%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO085+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 01:17:00 PM UTC 2026
% Result : Theorem 6.51s 1.39s
% Output : Proof 6.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 14 unt; 0 def)
% Number of atoms : 87 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 91 ( 40 ~; 27 |; 18 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 57 ( 1 sgn 28 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [C] :
( open(C)
<=> ? [P] : end_point(P,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn) ).
fof(f6_nnf,plain,
! [C] :
( ( ! [P] : ~ end_point(P,C)
| open(C) )
& ( ? [P] : end_point(P,C)
| ~ open(C) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [C,P] :
( ( ~ end_point(P,C)
| open(C) )
& ( end_point(sk6(C),C)
| ~ open(C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6])],[f6_nnf]) ).
cnf(c32,plain,
( end_point(sk6(X0),X0)
| ~ open(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi27,axiom,
ifeq(open(X0),true,end_point(sk6(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
fof(f16,conjecture,
! [C] :
( open(C)
=> ? [P,Q] :
( end_point(Q,C)
& end_point(P,C)
& P != Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_2_7_1) ).
fof(f16_neg,negated_conjecture,
~ ! [C] :
( open(C)
=> ? [P,Q] :
( end_point(Q,C)
& end_point(P,C)
& P != Q ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [C] :
( ! [P,Q] :
( ~ end_point(Q,C)
| ~ end_point(P,C)
| P = Q )
& open(C) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
! [P,Q] :
( ( ~ end_point(Q,sk13)
| ~ end_point(P,sk13)
| P = Q )
& open(sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f16_nnf]) ).
cnf(c48,plain,
open(sk13),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi40,negated_conjecture,
open(sk13) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(h0,plain,
end_point(sk6(sk13),sk13) = true,
inference(hyper_resolution,[status(thm)],[hi27,hi40]) ).
fof(f12,axiom,
! [C,P] :
( end_point(P,C)
=> ? [Q] :
( P != Q
& end_point(Q,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6) ).
fof(f12_nnf,plain,
! [C,P] :
( ? [Q] :
( P != Q
& end_point(Q,C) )
| ~ end_point(P,C) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [P,C] :
( ( P != sk10(C,P)
& end_point(sk10(C,P),C) )
| ~ end_point(P,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f12_nnf]) ).
cnf(c40,plain,
( end_point(sk10(X0,X1),X0)
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi35,axiom,
ifeq(end_point(X0,X1),true,end_point(sk10(X1,X0),X1),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(h4,plain,
end_point(sk10(sk13,sk6(sk13)),sk13) = true,
inference(hyper_resolution,[status(thm)],[hi35,h0]) ).
cnf(c49,plain,
( ~ end_point(X2,sk13)
| ~ end_point(X1,sk13)
| X1 = X2 ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi41,negated_conjecture,
ifeq(end_point(X0,sk13),true,ifeq(end_point(X1,sk13),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(h29,plain,
sk6(sk13) = sk10(sk13,sk6(sk13)),
inference(hyper_resolution,[status(thm)],[hi41,h0,h4]) ).
cnf(c41,plain,
( X1 != sk10(X0,X1)
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi44,axiom,
ifeq(end_point(X0,X1),true,ifeq(X0,sk10(X1,X0),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c41]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi44,h0,h29]) ).
cnf(t510,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f3,axiom,
! [P,C] :
( inner_point(P,C)
<=> ( ~ end_point(P,C)
& incident_c(P,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn) ).
fof(f3_nnf,plain,
! [P,C] :
( ( end_point(P,C)
| ~ incident_c(P,C)
| inner_point(P,C) )
& ( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [P,C] :
( ( end_point(P,C)
| ~ incident_c(P,C)
| inner_point(P,C) )
& ( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c21,plain,
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f5,axiom,
! [C] :
( closed(C)
<=> ~ ? [P] : end_point(P,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn) ).
fof(f5_nnf,plain,
! [C] :
( ( ? [P] : end_point(P,C)
| closed(C) )
& ( ! [P] : ~ end_point(P,C)
| ~ closed(C) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [C,P] :
( ( end_point(sk5(C),C)
| closed(C) )
& ( ~ end_point(P,C)
| ~ closed(C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f5_nnf]) ).
cnf(c30,plain,
( ~ end_point(X1,X0)
| ~ closed(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c21,c30,c41]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t510]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO085+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 10:47:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.51/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.51/1.39 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------