%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO041-2 : 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 01:16:41 PM UTC 2026
% Result : Unsatisfiable 24.77s 3.69s
% Output : Proof 24.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 14
% Syntax : Number of formulae : 128 ( 112 unt; 0 def)
% Number of atoms : 152 ( 93 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; 8 con; 0-5 aty)
% Number of variables : 183 ( 18 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f20,negated_conjecture,
v != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_is_w) ).
fof(f20_nnf,plain,
v != w,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
v != w,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
v != w,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t1,plain,
eq(v,w) = false,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t217,plain,
eq(v,w) = false,
inference(orient,[status(thm)],[t1]) ).
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(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/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(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/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(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/sandbox2/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(t75,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)],[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(t9191,plain,
true = ifeq(between(X1,X2,w),true,between(v,inner_pasch(X1,X2,w,v,u),X1),true),
inference(step,[status(thm)],[t75,t32]) ).
cnf(t502,plain,
ifeq(between(X1,X2,w),true,between(v,inner_pasch(X1,X2,w,v,u),X1),true) = true,
inference(orient,[status(thm)],[t9191]) ).
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(t15,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t53,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(orient,[status(thm)],[t15]) ).
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(t9167,plain,
extension(X1,X2,X3,X3) = X2,
inference(step,[status(thm)],[t130,t32]) ).
cnf(t224,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t9167]) ).
cnf(t226,plain,
true = between(X1,X2,X2),
inference(cp,[status(thm)],[t53,t224]) ).
cnf(t227,plain,
between(X1,X2,X2) = true,
inference(orient,[status(thm)],[t226]) ).
cnf(t503,plain,
true = ifeq(true,true,between(v,inner_pasch(X1,w,w,v,u),X1),true),
inference(cp,[status(thm)],[t502,t227]) ).
cnf(t9192,plain,
true = between(v,inner_pasch(X1,w,w,v,u),X1),
inference(step,[status(thm)],[t503,t32]) ).
cnf(t506,plain,
between(v,inner_pasch(X1,w,w,v,u),X1) = true,
inference(orient,[status(thm)],[t9192]) ).
cnf(t507,plain,
inner_pasch(v,w,w,v,u) = ifeq(true,true,v,inner_pasch(v,w,w,v,u)),
inference(cp,[status(thm)],[t33,t506]) ).
cnf(t9193,plain,
inner_pasch(v,w,w,v,u) = v,
inference(step,[status(thm)],[t507,t32]) ).
cnf(t530,plain,
inner_pasch(v,w,w,v,u) = v,
inference(orient,[status(thm)],[t9193]) ).
cnf(t531,plain,
true = ifeq(between(v,w,w),true,ifeq(between(u,v,w),true,between(w,v,u),true),true),
inference(cp,[status(thm)],[t39,t530]) ).
cnf(t9194,plain,
true = ifeq(true,true,ifeq(between(u,v,w),true,between(w,v,u),true),true),
inference(step,[status(thm)],[t531,t227]) ).
cnf(t9195,plain,
true = ifeq(between(u,v,w),true,between(w,v,u),true),
inference(step,[status(thm)],[t9194,t32]) ).
cnf(t9196,plain,
true = ifeq(true,true,between(w,v,u),true),
inference(step,[status(thm)],[t9195,t73]) ).
cnf(t9197,plain,
true = between(w,v,u),
inference(step,[status(thm)],[t9196,t32]) ).
cnf(t532,plain,
between(w,v,u) = true,
inference(orient,[status(thm)],[t9197]) ).
cnf(t533,plain,
true = ifeq(true,true,ifeq(between(X1,X2,u),true,between(X2,inner_pasch(w,v,u,X2,X1),w),true),true),
inference(cp,[status(thm)],[t38,t532]) ).
cnf(t9653,plain,
true = ifeq(between(X1,X2,u),true,between(X2,inner_pasch(w,v,u,X2,X1),w),true),
inference(step,[status(thm)],[t533,t32]) ).
cnf(t8888,plain,
ifeq(between(X1,X2,u),true,between(X2,inner_pasch(w,v,u,X2,X1),w),true) = true,
inference(orient,[status(thm)],[t9653]) ).
cnf(f19,hypothesis,
between(u,w,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_v) ).
fof(f19_nnf,plain,
between(u,w,v),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
between(u,w,v),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(t10,plain,
between(u,w,v) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t93,plain,
between(u,w,v) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t95,plain,
true = ifeq(between(X1,X2,v),true,ifeq(true,true,between(w,inner_pasch(X1,X2,v,w,u),X1),true),true),
inference(cp,[status(thm)],[t38,t93]) ).
cnf(t9228,plain,
true = ifeq(between(X1,X2,v),true,between(w,inner_pasch(X1,X2,v,w,u),X1),true),
inference(step,[status(thm)],[t95,t32]) ).
