%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO027-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 164.15s 24.08s
% Output : Proof 164.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 93 ( 77 unt; 0 def)
% Number of atoms : 121 ( 77 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 74 ( 46 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 161 ( 17 sgn 44 !; 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/sandbox/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(t216,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(t1275,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)],[t216]) ).
cnf(f38,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f38_nnf,plain,
between(u,v,w),
inference(nnf_transformation,[status(thm)],[f38]) ).
cnf(c38,plain,
between(u,v,w),
inference(cnf_transformation,[status(esa)],[f38_nnf]) ).
cnf(t9,plain,
between(u,v,w) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t804,plain,
between(u,v,w) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t1281,plain,
true = ifeq(true,true,ifeq(between(u,v,X1),true,ifeq(equidistant(v,w,v,X1),true,or(eq(u,v),eq(w,X1)),true),true),true),
inference(cp,[status(thm)],[t1275,t804]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t260,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t87142,plain,
true = ifeq(between(u,v,X1),true,ifeq(equidistant(v,w,v,X1),true,or(eq(u,v),eq(w,X1)),true),true),
inference(step,[status(thm)],[t1281,t260]) ).
cnf(f39,hypothesis,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f39_nnf,plain,
u != v,
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
u != v,
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
u != v,
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(t1,plain,
eq(u,v) = false,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t269,plain,
eq(u,v) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t87143,plain,
true = ifeq(between(u,v,X1),true,ifeq(equidistant(v,w,v,X1),true,or(false,eq(w,X1)),true),true),
inference(step,[status(thm)],[t87142,t269]) ).
cnf(t4,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t259,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t87144,plain,
true = ifeq(between(u,v,X1),true,ifeq(equidistant(v,w,v,X1),true,eq(w,X1),true),true),
inference(step,[status(thm)],[t87143,t259]) ).
cnf(t85253,plain,
ifeq(between(u,v,X1),true,ifeq(equidistant(v,w,v,X1),true,eq(w,X1),true),true) = true,
inference(orient,[status(thm)],[t87144]) ).
cnf(f40,negated_conjecture,
w != extension(u,v,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_an_extension) ).
fof(f40_nnf,plain,
w != extension(u,v,v,w),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
w != extension(u,v,v,w),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
w != extension(u,v,v,w),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t19,plain,
eq(w,extension(u,v,v,w)) = false,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t271,plain,
eq(w,extension(u,v,v,w)) = false,
inference(orient,[status(thm)],[t19]) ).
cnf(t85289,plain,
true = ifeq(between(u,v,extension(u,v,v,w)),true,ifeq(equidistant(v,w,v,extension(u,v,v,w)),true,false,true),true),
inference(cp,[status(thm)],[t85253,t271]) ).
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(t22,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t779,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t87145,plain,
true = ifeq(true,true,ifeq(equidistant(v,w,v,extension(u,v,v,w)),true,false,true),true),
inference(step,[status(thm)],[t85289,t779]) ).
cnf(t87146,plain,
true = ifeq(equidistant(v,w,v,extension(u,v,v,w)),true,false,true),
inference(step,[status(thm)],[t87145,t260]) ).
cnf(f34,axiom,
( U = V
| V != reflection(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
fof(f34_nnf,plain,
! [V,U] :
( U = V
| V != reflection(U,V) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [V,U] :
( U = V
| V != reflection(U,V) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
( X1 = X0
| X0 != reflection(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(u4,axiom,
ifeq(X0,reflection(X1,X0),X1,X0) = X0,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(f18,axiom,
reflection(U,V) = extension(U,V,U,V),
file('/export/starexec/sandbox/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(t41,plain,
ifeq(X1,extension(X2,X1,X2,X1),X2,X1) = X1,
inference(definition_unfolding,[status(thm)],[u4,d0]) ).
cnf(t261,plain,
ifeq(X1,extension(X2,X1,X2,X1),X2,X1) = X1,
inference(orient,[status(thm)],[t41]) ).
cnf(f20,axiom,
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox/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(hi16,axiom,
ifeq(equidistant(X0,X1,X2,X3),true,equidistant(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
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(h21,plain,
equidistant(V0,V1,V2,extension(V3,V2,V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi16,hi4]) ).
cnf(f32,axiom,
( V = reflection(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_1) ).
fof(f32_nnf,plain,
! [U,V] :
( V = reflection(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [U,V] :
( V = reflection(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
( X1 = reflection(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(hi29,axiom,
ifeq(X0,X1,X1,reflection(X0,X1)) = reflection(X0,X1),
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(hi27,axiom,
reflection(X0,X1) = extension(X0,X1,X0,X1),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t160,plain,
extension(equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),true,equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),true) = true,
inference(hyper_resolution,[status(thm)],[hi29,h21,hi27]) ).
cnf(t296,plain,
extension(equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),true,equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),true) = true,
inference(orient,[status(thm)],[t160]) ).
cnf(t305,plain,
true = ifeq(true,true,equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),true),
inference(cp,[status(thm)],[t261,t296]) ).
cnf(t85421,plain,
true = equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(step,[status(thm)],[t305,t260]) ).
cnf(t1418,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)) = true,
inference(orient,[status(thm)],[t85421]) ).
cnf(t87147,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t87146,t1418]) ).
cnf(t87148,plain,
true = false,
inference(step,[status(thm)],[t87147,t260]) ).
cnf(t85290,plain,
false = true,
inference(orient,[status(thm)],[t87148]) ).
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,c39,c40]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t85290]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO027-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n004.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Wed Sep 23 10:26:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 164.15/24.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 164.15/24.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------