O,A,A,C) )
=> coll(I,L,J) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,I,E,J,L] :
( ~ coll(I,L,J)
& coll(L,B,O)
& perp(L,C,B,O)
& coll(J,A,E)
& perp(J,C,A,E)
& perp(A,O,A,E)
& coll(I,A,O)
& perp(I,C,A,O)
& eqangle(O,C,C,A,O,C,C,B)
& eqangle(O,B,B,C,O,B,B,A)
& eqangle(O,A,A,B,O,A,A,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ coll(sk24,sk27,sk26)
& coll(sk27,sk21,sk23)
& perp(sk27,sk22,sk21,sk23)
& coll(sk26,sk20,sk25)
& perp(sk26,sk22,sk20,sk25)
& perp(sk20,sk23,sk20,sk25)
& coll(sk24,sk20,sk23)
& perp(sk24,sk22,sk20,sk23)
& eqangle(sk23,sk22,sk22,sk20,sk23,sk22,sk22,sk21)
& eqangle(sk23,sk21,sk21,sk22,sk23,sk21,sk21,sk20)
& eqangle(sk23,sk20,sk20,sk21,sk23,sk20,sk20,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c117,plain,
coll(sk24,sk20,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk24,sk20,sk23) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h1,plain,
coll(sk20,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi117]) ).
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(h11,plain,
coll(sk23,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1,h1]) ).
cnf(c122,plain,
coll(sk27,sk21,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi122,negated_conjecture,
coll(sk27,sk21,sk23) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h6,plain,
coll(sk23,sk23,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi122,hi122]) ).
cnf(h33,plain,
coll(sk27,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h6,h11]) ).
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]) ).
cnf(h72,plain,
coll(sk27,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h33]) ).
cnf(h116,plain,
coll(sk20,sk20,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,h72,h72]) ).
cnf(c120,plain,
coll(sk26,sk20,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
coll(sk26,sk20,sk25) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h5,plain,
coll(sk26,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi120]) ).
cnf(h19,plain,
coll(sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h5,h5]) ).
cnf(h191,plain,
coll(sk26,sk27,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h19,h116]) ).
cnf(h245,plain,
coll(sk26,sk20,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi0,h191]) ).
cnf(h2,plain,
coll(sk24,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi117]) ).
cnf(h13,plain,
coll(sk20,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h2]) ).
cnf(h48,plain,
coll(sk26,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h19,h13]) ).
cnf(h87,plain,
coll(sk26,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h48]) ).
cnf(t72,plain,
coll(sk24,sk27,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h87,h245]) ).
cnf(t627,plain,
coll(sk24,sk27,sk26) = true,
inference(orient,[status(thm)],[t72]) ).
cnf(c123,plain,
~ coll(sk24,sk27,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
coll(sk24,sk27,sk26) != true,
inference(equality_encoding,[status(esa)],[c123]) ).
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
% 0.00/0.02 % Problem : GEO620+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n015.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Wed Sep 23 12:37:45 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.99/6.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.99/6.62 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------