%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO029-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 01:16:37 PM UTC 2026
% Result : Unsatisfiable 177.38s 38.17s
% Output : Proof 177.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 102 ( 90 unt; 0 def)
% Number of atoms : 130 ( 69 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 74 ( 46 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 227 ( 20 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f37,axiom,
( W = X
| U = V
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
fof(f37_nnf,plain,
! [U,V,W,X] :
( W = X
| U = V
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [U,V,W,X] :
( W = X
| U = V
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
( X2 = X3
| X0 = X1
| ~ equidistant(X1,X2,X1,X3)
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(t45,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X1,X2,X4),true,ifeq(equidistant(X2,X3,X2,X4),true,or(eq(X1,X2),eq(X3,X4)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t99,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X1,X2,X4),true,ifeq(equidistant(X2,X3,X2,X4),true,or(eq(X1,X2),eq(X3,X4)),true),true),true) = true,
inference(orient,[status(thm)],[t45]) ).
cnf(f3,axiom,
between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
fof(f3_nnf,plain,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t21,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t251,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t261,plain,
true = ifeq(between(X1,X2,X3),true,ifeq(true,true,ifeq(equidistant(X2,X3,X2,extension(X1,X2,X4,X5)),true,or(eq(X1,X2),eq(X3,extension(X1,X2,X4,X5))),true),true),true),
inference(cp,[status(thm)],[t99,t251]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t52,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t360347,plain,
true = ifeq(between(X1,X2,X3),true,ifeq(equidistant(X2,X3,X2,extension(X1,X2,X4,X5)),true,or(eq(X1,X2),eq(X3,extension(X1,X2,X4,X5))),true),true),
inference(step,[status(thm)],[t261,t52]) ).
cnf(t356975,plain,
ifeq(between(X1,X2,X3),true,ifeq(equidistant(X2,X3,X2,extension(X1,X2,X4,X5)),true,or(eq(X1,X2),eq(X3,extension(X1,X2,X4,X5))),true),true) = true,
inference(orient,[status(thm)],[t360347]) ).
cnf(f39,negated_conjecture,
extension(u,v,u,v) != extension(u,v,v,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_extensions) ).
fof(f39_nnf,plain,
extension(u,v,u,v) != extension(u,v,v,u),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
extension(u,v,u,v) != extension(u,v,v,u),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
extension(u,v,u,v) != extension(u,v,v,u),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(t29,plain,
eq(extension(u,v,u,v),extension(u,v,v,u)) = false,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t400,plain,
eq(extension(u,v,u,v),extension(u,v,v,u)) = false,
inference(orient,[status(thm)],[t29]) ).
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(t18,plain,
extension(X1,X2,X1,X2) = reflection(X1,X2),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t409,plain,
extension(X1,X2,X1,X2) = reflection(X1,X2),
inference(orient,[status(thm)],[t18]) ).
cnf(t357617,plain,
eq(reflection(u,v),extension(u,v,v,u)) = false,
inference(step,[status(thm)],[t400,t409]) ).
cnf(t411,plain,
eq(reflection(u,v),extension(u,v,v,u)) = false,
inference(rw,[status(thm)],[t357617]) ).
cnf(t797,plain,
eq(reflection(u,v),extension(u,v,v,u)) = false,
inference(orient,[status(thm)],[t411]) ).
cnf(t357569,plain,
true = ifeq(between(u,v,reflection(u,v)),true,ifeq(equidistant(v,reflection(u,v),v,extension(u,v,v,u)),true,or(eq(u,v),false),true),true),
inference(cp,[status(thm)],[t356975,t797]) ).
cnf(f30,axiom,
between(U,V,reflection(U,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
fof(f30_nnf,plain,
! [U,V] : between(U,V,reflection(U,V)),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [U,V] : between(U,V,reflection(U,V)),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
between(X0,X1,reflection(X0,X1)),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(t16,plain,
between(X1,X2,reflection(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t277,plain,
between(X1,X2,reflection(X1,X2)) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t360348,plain,
true = ifeq(true,true,ifeq(equidistant(v,reflection(u,v),v,extension(u,v,v,u)),true,or(eq(u,v),false),true),true),
inference(step,[status(thm)],[t357569,t277]) ).
