%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO059-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 4.62s 6.09s
% Output : Proof 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 96 ( 92 unt; 0 def)
% Number of atoms : 104 ( 67 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 27 ~; 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 : 13 ( 13 usr; 10 con; 0-4 aty)
% Number of variables : 118 ( 6 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t19,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(t83,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)],[t19]) ).
cnf(f0,axiom,
equidistant(X,Y,Y,X),
file('/export/starexec/sandbox2/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(t8,plain,
equidistant(X1,X2,X2,X1) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t42,plain,
equidistant(X1,X2,X2,X1) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t84,plain,
true = ifeq(true,true,ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X2,X1,X3,X4),true),true),
inference(cp,[status(thm)],[t83,t42]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t43,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t418,plain,
true = ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X2,X1,X3,X4),true),
inference(step,[status(thm)],[t84,t43]) ).
cnf(t104,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t418]) ).
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(t16,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t51,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t30,axiom,
sF0 = extension(u,v,u,v),
introduced(definition) ).
cnf(t45,plain,
extension(u,v,u,v) = sF0,
inference(orient,[status(thm)],[t30]) ).
cnf(t52,plain,
true = equidistant(v,sF0,u,v),
inference(cp,[status(thm)],[t51,t45]) ).
cnf(t53,plain,
equidistant(v,sF0,u,v) = true,
inference(orient,[status(thm)],[t52]) ).
cnf(t90,plain,
true = ifeq(true,true,ifeq(equidistant(v,sF0,X1,X2),true,equidistant(u,v,X1,X2),true),true),
inference(cp,[status(thm)],[t83,t53]) ).
cnf(t442,plain,
true = ifeq(equidistant(v,sF0,X1,X2),true,equidistant(u,v,X1,X2),true),
inference(step,[status(thm)],[t90,t43]) ).
cnf(t267,plain,
ifeq(equidistant(v,sF0,X1,X2),true,equidistant(u,v,X1,X2),true) = true,
inference(orient,[status(thm)],[t442]) ).
cnf(t85,plain,
true = ifeq(equidistant(X1,X2,X3,X4),true,ifeq(true,true,equidistant(X3,X4,X2,X1),true),true),
inference(cp,[status(thm)],[t83,t42]) ).
cnf(t423,plain,
true = ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X3,X4,X2,X1),true),
inference(step,[status(thm)],[t85,t43]) ).
cnf(t133,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X3,X4,X2,X1),true) = true,
inference(orient,[status(thm)],[t423]) ).
cnf(t31,axiom,
sF1 = extension(extension(u,v,u,v),v,extension(u,v,u,v),v),
introduced(definition) ).
cnf(t399,plain,
sF1 = extension(sF0,v,extension(u,v,u,v),v),
inference(step,[status(thm)],[t31,t45]) ).
cnf(t400,plain,
sF1 = extension(sF0,v,sF0,v),
inference(step,[status(thm)],[t399,t45]) ).
cnf(t62,plain,
extension(sF0,v,sF0,v) = sF1,
inference(orient,[status(thm)],[t400]) ).
cnf(t65,plain,
true = equidistant(v,sF1,sF0,v),
inference(cp,[status(thm)],[t51,t62]) ).
cnf(t68,plain,
equidistant(v,sF1,sF0,v) = true,
inference(orient,[status(thm)],[t65]) ).
cnf(t113,plain,
true = ifeq(true,true,equidistant(sF1,v,sF0,v),true),
inference(cp,[status(thm)],[t104,t68]) ).
cnf(t421,plain,
true = equidistant(sF1,v,sF0,v),
inference(step,[status(thm)],[t113,t43]) ).
cnf(t123,plain,
equidistant(sF1,v,sF0,v) = true,
inference(orient,[status(thm)],[t421]) ).
cnf(t144,plain,
true = ifeq(true,true,equidistant(sF0,v,v,sF1),true),
inference(cp,[status(thm)],[t133,t123]) ).
cnf(t427,plain,
true = equidistant(sF0,v,v,sF1),
inference(step,[status(thm)],[t144,t43]) ).
