%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 01:16:50 PM UTC 2026
% Result : Unsatisfiable 5.41s 6.96s
% Output : Proof 5.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 95 ( 79 unt; 0 def)
% Number of atoms : 115 ( 54 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 38 ~; 20 |; 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; 9 con; 0-4 aty)
% Number of variables : 192 ( 12 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f21,axiom,
( equidistant(V,U,W,X)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
fof(f21_nnf,plain,
! [U,V,W,X] :
( equidistant(V,U,W,X)
| ~ equidistant(U,V,W,X) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [U,V,W,X] :
( equidistant(V,U,W,X)
| ~ equidistant(U,V,W,X) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t28,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t132,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t28]) ).
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(t37,plain,
ifeq(equidistant(X1,X2,X3,X4),true,ifeq(equidistant(X1,X2,X5,X6),true,equidistant(X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t255,plain,
ifeq(equidistant(X1,X2,X3,X4),true,ifeq(equidistant(X1,X2,X5,X6),true,equidistant(X3,X4,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t37]) ).
cnf(f31,axiom,
equidistant(V,reflection(U,V),U,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
fof(f31_nnf,plain,
! [V,U] : equidistant(V,reflection(U,V),U,V),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [V,U] : equidistant(V,reflection(U,V),U,V),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
equidistant(X0,reflection(X1,X0),X1,X0),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(u1,axiom,
equidistant(X0,reflection(X1,X0),X1,X0) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(f18,axiom,
reflection(U,V) = extension(U,V,U,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
fof(f18_nnf,plain,
! [U,V] : reflection(U,V) = extension(U,V,U,V),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [U,V] : reflection(U,V) = extension(U,V,U,V),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
reflection(X0,X1) = extension(X0,X1,X0,X1),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(d0,axiom,
reflection(X0,X1) = extension(X0,X1,X0,X1),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t21,plain,
equidistant(X1,extension(X2,X1,X2,X1),X2,X1) = true,
inference(definition_unfolding,[status(thm)],[u1,d0]) ).
cnf(t85,plain,
equidistant(X1,extension(X2,X1,X2,X1),X2,X1) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t52,axiom,
sF0 = extension(u,v,u,v),
introduced(definition) ).
cnf(t71,plain,
extension(u,v,u,v) = sF0,
inference(orient,[status(thm)],[t52]) ).
cnf(t86,plain,
true = equidistant(v,sF0,u,v),
inference(cp,[status(thm)],[t85,t71]) ).
cnf(t87,plain,
equidistant(v,sF0,u,v) = true,
inference(orient,[status(thm)],[t86]) ).
cnf(t262,plain,
true = ifeq(true,true,ifeq(equidistant(v,sF0,X1,X2),true,equidistant(u,v,X1,X2),true),true),
inference(cp,[status(thm)],[t255,t87]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t70,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t499,plain,
true = ifeq(equidistant(v,sF0,X1,X2),true,equidistant(u,v,X1,X2),true),
inference(step,[status(thm)],[t262,t70]) ).
cnf(t405,plain,
ifeq(equidistant(v,sF0,X1,X2),true,equidistant(u,v,X1,X2),true) = true,
inference(orient,[status(thm)],[t499]) ).
cnf(f20,axiom,
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f20_nnf,plain,
! [U,V,W,X] :
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [U,V,W,X] :
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t30,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t148,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(f22,axiom,
( equidistant(U,V,X,W)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).
fof(f22_nnf,plain,
! [U,V,W,X] :
( equidistant(U,V,X,W)
| ~ equidistant(U,V,W,X) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [U,V,W,X] :
( equidistant(U,V,X,W)
| ~ equidistant(U,V,W,X) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( equidistant(X0,X1,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t27,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t116,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(f4,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/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(t119,plain,
true = ifeq(true,true,equidistant(X1,extension(X2,X1,X3,X4),X4,X3),true),
inference(cp,[status(thm)],[t116,t88]) ).
cnf(t476,plain,
true = equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(step,[status(thm)],[t119,t70]) ).
cnf(t141,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3) = true,
inference(orient,[status(thm)],[t476]) ).
cnf(t159,plain,
true = ifeq(true,true,equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),true),
inference(cp,[status(thm)],[t148,t141]) ).
cnf(t484,plain,
true = equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(step,[status(thm)],[t159,t70]) ).
cnf(t171,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)) = true,
inference(orient,[status(thm)],[t484]) ).
cnf(t53,axiom,
sF1 = extension(extension(u,v,u,v),v,extension(u,v,u,v),v),
introduced(definition) ).
cnf(t487,plain,
sF1 = extension(sF0,v,extension(u,v,u,v),v),
inference(step,[status(thm)],[t53,t71]) ).
cnf(t488,plain,
sF1 = extension(sF0,v,sF0,v),
inference(step,[status(thm)],[t487,t71]) ).
cnf(t176,plain,
extension(sF0,v,sF0,v) = sF1,
inference(orient,[status(thm)],[t488]) ).
cnf(t188,plain,
true = equidistant(v,sF0,v,sF1),
inference(cp,[status(thm)],[t171,t176]) ).
cnf(t212,plain,
equidistant(v,sF0,v,sF1) = true,
inference(orient,[status(thm)],[t188]) ).
cnf(t414,plain,
true = ifeq(true,true,equidistant(u,v,v,sF1),true),
inference(cp,[status(thm)],[t405,t212]) ).
cnf(t500,plain,
true = equidistant(u,v,v,sF1),
inference(step,[status(thm)],[t414,t70]) ).
cnf(t416,plain,
equidistant(u,v,v,sF1) = true,
inference(orient,[status(thm)],[t500]) ).
cnf(t420,plain,
true = ifeq(true,true,equidistant(v,u,v,sF1),true),
inference(cp,[status(thm)],[t132,t416]) ).
cnf(t502,plain,
true = equidistant(v,u,v,sF1),
inference(step,[status(thm)],[t420,t70]) ).
cnf(f41,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_congruence) ).
fof(f41_nnf,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c41,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(u6,axiom,
equidistant(v,u,v,reflection(reflection(u,v),v)) = false,
inference(equality_encoding,[status(esa)],[c41]) ).
cnf(t35,plain,
equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)) = false,
inference(definition_unfolding,[status(thm)],[u6,d0]) ).
cnf(t490,plain,
equidistant(v,u,v,extension(sF0,v,extension(u,v,u,v),v)) = false,
inference(step,[status(thm)],[t35,t71]) ).
cnf(t491,plain,
equidistant(v,u,v,extension(sF0,v,sF0,v)) = false,
inference(step,[status(thm)],[t490,t71]) ).
cnf(t492,plain,
equidistant(v,u,v,sF1) = false,
inference(step,[status(thm)],[t491,t176]) ).
cnf(t218,plain,
equidistant(v,u,v,sF1) = false,
inference(orient,[status(thm)],[t492]) ).
cnf(t503,plain,
true = false,
inference(step,[status(thm)],[t502,t218]) ).
cnf(t437,plain,
false = true,
inference(orient,[status(thm)],[t503]) ).
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,c41]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t437]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/6.19 % Computer : n002.cluster.edu
% 0.10/6.19 % Model : x86_64 x86_64
% 0.10/6.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.19 % Memory : 8046.5625MB
% 0.10/6.19 % OS : Linux 6.8.0-71-generic
% 0.10/6.19 % CPULimit : 300
% 0.10/6.19 % WCLimit : 300
% 0.10/6.19 % DateTime : Wed Sep 23 10:40:27 UTC 2026
% 0.10/6.19 % CPUTime :
% 0.10/6.19 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.41/6.96 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.41/6.96 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------