%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO040-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 01:16:41 PM UTC 2026
% Result : Unsatisfiable 8.68s 1.53s
% Output : Proof 8.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 63 unt; 0 def)
% Number of atoms : 95 ( 48 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 38 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-5 aty)
% Number of variables : 86 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f20,negated_conjecture,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u_is_v) ).
fof(f20_nnf,plain,
u != v,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
u != v,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
u != v,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t1,plain,
eq(u,v) = false,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t217,plain,
eq(u,v) = false,
inference(orient,[status(thm)],[t1]) ).
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(t16,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)],[t16]) ).
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(t39,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(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(t38,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(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(t9,plain,
between(u,v,w) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t73,plain,
between(u,v,w) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t74,plain,
true = ifeq(true,true,ifeq(between(X1,X2,w),true,between(X2,inner_pasch(u,v,w,X2,X1),u),true),true),
inference(cp,[status(thm)],[t38,t73]) ).
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(t569,plain,
true = ifeq(between(X1,X2,w),true,between(X2,inner_pasch(u,v,w,X2,X1),u),true),
inference(step,[status(thm)],[t74,t32]) ).
cnf(t457,plain,
ifeq(between(X1,X2,w),true,between(X2,inner_pasch(u,v,w,X2,X1),u),true) = true,
inference(orient,[status(thm)],[t569]) ).
cnf(f19,hypothesis,
between(v,u,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_between_v_and_w) ).
fof(f19_nnf,plain,
between(v,u,w),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
between(v,u,w),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(t10,plain,
between(v,u,w) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t93,plain,
between(v,u,w) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t461,plain,
true = ifeq(true,true,between(u,inner_pasch(u,v,w,u,v),u),true),
inference(cp,[status(thm)],[t457,t93]) ).
cnf(t571,plain,
true = between(u,inner_pasch(u,v,w,u,v),u),
inference(step,[status(thm)],[t461,t32]) ).
cnf(t483,plain,
between(u,inner_pasch(u,v,w,u,v),u) = true,
inference(orient,[status(thm)],[t571]) ).
cnf(t484,plain,
inner_pasch(u,v,w,u,v) = ifeq(true,true,u,inner_pasch(u,v,w,u,v)),
inference(cp,[status(thm)],[t33,t483]) ).
cnf(t572,plain,
inner_pasch(u,v,w,u,v) = u,
inference(step,[status(thm)],[t484,t32]) ).
cnf(t504,plain,
inner_pasch(u,v,w,u,v) = u,
inference(orient,[status(thm)],[t572]) ).
cnf(t505,plain,
true = ifeq(between(u,v,w),true,ifeq(between(v,u,w),true,between(v,u,v),true),true),
inference(cp,[status(thm)],[t39,t504]) ).
cnf(t573,plain,
true = ifeq(true,true,ifeq(between(v,u,w),true,between(v,u,v),true),true),
inference(step,[status(thm)],[t505,t73]) ).
cnf(t574,plain,
true = ifeq(between(v,u,w),true,between(v,u,v),true),
inference(step,[status(thm)],[t573,t32]) ).
cnf(t575,plain,
true = ifeq(true,true,between(v,u,v),true),
inference(step,[status(thm)],[t574,t93]) ).
cnf(t576,plain,
true = between(v,u,v),
inference(step,[status(thm)],[t575,t32]) ).
cnf(t506,plain,
between(v,u,v) = true,
inference(orient,[status(thm)],[t576]) ).
cnf(t507,plain,
u = ifeq(true,true,v,u),
inference(cp,[status(thm)],[t33,t506]) ).
cnf(t577,plain,
u = v,
inference(step,[status(thm)],[t507,t32]) ).
cnf(t527,plain,
u = v,
inference(orient,[status(thm)],[t577]) ).
cnf(t582,plain,
eq(v,v) = false,
inference(step,[status(thm)],[t217,t527]) ).
cnf(t0,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t148,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t583,plain,
true = false,
inference(step,[status(thm)],[t582,t148]) ).
cnf(t530,plain,
true = false,
inference(rw,[status(thm)],[t583]) ).
cnf(t536,plain,
false = true,
inference(orient,[status(thm)],[t530]) ).
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,t536]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO040-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 10:31:34 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.68/1.53 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.68/1.53 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------