cnf(t860,plain,
ifeq(between(X1,X2,v),true,between(w,inner_pasch(X1,X2,v,w,u),X1),true) = true,
inference(orient,[status(thm)],[t9228]) ).
cnf(t861,plain,
true = ifeq(true,true,between(w,inner_pasch(X1,v,v,w,u),X1),true),
inference(cp,[status(thm)],[t860,t227]) ).
cnf(t9229,plain,
true = between(w,inner_pasch(X1,v,v,w,u),X1),
inference(step,[status(thm)],[t861,t32]) ).
cnf(t868,plain,
between(w,inner_pasch(X1,v,v,w,u),X1) = true,
inference(orient,[status(thm)],[t9229]) ).
cnf(t869,plain,
inner_pasch(w,v,v,w,u) = ifeq(true,true,w,inner_pasch(w,v,v,w,u)),
inference(cp,[status(thm)],[t33,t868]) ).
cnf(t9230,plain,
inner_pasch(w,v,v,w,u) = w,
inference(step,[status(thm)],[t869,t32]) ).
cnf(t896,plain,
inner_pasch(w,v,v,w,u) = w,
inference(orient,[status(thm)],[t9230]) ).
cnf(t897,plain,
true = ifeq(between(w,v,v),true,ifeq(between(u,w,v),true,between(v,w,u),true),true),
inference(cp,[status(thm)],[t39,t896]) ).
cnf(t9231,plain,
true = ifeq(true,true,ifeq(between(u,w,v),true,between(v,w,u),true),true),
inference(step,[status(thm)],[t897,t227]) ).
cnf(t9232,plain,
true = ifeq(between(u,w,v),true,between(v,w,u),true),
inference(step,[status(thm)],[t9231,t32]) ).
cnf(t9233,plain,
true = ifeq(true,true,between(v,w,u),true),
inference(step,[status(thm)],[t9232,t93]) ).
cnf(t9234,plain,
true = between(v,w,u),
inference(step,[status(thm)],[t9233,t32]) ).
cnf(t898,plain,
between(v,w,u) = true,
inference(orient,[status(thm)],[t9234]) ).
cnf(t8980,plain,
true = ifeq(true,true,between(w,inner_pasch(w,v,u,w,v),w),true),
inference(cp,[status(thm)],[t8888,t898]) ).
cnf(t9656,plain,
true = between(w,inner_pasch(w,v,u,w,v),w),
inference(step,[status(thm)],[t8980,t32]) ).
cnf(t9067,plain,
between(w,inner_pasch(w,v,u,w,v),w) = true,
inference(orient,[status(thm)],[t9656]) ).
cnf(t9068,plain,
inner_pasch(w,v,u,w,v) = ifeq(true,true,w,inner_pasch(w,v,u,w,v)),
inference(cp,[status(thm)],[t33,t9067]) ).
cnf(t9657,plain,
inner_pasch(w,v,u,w,v) = w,
inference(step,[status(thm)],[t9068,t32]) ).
cnf(t9100,plain,
inner_pasch(w,v,u,w,v) = w,
inference(orient,[status(thm)],[t9657]) ).
cnf(t9101,plain,
true = ifeq(between(w,v,u),true,ifeq(between(v,w,u),true,between(v,w,v),true),true),
inference(cp,[status(thm)],[t39,t9100]) ).
cnf(t9658,plain,
true = ifeq(true,true,ifeq(between(v,w,u),true,between(v,w,v),true),true),
inference(step,[status(thm)],[t9101,t532]) ).
cnf(t9659,plain,
true = ifeq(between(v,w,u),true,between(v,w,v),true),
inference(step,[status(thm)],[t9658,t32]) ).
cnf(t9660,plain,
true = ifeq(true,true,between(v,w,v),true),
inference(step,[status(thm)],[t9659,t898]) ).
cnf(t9661,plain,
true = between(v,w,v),
inference(step,[status(thm)],[t9660,t32]) ).
cnf(t9102,plain,
between(v,w,v) = true,
inference(orient,[status(thm)],[t9661]) ).
cnf(t9103,plain,
w = ifeq(true,true,v,w),
inference(cp,[status(thm)],[t33,t9102]) ).
cnf(t9662,plain,
w = v,
inference(step,[status(thm)],[t9103,t32]) ).
cnf(t9135,plain,
v = w,
inference(orient,[status(thm)],[t9662]) ).
cnf(t9667,plain,
eq(w,w) = false,
inference(step,[status(thm)],[t217,t9135]) ).
cnf(t0,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t148,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t9668,plain,
true = false,
inference(step,[status(thm)],[t9667,t148]) ).
cnf(t9139,plain,
true = false,
inference(rw,[status(thm)],[t9668]) ).
cnf(t9143,plain,
false = true,
inference(orient,[status(thm)],[t9139]) ).
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,t9143]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO041-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 10:32:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.77/3.69 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.77/3.69 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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