%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO042-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 01:16:42 PM UTC 2026
% Result : Unsatisfiable 13.71s 2.19s
% Output : Proof 13.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 13
% Syntax : Number of formulae : 105 ( 89 unt; 0 def)
% Number of atoms : 129 ( 66 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 : 178 ( 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/sandbox2/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/sandbox2/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/sandbox2/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(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(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/sandbox2/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/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(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(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(t1625,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)],[t1625]) ).
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(t242,plain,
true = ifeq(true,true,ifeq(between(X1,X2,X3),true,between(X2,inner_pasch(X4,X3,X3,X2,X1),X4),true),true),
inference(cp,[status(thm)],[t41,t241]) ).
cnf(t1739,plain,
true = ifeq(between(X1,X2,X3),true,between(X2,inner_pasch(X4,X3,X3,X2,X1),X4),true),
inference(step,[status(thm)],[t242,t32]) ).
cnf(t1474,plain,
ifeq(between(X1,X2,X3),true,between(X2,inner_pasch(X4,X3,X3,X2,X1),X4),true) = true,
inference(orient,[status(thm)],[t1739]) ).
cnf(f19,hypothesis,
between(v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_v_and_x) ).
fof(f19_nnf,plain,
between(v,w,x),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
between(v,w,x),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(t10,plain,
between(v,w,x) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t39,plain,
between(v,w,x) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t44,plain,
true = ifeq(true,true,ifeq(between(X1,X2,x),true,between(X2,inner_pasch(v,w,x,X2,X1),v),true),true),
inference(cp,[status(thm)],[t41,t39]) ).
cnf(t1650,plain,
true = ifeq(between(X1,X2,x),true,between(X2,inner_pasch(v,w,x,X2,X1),v),true),
inference(step,[status(thm)],[t44,t32]) ).
cnf(t538,plain,
ifeq(between(X1,X2,x),true,between(X2,inner_pasch(v,w,x,X2,X1),v),true) = true,
inference(orient,[status(thm)],[t1650]) ).
cnf(f18,hypothesis,
between(u,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_x) ).
fof(f18_nnf,plain,
between(u,v,x),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
between(u,v,x),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t9,plain,
between(u,v,x) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t40,plain,
between(u,v,x) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t542,plain,
true = ifeq(true,true,between(v,inner_pasch(v,w,x,v,u),v),true),
inference(cp,[status(thm)],[t538,t40]) ).
cnf(t1652,plain,
true = between(v,inner_pasch(v,w,x,v,u),v),
inference(step,[status(thm)],[t542,t32]) ).
cnf(t564,plain,
between(v,inner_pasch(v,w,x,v,u),v) = true,
inference(orient,[status(thm)],[t1652]) ).
cnf(t565,plain,
inner_pasch(v,w,x,v,u) = ifeq(true,true,v,inner_pasch(v,w,x,v,u)),
inference(cp,[status(thm)],[t33,t564]) ).
cnf(t1653,plain,
inner_pasch(v,w,x,v,u) = v,
inference(step,[status(thm)],[t565,t32]) ).
cnf(t585,plain,
inner_pasch(v,w,x,v,u) = v,
inference(orient,[status(thm)],[t1653]) ).
cnf(t586,plain,
true = ifeq(between(v,w,x),true,ifeq(between(u,v,x),true,between(w,v,u),true),true),
inference(cp,[status(thm)],[t48,t585]) ).
cnf(t1654,plain,
true = ifeq(true,true,ifeq(between(u,v,x),true,between(w,v,u),true),true),
inference(step,[status(thm)],[t586,t39]) ).
cnf(t1655,plain,
true = ifeq(between(u,v,x),true,between(w,v,u),true),
inference(step,[status(thm)],[t1654,t32]) ).
cnf(t1656,plain,
true = ifeq(true,true,between(w,v,u),true),
inference(step,[status(thm)],[t1655,t40]) ).
cnf(t1657,plain,
true = between(w,v,u),
inference(step,[status(thm)],[t1656,t32]) ).
cnf(t587,plain,
between(w,v,u) = true,
inference(orient,[status(thm)],[t1657]) ).
cnf(t1494,plain,
true = ifeq(true,true,between(v,inner_pasch(X1,u,u,v,w),X1),true),
inference(cp,[status(thm)],[t1474,t587]) ).
cnf(t1746,plain,
true = between(v,inner_pasch(X1,u,u,v,w),X1),
inference(step,[status(thm)],[t1494,t32]) ).
cnf(t1576,plain,
between(v,inner_pasch(X1,u,u,v,w),X1) = true,
inference(orient,[status(thm)],[t1746]) ).
cnf(t1577,plain,
inner_pasch(v,u,u,v,w) = ifeq(true,true,v,inner_pasch(v,u,u,v,w)),
inference(cp,[status(thm)],[t33,t1576]) ).
cnf(t1747,plain,
inner_pasch(v,u,u,v,w) = v,
inference(step,[status(thm)],[t1577,t32]) ).
cnf(t1608,plain,
inner_pasch(v,u,u,v,w) = v,
inference(orient,[status(thm)],[t1747]) ).
cnf(t1609,plain,
true = ifeq(between(v,u,u),true,ifeq(between(w,v,u),true,between(u,v,w),true),true),
inference(cp,[status(thm)],[t48,t1608]) ).
cnf(t1748,plain,
true = ifeq(true,true,ifeq(between(w,v,u),true,between(u,v,w),true),true),
inference(step,[status(thm)],[t1609,t241]) ).
cnf(t1749,plain,
true = ifeq(between(w,v,u),true,between(u,v,w),true),
inference(step,[status(thm)],[t1748,t32]) ).
cnf(t1750,plain,
true = ifeq(true,true,between(u,v,w),true),
inference(step,[status(thm)],[t1749,t587]) ).
cnf(t1751,plain,
true = between(u,v,w),
inference(step,[status(thm)],[t1750,t32]) ).
cnf(f20,negated_conjecture,
~ between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_between_u_and_w) ).
fof(f20_nnf,plain,
~ between(u,v,w),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
~ between(u,v,w),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
~ between(u,v,w),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t8,plain,
between(u,v,w) = false,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t217,plain,
between(u,v,w) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t1752,plain,
true = false,
inference(step,[status(thm)],[t1751,t217]) ).
cnf(t1610,plain,
false = true,
inference(orient,[status(thm)],[t1752]) ).
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,c20]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1610]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO042-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n008.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 10:32:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.71/2.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.71/2.19 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------