%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO042-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 21.70s 3.22s
% Output : Proof 21.70s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t65,axiom,
sF1 = ifeq(between(u,v,w),true,false,true),
introduced(definition) ).
cnf(f53,negated_conjecture,
~ between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_between_u_and_w) ).
fof(f53_nnf,plain,
~ between(u,v,w),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
~ between(u,v,w),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
~ between(u,v,w),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(t10,plain,
between(u,v,w) = false,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(t76,plain,
between(u,v,w) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t64,axiom,
sF0 = between(u,v,w),
introduced(definition) ).
cnf(t10219,plain,
sF0 = false,
inference(step,[status(thm)],[t64,t76]) ).
cnf(t79,plain,
false = sF0,
inference(orient,[status(thm)],[t10219]) ).
cnf(t10228,plain,
between(u,v,w) = sF0,
inference(step,[status(thm)],[t76,t79]) ).
cnf(t88,plain,
between(u,v,w) = sF0,
inference(orient,[status(thm)],[t10228]) ).
cnf(t10234,plain,
sF1 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t65,t88]) ).
cnf(t10235,plain,
sF1 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t10234,t79]) ).
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(t23,plain,
ifeq(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t7,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t73,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t10222,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = sF0,
inference(step,[status(thm)],[t73,t79]) ).
cnf(t82,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = sF0,
inference(orient,[status(thm)],[t10222]) ).
cnf(t10232,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t23,t82]) ).
cnf(t10233,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t10232,t79]) ).
cnf(t104,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t10233]) ).
cnf(t10236,plain,
sF1 = true,
inference(step,[status(thm)],[t10235,t104]) ).
cnf(t106,plain,
true = sF1,
inference(orient,[status(thm)],[t10236]) ).
cnf(f45,axiom,
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
fof(f45_nnf,plain,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(t31,plain,
ifeq(between(X1,X2,X3),true,between(X3,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t10265,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),true) = true,
inference(step,[status(thm)],[t31,t106]) ).
cnf(t10266,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = true,
inference(step,[status(thm)],[t10265,t106]) ).
cnf(t10267,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = sF1,
inference(step,[status(thm)],[t10266,t106]) ).
cnf(t141,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = sF1,
inference(orient,[status(thm)],[t10267]) ).
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(t53,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(t10412,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),true,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
inference(step,[status(thm)],[t53,t106]) ).
cnf(t10413,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
inference(step,[status(thm)],[t10412,t106]) ).
cnf(t10414,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),sF1),true) = true,
inference(step,[status(thm)],[t10413,t106]) ).
cnf(t10415,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),sF1),sF1) = true,
inference(step,[status(thm)],[t10414,t106]) ).
cnf(t10416,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),sF1),sF1) = sF1,
inference(step,[status(thm)],[t10415,t106]) ).
cnf(t568,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),sF1),sF1) = sF1,
inference(orient,[status(thm)],[t10416]) ).
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(t22,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t103,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(orient,[status(thm)],[t22]) ).
cnf(t10256,plain,
ifeq(between(X1,X2,X1),sF1,X1,X2) = X2,
inference(step,[status(thm)],[t103,t106]) ).
cnf(t128,plain,
ifeq(between(X1,X2,X1),sF1,X1,X2) = X2,
inference(rw,[status(thm)],[t10256]) ).
cnf(t136,plain,
ifeq(between(X1,X2,X1),sF1,X1,X2) = X2,
inference(orient,[status(thm)],[t128]) ).
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(t52,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(t10397,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),true,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
inference(step,[status(thm)],[t52,t106]) ).
cnf(t10398,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
inference(step,[status(thm)],[t10397,t106]) ).
cnf(t10399,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),sF1),true) = true,
inference(step,[status(thm)],[t10398,t106]) ).
cnf(t10400,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),sF1),sF1) = true,
inference(step,[status(thm)],[t10399,t106]) ).
cnf(t10401,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),sF1),sF1) = sF1,
inference(step,[status(thm)],[t10400,t106]) ).
cnf(t487,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),sF1),sF1) = sF1,
inference(orient,[status(thm)],[t10401]) ).
cnf(f51,hypothesis,
between(u,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_x) ).
fof(f51_nnf,plain,
between(u,v,x),
inference(nnf_transformation,[status(thm)],[f51]) ).
cnf(c51,plain,
between(u,v,x),
inference(cnf_transformation,[status(esa)],[f51_nnf]) ).
