%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ022-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 02:31:52 PM UTC 2026
% Result : Unsatisfiable 5.48s 11.31s
% Output : Proof 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 33 unt; 0 def)
% Number of atoms : 65 ( 14 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 25 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( borders(X,Y)
| ~ borders(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_borders) ).
fof(f0_nnf,plain,
! [Y,X] :
( borders(X,Y)
| ~ borders(Y,X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [Y,X] :
( borders(X,Y)
| ~ borders(Y,X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( borders(X1,X0)
| ~ borders(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(borders(X0,X1),true,borders(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f22,negated_conjecture,
borders(indian,northern_territory),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indian_nt) ).
fof(f22_nnf,plain,
borders(indian,northern_territory),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
borders(indian,northern_territory),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi22,negated_conjecture,
borders(indian,northern_territory) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h10,plain,
borders(northern_territory,indian) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi22]) ).
cnf(f21,negated_conjecture,
borders(indian,western_australia),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indian_wa) ).
fof(f21_nnf,plain,
borders(indian,western_australia),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
borders(indian,western_australia),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(hi21,negated_conjecture,
borders(indian,western_australia) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h9,plain,
borders(western_australia,indian) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi21]) ).
cnf(f32,negated_conjecture,
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_borders) ).
fof(f32_nnf,plain,
! [State1,State2,Ocean] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [State1,State2,Ocean] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
( ~ ocean(X2)
| ~ borders(X1,X2)
| ~ borders(X0,X2)
| ~ borders(X0,X1)
| ~ state(X1)
| ~ state(X0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(hi32,negated_conjecture,
ifeq(state(X0),true,ifeq(state(X1),true,ifeq(borders(X0,X1),true,ifeq(borders(X0,X2),true,ifeq(borders(X1,X2),true,ifeq(ocean(X2),true,false,true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(f5,negated_conjecture,
state(western_australia),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',western_australia) ).
fof(f5_nnf,plain,
state(western_australia),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
state(western_australia),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,negated_conjecture,
state(western_australia) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f6,negated_conjecture,
state(northern_territory),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',northern_territory) ).
fof(f6_nnf,plain,
state(northern_territory),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
state(northern_territory),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(hi6,negated_conjecture,
state(northern_territory) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f12,negated_conjecture,
borders(western_australia,northern_territory),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wa_nt) ).
fof(f12_nnf,plain,
borders(western_australia,northern_territory),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
borders(western_australia,northern_territory),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,negated_conjecture,
borders(western_australia,northern_territory) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f2,negated_conjecture,
ocean(indian),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indian) ).
fof(f2_nnf,plain,
ocean(indian),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
ocean(indian),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi2,negated_conjecture,
ocean(indian) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi32,hi5,hi6,hi12,h9,h10,hi2]) ).
cnf(t247,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t247]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ022-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/10.39 % Computer : n002.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Thu Sep 24 06:43:31 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.48/11.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.48/11.31 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------