%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO021-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 6.37s 1.45s
% Output : Proof 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 47 unt; 0 def)
% Number of atoms : 67 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 36 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 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 : 66 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t24,plain,
ifeq(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t64,plain,
ifeq(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,false,true) = true,
inference(orient,[status(thm)],[t24]) ).
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(t25,plain,
ifeq(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t65,plain,
ifeq(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),true,false,true) = true,
inference(orient,[status(thm)],[t25]) ).
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(t26,plain,
ifeq(between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t66,plain,
ifeq(between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),true,false,true) = true,
inference(orient,[status(thm)],[t26]) ).
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(f21,hypothesis,
equidistant(u,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
fof(f21_nnf,plain,
equidistant(u,v,w,x),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
equidistant(u,v,w,x),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(hi18,axiom,
equidistant(u,v,w,x) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
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(h2,plain,
equidistant(w,x,v,u) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi18,hi0]) ).
cnf(f20,axiom,
( equidistant(V,U,W,X)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
fof(f20_nnf,plain,
! [U,V,W,X] :
( equidistant(V,U,W,X)
| ~ equidistant(U,V,W,X) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [U,V,W,X] :
( equidistant(V,U,W,X)
| ~ equidistant(U,V,W,X) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi17,axiom,
ifeq(equidistant(X0,X1,X2,X3),true,equidistant(X1,X0,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t19,plain,
equidistant(x,w,v,u) = true,
inference(hyper_resolution,[status(thm)],[hi17,h2]) ).
cnf(t120,plain,
equidistant(x,w,v,u) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t42,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(f22,negated_conjecture,
~ equidistant(x,w,v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetry) ).
fof(f22_nnf,plain,
~ equidistant(x,w,v,u),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ equidistant(x,w,v,u),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
~ equidistant(x,w,v,u),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c22]) ).
cnf(g0_0,plain,
true != ifeq(equidistant(x,w,v,u),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(equidistant(x,w,v,u),true,false,ifeq(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,false,true)),
inference(rw,[status(thm)],[g0_0,t64]) ).
cnf(g0_2,plain,
true != ifeq(equidistant(x,w,v,u),true,false,ifeq(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,false,ifeq(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),true,false,true))),
inference(rw,[status(thm)],[g0_1,t65]) ).
cnf(g0_3,plain,
true != ifeq(equidistant(x,w,v,u),true,false,ifeq(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,false,ifeq(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),true,false,ifeq(between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),true,false,true)))),
inference(rw,[status(thm)],[g0_2,t66]) ).
cnf(g0_4,plain,
true != ifeq(equidistant(x,w,v,u),true,false,ifeq(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,false,ifeq(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),true,false,ifeq(between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),true,false,equidistant(x,w,v,u))))),
inference(rw,[status(thm)],[g0_3,t120]) ).
cnf(g0_5,plain,
true != ifeq(true,true,false,ifeq(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,false,ifeq(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),true,false,ifeq(between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),true,false,equidistant(x,w,v,u))))),
inference(rw,[status(thm)],[g0_4,t120]) ).
cnf(g0_6,plain,
true != false,
inference(rw,[status(thm)],[g0_5,t42]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO021-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 10:28:04 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.37/1.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.37/1.45 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------