cnf(t166,plain,
equidistant(sF0,v,v,sF1) = true,
inference(orient,[status(thm)],[t427]) ).
cnf(t170,plain,
true = ifeq(true,true,equidistant(v,sF0,v,sF1),true),
inference(cp,[status(thm)],[t104,t166]) ).
cnf(t434,plain,
true = equidistant(v,sF0,v,sF1),
inference(step,[status(thm)],[t170,t43]) ).
cnf(t213,plain,
equidistant(v,sF0,v,sF1) = true,
inference(orient,[status(thm)],[t434]) ).
cnf(t269,plain,
true = ifeq(true,true,equidistant(u,v,v,sF1),true),
inference(cp,[status(thm)],[t267,t213]) ).
cnf(t444,plain,
true = equidistant(u,v,v,sF1),
inference(step,[status(thm)],[t269,t43]) ).
cnf(t302,plain,
equidistant(u,v,v,sF1) = true,
inference(orient,[status(thm)],[t444]) ).
cnf(t308,plain,
true = ifeq(true,true,equidistant(v,u,v,sF1),true),
inference(cp,[status(thm)],[t104,t302]) ).
cnf(t446,plain,
true = equidistant(v,u,v,sF1),
inference(step,[status(thm)],[t308,t43]) ).
cnf(f19,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_congruence) ).
fof(f19_nnf,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(u1,axiom,
equidistant(v,u,v,reflection(reflection(u,v),v)) = false,
inference(equality_encoding,[status(esa)],[c19]) ).
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(t18,plain,
equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)) = false,
inference(definition_unfolding,[status(thm)],[u1,d0]) ).
cnf(t396,plain,
equidistant(v,u,v,extension(sF0,v,extension(u,v,u,v),v)) = false,
inference(step,[status(thm)],[t18,t45]) ).
cnf(t397,plain,
equidistant(v,u,v,extension(sF0,v,sF0,v)) = false,
inference(step,[status(thm)],[t396,t45]) ).
cnf(t56,plain,
equidistant(v,u,v,extension(sF0,v,sF0,v)) = false,
inference(orient,[status(thm)],[t397]) ).
cnf(t401,plain,
equidistant(v,u,v,sF1) = false,
inference(step,[status(thm)],[t56,t62]) ).
cnf(t63,plain,
equidistant(v,u,v,sF1) = false,
inference(rw,[status(thm)],[t401]) ).
cnf(t67,plain,
equidistant(v,u,v,sF1) = false,
inference(orient,[status(thm)],[t63]) ).
cnf(t32,axiom,
sF2 = equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
introduced(definition) ).
cnf(t402,plain,
sF2 = equidistant(v,u,v,extension(sF0,v,extension(u,v,u,v),v)),
inference(step,[status(thm)],[t32,t45]) ).
cnf(t403,plain,
sF2 = equidistant(v,u,v,extension(sF0,v,sF0,v)),
inference(step,[status(thm)],[t402,t45]) ).
cnf(t404,plain,
sF2 = equidistant(v,u,v,sF1),
inference(step,[status(thm)],[t403,t62]) ).
cnf(t405,plain,
sF2 = false,
inference(step,[status(thm)],[t404,t67]) ).
cnf(t69,plain,
false = sF2,
inference(orient,[status(thm)],[t405]) ).
cnf(t416,plain,
equidistant(v,u,v,sF1) = sF2,
inference(step,[status(thm)],[t67,t69]) ).
cnf(t79,plain,
equidistant(v,u,v,sF1) = sF2,
inference(orient,[status(thm)],[t416]) ).
cnf(t447,plain,
true = sF2,
inference(step,[status(thm)],[t446,t79]) ).
cnf(t311,plain,
true = sF2,
inference(orient,[status(thm)],[t447]) ).
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,c19]) ).
cnf(g0_0,plain,
sF2 != false,
inference(rw,[status(thm)],[goal_0,t311]) ).
cnf(g0_1,plain,
sF2 != sF2,
inference(rw,[status(thm)],[g0_0,t69]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO059-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n019.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 10:38:34 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.62/6.09 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.62/6.09 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------