%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO027-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 36.60s 5.08s
% Output : Proof 36.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 83 ( 71 unt; 0 def)
% Number of atoms : 123 ( 51 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 98 ( 58 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 160 ( 12 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f20,negated_conjecture,
w != extension(u,v,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_an_extension) ).
fof(f20_nnf,plain,
w != extension(u,v,v,w),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
w != extension(u,v,v,w),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
w != extension(u,v,v,w),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t15,plain,
eq(w,extension(u,v,v,w)) = false,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t3272,plain,
eq(w,extension(u,v,v,w)) = false,
inference(orient,[status(thm)],[t15]) ).
cnf(f2,axiom,
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t26,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t277,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
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(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(h1,plain,
equidistant(V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi0,hi0]) ).
cnf(f4,axiom,
equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/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(hi4,axiom,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h49,plain,
equidistant(V0,V1,V2,extension(V3,V2,V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi4,h1]) ).
cnf(f5,axiom,
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
fof(f5_nnf,plain,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(equidistant(X0,X1,X2,X3),true,ifeq(equidistant(X1,X4,X3,X5),true,ifeq(equidistant(X0,X6,X2,X7),true,ifeq(equidistant(X1,X6,X3,X7),true,ifeq(between(X0,X1,X4),true,ifeq(between(X2,X3,X5),true,or(eq(X0,X1),equidistant(X4,X6,X5,X7)),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f18,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f18_nnf,plain,
between(u,v,w),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
between(u,v,w),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi15,axiom,
between(u,v,w) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(f3,axiom,
between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/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(hi3,axiom,
between(X0,X1,extension(X0,X1,X2,X3)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t41,plain,
or(eq(u,v),equidistant(w,X1,extension(u,v,v,w),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi5,h1,h49,h1,h1,hi15,hi3]) ).
cnf(t980,plain,
or(eq(u,v),equidistant(w,X1,extension(u,v,v,w),X1)) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(f19,hypothesis,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f19_nnf,plain,
u != v,
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
u != v,
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
u != v,
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t1,plain,
eq(u,v) = false,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t3280,plain,
eq(u,v) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t3665,plain,
or(false,equidistant(w,X1,extension(u,v,v,w),X1)) = true,
inference(step,[status(thm)],[t980,t3280]) ).
cnf(t4,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t275,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t3666,plain,
equidistant(w,X1,extension(u,v,v,w),X1) = true,
inference(step,[status(thm)],[t3665,t275]) ).
cnf(t3292,plain,
equidistant(w,X1,extension(u,v,v,w),X1) = true,
inference(rw,[status(thm)],[t3666]) ).
cnf(t3547,plain,
equidistant(w,X1,extension(u,v,v,w),X1) = true,
inference(orient,[status(thm)],[t3292]) ).
cnf(t3548,plain,
extension(u,v,v,w) = ifeq(true,true,w,extension(u,v,v,w)),
inference(cp,[status(thm)],[t277,t3547]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t276,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t3713,plain,
extension(u,v,v,w) = w,
inference(step,[status(thm)],[t3548,t276]) ).
cnf(t3557,plain,
extension(u,v,v,w) = w,
inference(orient,[status(thm)],[t3713]) ).
cnf(t3714,plain,
eq(w,w) = false,
inference(step,[status(thm)],[t3272,t3557]) ).
cnf(t0,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t996,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t3715,plain,
true = false,
inference(step,[status(thm)],[t3714,t996]) ).
cnf(t3622,plain,
true = false,
inference(rw,[status(thm)],[t3715]) ).
cnf(t3624,plain,
false = true,
inference(orient,[status(thm)],[t3622]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c19,c20]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3624]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO027-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 10:28:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 36.60/5.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.60/5.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------