%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO022-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 6.63s 1.34s
% Output : Proof 6.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 38 unt; 0 def)
% Number of atoms : 58 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 30 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-4 aty)
% Number of variables : 56 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f28,negated_conjecture,
~ equidistant(u,v,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity) ).
fof(f28_nnf,plain,
~ equidistant(u,v,y,z),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
~ equidistant(u,v,y,z),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ equidistant(u,v,y,z),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t45,plain,
ifeq(equidistant(u,v,y,z),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(f19,axiom,
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f19_nnf,plain,
! [U,V,W,X] :
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [U,V,W,X] :
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi16,axiom,
ifeq(equidistant(X0,X1,X2,X3),true,equidistant(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f26,hypothesis,
equidistant(u,v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
fof(f26_nnf,plain,
equidistant(u,v,w,x),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
equidistant(u,v,w,x),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(hi23,axiom,
equidistant(u,v,w,x) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h6,plain,
equidistant(w,x,u,v) = true,
inference(hyper_resolution,[status(thm)],[hi16,hi23]) ).
cnf(f1,axiom,
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
fof(f1_nnf,plain,
! [X,Y,Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(equidistant(X0,X1,X2,X3),true,ifeq(equidistant(X0,X1,X4,X5),true,equidistant(X2,X3,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f27,hypothesis,
equidistant(w,x,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_to_x_equals_y_to_z) ).
fof(f27_nnf,plain,
equidistant(w,x,y,z),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
equidistant(w,x,y,z),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi24,axiom,
equidistant(w,x,y,z) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t14,plain,
equidistant(u,v,y,z) = true,
inference(hyper_resolution,[status(thm)],[hi1,h6,hi24]) ).
cnf(t73,plain,
equidistant(u,v,y,z) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t361,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t45,t73]) ).
cnf(t36,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t63,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t36]) ).
cnf(t362,plain,
false = true,
inference(step,[status(thm)],[t361,t63]) ).
cnf(t358,plain,
false = true,
inference(orient,[status(thm)],[t362]) ).
cnf(f9,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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,c28]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t358]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO022-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n016.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 10:30:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.63/1.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.63/1.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------