%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO020-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:16:35 PM UTC 2026
% Result : Unsatisfiable 7.68s 1.54s
% Output : Proof 7.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 38 unt; 0 def)
% Number of atoms : 50 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 29 ~; 8 |; 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 : 10 ( 10 usr; 9 con; 0-4 aty)
% Number of variables : 48 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
file('/export/starexec/sandbox/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(f0,axiom,
equidistant(X,Y,Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
fof(f0_nnf,plain,
! [X,Y] : equidistant(X,Y,Y,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] : equidistant(X,Y,Y,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
equidistant(X0,X1,X1,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
equidistant(V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi0,hi0]) ).
cnf(f18,hypothesis,
equidistant(u,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
fof(f18_nnf,plain,
equidistant(u,v,w,x),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
equidistant(u,v,w,x),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi15,axiom,
equidistant(u,v,w,x) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h3,plain,
equidistant(w,x,u,v) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi15,h0]) ).
cnf(t18,plain,
equidistant(x,w,u,v) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi0,h3]) ).
cnf(t130,plain,
equidistant(x,w,u,v) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t40,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t20]) ).
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(f19,negated_conjecture,
~ equidistant(x,w,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetry) ).
fof(f19_nnf,plain,
~ equidistant(x,w,u,v),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
~ equidistant(x,w,u,v),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
~ equidistant(x,w,u,v),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c19]) ).
cnf(g0_0,plain,
true != ifeq(equidistant(x,w,u,v),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(equidistant(x,w,u,v),true,false,equidistant(x,w,u,v)),
inference(rw,[status(thm)],[g0_0,t130]) ).
cnf(g0_2,plain,
true != ifeq(true,true,false,equidistant(x,w,u,v)),
inference(rw,[status(thm)],[g0_1,t130]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t40]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO020-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 10:30:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.68/1.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.68/1.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------