%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO043-2 : 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 01:16:43 PM UTC 2026
% Result : Unsatisfiable 20.69s 3.10s
% Output : Proof 20.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 13
% Syntax : Number of formulae : 120 ( 104 unt; 0 def)
% Number of atoms : 144 ( 81 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 42 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-5 aty)
% Number of variables : 181 ( 18 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
fof(f7_nnf,plain,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t23,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t48,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(f6,axiom,
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f6_nnf,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t15,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t33,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(f8,axiom,
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
fof(f8_nnf,plain,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t24,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t41,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(f19,hypothesis,
between(u,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_between_u_and_x) ).
fof(f19_nnf,plain,
between(u,w,x),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
between(u,w,x),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(t9,plain,
between(u,w,x) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t39,plain,
between(u,w,x) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t46,plain,
true = ifeq(between(X1,X2,x),true,ifeq(true,true,between(w,inner_pasch(X1,X2,x,w,u),X1),true),true),
inference(cp,[status(thm)],[t41,t39]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t10626,plain,
true = ifeq(between(X1,X2,x),true,between(w,inner_pasch(X1,X2,x,w,u),X1),true),
inference(step,[status(thm)],[t46,t32]) ).
cnf(t564,plain,
ifeq(between(X1,X2,x),true,between(w,inner_pasch(X1,X2,x,w,u),X1),true) = true,
inference(orient,[status(thm)],[t10626]) ).
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(t14,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t38,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(orient,[status(thm)],[t14]) ).
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(t21,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t34,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(orient,[status(thm)],[t21]) ).
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(t20,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t129,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t130,plain,
extension(X1,X2,X3,X3) = ifeq(true,true,X2,extension(X1,X2,X3,X3)),
inference(cp,[status(thm)],[t34,t129]) ).
cnf(t10599,plain,
extension(X1,X2,X3,X3) = X2,
inference(step,[status(thm)],[t130,t32]) ).
cnf(t238,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t10599]) ).
cnf(t240,plain,
true = between(X1,X2,X2),
inference(cp,[status(thm)],[t38,t238]) ).
cnf(t241,plain,
between(X1,X2,X2) = true,
inference(orient,[status(thm)],[t240]) ).
cnf(t565,plain,
true = ifeq(true,true,between(w,inner_pasch(X1,x,x,w,u),X1),true),
inference(cp,[status(thm)],[t564,t241]) ).
cnf(t10627,plain,
true = between(w,inner_pasch(X1,x,x,w,u),X1),
inference(step,[status(thm)],[t565,t32]) ).
cnf(t569,plain,
between(w,inner_pasch(X1,x,x,w,u),X1) = true,
inference(orient,[status(thm)],[t10627]) ).
cnf(t570,plain,
inner_pasch(w,x,x,w,u) = ifeq(true,true,w,inner_pasch(w,x,x,w,u)),
inference(cp,[status(thm)],[t33,t569]) ).
cnf(t10628,plain,
inner_pasch(w,x,x,w,u) = w,
inference(step,[status(thm)],[t570,t32]) ).
cnf(t594,plain,
inner_pasch(w,x,x,w,u) = w,
inference(orient,[status(thm)],[t10628]) ).
cnf(t595,plain,
true = ifeq(between(w,x,x),true,ifeq(between(u,w,x),true,between(x,w,u),true),true),
inference(cp,[status(thm)],[t48,t594]) ).
cnf(t10629,plain,
true = ifeq(true,true,ifeq(between(u,w,x),true,between(x,w,u),true),true),
inference(step,[status(thm)],[t595,t241]) ).
cnf(t10630,plain,
true = ifeq(between(u,w,x),true,between(x,w,u),true),
inference(step,[status(thm)],[t10629,t32]) ).
cnf(t10631,plain,
true = ifeq(true,true,between(x,w,u),true),
inference(step,[status(thm)],[t10630,t39]) ).
cnf(t10632,plain,
true = between(x,w,u),
inference(step,[status(thm)],[t10631,t32]) ).
cnf(t596,plain,
between(x,w,u) = true,
inference(orient,[status(thm)],[t10632]) ).
cnf(t598,plain,
true = ifeq(between(X1,X2,u),true,ifeq(true,true,between(w,inner_pasch(X1,X2,u,w,x),X1),true),true),
inference(cp,[status(thm)],[t41,t596]) ).
cnf(t11165,plain,
true = ifeq(between(X1,X2,u),true,between(w,inner_pasch(X1,X2,u,w,x),X1),true),
inference(step,[status(thm)],[t598,t32]) ).
cnf(t10335,plain,
ifeq(between(X1,X2,u),true,between(w,inner_pasch(X1,X2,u,w,x),X1),true) = true,
inference(orient,[status(thm)],[t11165]) ).