cnf(t11,plain,
between(u,v,x) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
cnf(t77,plain,
between(u,v,x) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t10243,plain,
between(u,v,x) = sF1,
inference(step,[status(thm)],[t77,t106]) ).
cnf(t115,plain,
between(u,v,x) = sF1,
inference(orient,[status(thm)],[t10243]) ).
cnf(t500,plain,
sF1 = ifeq(sF1,sF1,ifeq(between(X1,X2,x),sF1,between(v,inner_pasch(u,v,x,X2,X1),X1),sF1),sF1),
inference(cp,[status(thm)],[t487,t115]) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t98,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t18]) ).
cnf(t10844,plain,
sF1 = ifeq(between(X1,X2,x),sF1,between(v,inner_pasch(u,v,x,X2,X1),X1),sF1),
inference(step,[status(thm)],[t500,t98]) ).
cnf(t9171,plain,
ifeq(between(X1,X2,x),sF1,between(v,inner_pasch(u,v,x,X2,X1),X1),sF1) = sF1,
inference(orient,[status(thm)],[t10844]) ).
cnf(f52,hypothesis,
between(v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_between_v_and_x) ).
fof(f52_nnf,plain,
between(v,w,x),
inference(nnf_transformation,[status(thm)],[f52]) ).
cnf(c52,plain,
between(v,w,x),
inference(cnf_transformation,[status(esa)],[f52_nnf]) ).
cnf(t12,plain,
between(v,w,x) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(t78,plain,
between(v,w,x) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t10245,plain,
between(v,w,x) = sF1,
inference(step,[status(thm)],[t78,t106]) ).
cnf(t117,plain,
between(v,w,x) = sF1,
inference(orient,[status(thm)],[t10245]) ).
cnf(t9173,plain,
sF1 = ifeq(sF1,sF1,between(v,inner_pasch(u,v,x,w,v),v),sF1),
inference(cp,[status(thm)],[t9171,t117]) ).
cnf(t10847,plain,
sF1 = between(v,inner_pasch(u,v,x,w,v),v),
inference(step,[status(thm)],[t9173,t98]) ).
cnf(t9370,plain,
between(v,inner_pasch(u,v,x,w,v),v) = sF1,
inference(orient,[status(thm)],[t10847]) ).
cnf(t9371,plain,
inner_pasch(u,v,x,w,v) = ifeq(sF1,sF1,v,inner_pasch(u,v,x,w,v)),
inference(cp,[status(thm)],[t136,t9370]) ).
cnf(t10848,plain,
inner_pasch(u,v,x,w,v) = v,
inference(step,[status(thm)],[t9371,t98]) ).
cnf(t9399,plain,
inner_pasch(u,v,x,w,v) = v,
inference(orient,[status(thm)],[t10848]) ).
cnf(t9401,plain,
sF1 = ifeq(between(u,v,x),sF1,ifeq(between(v,w,x),sF1,between(w,v,u),sF1),sF1),
inference(cp,[status(thm)],[t568,t9399]) ).
cnf(t10849,plain,
sF1 = ifeq(sF1,sF1,ifeq(between(v,w,x),sF1,between(w,v,u),sF1),sF1),
inference(step,[status(thm)],[t9401,t115]) ).
cnf(t10850,plain,
sF1 = ifeq(between(v,w,x),sF1,between(w,v,u),sF1),
inference(step,[status(thm)],[t10849,t98]) ).
cnf(t10851,plain,
sF1 = ifeq(sF1,sF1,between(w,v,u),sF1),
inference(step,[status(thm)],[t10850,t117]) ).
cnf(t10852,plain,
sF1 = between(w,v,u),
inference(step,[status(thm)],[t10851,t98]) ).
cnf(t9402,plain,
between(w,v,u) = sF1,
inference(orient,[status(thm)],[t10852]) ).
cnf(t9405,plain,
sF1 = ifeq(sF1,sF1,between(u,v,w),sF1),
inference(cp,[status(thm)],[t141,t9402]) ).
cnf(t10853,plain,
sF1 = between(u,v,w),
inference(step,[status(thm)],[t9405,t98]) ).
cnf(t10854,plain,
sF1 = sF0,
inference(step,[status(thm)],[t10853,t88]) ).
cnf(t9440,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t10854]) ).
cnf(t10873,plain,
true = sF0,
inference(step,[status(thm)],[t106,t9440]) ).
cnf(t9459,plain,
true = sF0,
inference(orient,[status(thm)],[t10873]) ).
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,c53]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t9459]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t79]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO042-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 10:31:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 21.70/3.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.70/3.22 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------