cnf(t360349,plain,
true = ifeq(equidistant(v,reflection(u,v),v,extension(u,v,v,u)),true,or(eq(u,v),false),true),
inference(step,[status(thm)],[t360348,t52]) ).
cnf(f27,axiom,
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
fof(f27_nnf,plain,
! [U,V,W,X,Y,Z] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [U,V,W,X,Y,Z] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t40,plain,
ifeq(equidistant(X1,X2,X3,X4),true,ifeq(equidistant(X3,X4,X5,X6),true,equidistant(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t64,plain,
ifeq(equidistant(X1,X2,X3,X4),true,ifeq(equidistant(X3,X4,X5,X6),true,equidistant(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t40]) ).
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(t17,plain,
equidistant(X1,reflection(X2,X1),X2,X1) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(t214,plain,
equidistant(X1,reflection(X2,X1),X2,X1) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t229,plain,
true = ifeq(true,true,ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X2,reflection(X1,X2),X3,X4),true),true),
inference(cp,[status(thm)],[t64,t214]) ).
cnf(t357637,plain,
true = ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X2,reflection(X1,X2),X3,X4),true),
inference(step,[status(thm)],[t229,t52]) ).
cnf(t823,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X2,reflection(X1,X2),X3,X4),true) = true,
inference(orient,[status(thm)],[t357637]) ).
cnf(f25,axiom,
( equidistant(X,W,U,V)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
fof(f25_nnf,plain,
! [U,V,W,X] :
( equidistant(X,W,U,V)
| ~ equidistant(U,V,W,X) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [U,V,W,X] :
( equidistant(X,W,U,V)
| ~ equidistant(U,V,W,X) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( equidistant(X3,X2,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t36,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X4,X3,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t73,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X4,X3,X1,X2),true) = true,
inference(orient,[status(thm)],[t36]) ).
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(t26,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t177,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(t188,plain,
true = ifeq(true,true,equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),true),
inference(cp,[status(thm)],[t73,t177]) ).
cnf(t357631,plain,
true = equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(step,[status(thm)],[t188,t52]) ).
cnf(t748,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)) = true,
inference(orient,[status(thm)],[t357631]) ).
cnf(t825,plain,
true = ifeq(true,true,equidistant(X1,reflection(X2,X1),X3,extension(X4,X3,X1,X2)),true),
inference(cp,[status(thm)],[t823,t748]) ).
cnf(t357651,plain,
true = equidistant(X1,reflection(X2,X1),X3,extension(X4,X3,X1,X2)),
inference(step,[status(thm)],[t825,t52]) ).
cnf(t1214,plain,
equidistant(X1,reflection(X2,X1),X3,extension(X4,X3,X1,X2)) = true,
inference(orient,[status(thm)],[t357651]) ).
cnf(t360350,plain,
true = ifeq(true,true,or(eq(u,v),false),true),
inference(step,[status(thm)],[t360349,t1214]) ).
cnf(t360351,plain,
true = or(eq(u,v),false),
inference(step,[status(thm)],[t360350,t52]) ).
cnf(t2,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t57,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t360352,plain,
true = eq(u,v),
inference(step,[status(thm)],[t360351,t57]) ).
cnf(f38,hypothesis,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
fof(f38_nnf,plain,
u != v,
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
u != v,
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
u != v,
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t1,plain,
eq(u,v) = false,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t391,plain,
eq(u,v) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t360353,plain,
true = false,
inference(step,[status(thm)],[t360352,t391]) ).
cnf(t357572,plain,
false = true,
inference(orient,[status(thm)],[t360353]) ).
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,c38,c39]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t357572]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO029-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/12.25 % Computer : n013.cluster.edu
% 0.10/12.25 % Model : x86_64 x86_64
% 0.10/12.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/12.25 % Memory : 8046.5625MB
% 0.10/12.25 % OS : Linux 6.8.0-71-generic
% 0.10/12.25 % CPULimit : 300
% 0.10/12.25 % WCLimit : 300
% 0.10/12.25 % DateTime : Wed Sep 23 10:28:03 UTC 2026
% 0.10/12.25 % CPUTime :
% 0.10/12.25 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 177.38/38.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 177.38/38.17 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------