%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO024-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 01:16:36 PM UTC 2026
% Result : Unsatisfiable 5.56s 6.34s
% Output : Proof 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 44 unt; 0 def)
% Number of atoms : 44 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 19 ( 19 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 46 ( 8 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f35,negated_conjecture,
~ equidistant(u,u,v,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_congruence) ).
fof(f35_nnf,plain,
~ equidistant(u,u,v,v),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
~ equidistant(u,u,v,v),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c35,plain,
~ equidistant(u,u,v,v),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t10,plain,
equidistant(u,u,v,v) = false,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(t58,plain,
equidistant(u,u,v,v) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t46,axiom,
sF0 = equidistant(u,u,v,v),
introduced(definition) ).
cnf(t115,plain,
sF0 = false,
inference(step,[status(thm)],[t46,t58]) ).
cnf(t63,plain,
false = sF0,
inference(orient,[status(thm)],[t115]) ).
cnf(t124,plain,
equidistant(u,u,v,v) = sF0,
inference(step,[status(thm)],[t58,t63]) ).
cnf(t72,plain,
equidistant(u,u,v,v) = sF0,
inference(orient,[status(thm)],[t124]) ).
cnf(f4,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f4_nnf,plain,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t22,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t88,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(f28,axiom,
V = extension(U,V,W,W),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
fof(f28_nnf,plain,
! [V,U,W] : V = extension(U,V,W,W),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [V,U,W] : V = extension(U,V,W,W),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
X0 = extension(X1,X0,X2,X2),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t12,plain,
extension(X1,X2,X3,X3) = X2,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t60,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t90,plain,
true = equidistant(X1,X1,X2,X2),
inference(cp,[status(thm)],[t88,t60]) ).
cnf(t92,plain,
equidistant(X1,X1,X2,X2) = true,
inference(orient,[status(thm)],[t90]) ).
cnf(t131,plain,
true = sF0,
inference(step,[status(thm)],[t72,t92]) ).
cnf(t93,plain,
true = sF0,
inference(rw,[status(thm)],[t131]) ).
cnf(t94,plain,
true = sF0,
inference(orient,[status(thm)],[t93]) ).
cnf(f9,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
fof(f9_nnf,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f10,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
fof(f10_nnf,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f11,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f11_nnf,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c35]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t94]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t63]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO024-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.58 % Computer : n014.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Wed Sep 23 10:25:40 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.58 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.56/6.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.56/6.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------