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(t8,plain,
between(u,v,w) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t40,plain,
between(u,v,w) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t47,plain,
true = ifeq(between(X1,X2,w),true,ifeq(true,true,between(v,inner_pasch(X1,X2,w,v,u),X1),true),true),
inference(cp,[status(thm)],[t41,t40]) ).
cnf(t10645,plain,
true = ifeq(between(X1,X2,w),true,between(v,inner_pasch(X1,X2,w,v,u),X1),true),
inference(step,[status(thm)],[t47,t32]) ).
cnf(t708,plain,
ifeq(between(X1,X2,w),true,between(v,inner_pasch(X1,X2,w,v,u),X1),true) = true,
inference(orient,[status(thm)],[t10645]) ).
cnf(t709,plain,
true = ifeq(true,true,between(v,inner_pasch(X1,w,w,v,u),X1),true),
inference(cp,[status(thm)],[t708,t241]) ).
cnf(t10646,plain,
true = between(v,inner_pasch(X1,w,w,v,u),X1),
inference(step,[status(thm)],[t709,t32]) ).
cnf(t714,plain,
between(v,inner_pasch(X1,w,w,v,u),X1) = true,
inference(orient,[status(thm)],[t10646]) ).
cnf(t715,plain,
inner_pasch(v,w,w,v,u) = ifeq(true,true,v,inner_pasch(v,w,w,v,u)),
inference(cp,[status(thm)],[t33,t714]) ).
cnf(t10647,plain,
inner_pasch(v,w,w,v,u) = v,
inference(step,[status(thm)],[t715,t32]) ).
cnf(t740,plain,
inner_pasch(v,w,w,v,u) = v,
inference(orient,[status(thm)],[t10647]) ).
cnf(t741,plain,
true = ifeq(between(v,w,w),true,ifeq(between(u,v,w),true,between(w,v,u),true),true),
inference(cp,[status(thm)],[t48,t740]) ).
cnf(t10648,plain,
true = ifeq(true,true,ifeq(between(u,v,w),true,between(w,v,u),true),true),
inference(step,[status(thm)],[t741,t241]) ).
cnf(t10649,plain,
true = ifeq(between(u,v,w),true,between(w,v,u),true),
inference(step,[status(thm)],[t10648,t32]) ).
cnf(t10650,plain,
true = ifeq(true,true,between(w,v,u),true),
inference(step,[status(thm)],[t10649,t40]) ).
cnf(t10651,plain,
true = between(w,v,u),
inference(step,[status(thm)],[t10650,t32]) ).
cnf(t742,plain,
between(w,v,u) = true,
inference(orient,[status(thm)],[t10651]) ).
cnf(t10435,plain,
true = ifeq(true,true,between(w,inner_pasch(w,v,u,w,x),w),true),
inference(cp,[status(thm)],[t10335,t742]) ).
cnf(t11168,plain,
true = between(w,inner_pasch(w,v,u,w,x),w),
inference(step,[status(thm)],[t10435,t32]) ).
cnf(t10531,plain,
between(w,inner_pasch(w,v,u,w,x),w) = true,
inference(orient,[status(thm)],[t11168]) ).
cnf(t10532,plain,
inner_pasch(w,v,u,w,x) = ifeq(true,true,w,inner_pasch(w,v,u,w,x)),
inference(cp,[status(thm)],[t33,t10531]) ).
cnf(t11169,plain,
inner_pasch(w,v,u,w,x) = w,
inference(step,[status(thm)],[t10532,t32]) ).
cnf(t10562,plain,
inner_pasch(w,v,u,w,x) = w,
inference(orient,[status(thm)],[t11169]) ).
cnf(t10563,plain,
true = ifeq(between(w,v,u),true,ifeq(between(x,w,u),true,between(v,w,x),true),true),
inference(cp,[status(thm)],[t48,t10562]) ).
cnf(t11170,plain,
true = ifeq(true,true,ifeq(between(x,w,u),true,between(v,w,x),true),true),
inference(step,[status(thm)],[t10563,t742]) ).
cnf(t11171,plain,
true = ifeq(between(x,w,u),true,between(v,w,x),true),
inference(step,[status(thm)],[t11170,t32]) ).
cnf(t11172,plain,
true = ifeq(true,true,between(v,w,x),true),
inference(step,[status(thm)],[t11171,t596]) ).
cnf(t11173,plain,
true = between(v,w,x),
inference(step,[status(thm)],[t11172,t32]) ).
cnf(f20,negated_conjecture,
~ between(v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_between_v_and_x) ).
fof(f20_nnf,plain,
~ between(v,w,x),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
~ between(v,w,x),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
~ between(v,w,x),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t10,plain,
between(v,w,x) = false,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t217,plain,
between(v,w,x) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t11174,plain,
true = false,
inference(step,[status(thm)],[t11173,t217]) ).
cnf(t10564,plain,
false = true,
inference(orient,[status(thm)],[t11174]) ).
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,c20]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t10564]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO043-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Wed Sep 23 10:33:19 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 20.69/3.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.69/3.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------