%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO028-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 01:16:37 PM UTC 2026
% Result : Unsatisfiable 176.05s 36.47s
% Output : Proof 176.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 17
% Syntax : Number of formulae : 160 ( 148 unt; 0 def)
% Number of atoms : 188 ( 132 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 75 ( 47 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 19 ( 19 usr; 15 con; 0-4 aty)
% Number of variables : 219 ( 14 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t55,axiom,
sF3 = ifeq(extension(u,v,w,x),extension(u,v,y,z),false,true),
introduced(definition) ).
cnf(t52,axiom,
sF0 = extension(u,v,w,x),
introduced(definition) ).
cnf(t74,plain,
extension(u,v,w,x) = sF0,
inference(orient,[status(thm)],[t52]) ).
cnf(t45556,plain,
sF3 = ifeq(sF0,extension(u,v,y,z),false,true),
inference(step,[status(thm)],[t55,t74]) ).
cnf(t53,axiom,
sF1 = extension(u,v,y,z),
introduced(definition) ).
cnf(t75,plain,
extension(u,v,y,z) = sF1,
inference(orient,[status(thm)],[t53]) ).
cnf(t45557,plain,
sF3 = ifeq(sF0,sF1,false,true),
inference(step,[status(thm)],[t45556,t75]) ).
cnf(t54,axiom,
sF2 = eq(extension(u,v,w,x),extension(u,v,y,z)),
introduced(definition) ).
cnf(t45527,plain,
sF2 = eq(sF0,extension(u,v,y,z)),
inference(step,[status(thm)],[t54,t74]) ).
cnf(t45528,plain,
sF2 = eq(sF0,sF1),
inference(step,[status(thm)],[t45527,t75]) ).
cnf(f40,negated_conjecture,
extension(u,v,w,x) != extension(u,v,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_extensions) ).
fof(f40_nnf,plain,
extension(u,v,w,x) != extension(u,v,y,z),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
extension(u,v,w,x) != extension(u,v,y,z),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
extension(u,v,w,x) != extension(u,v,y,z),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t28,plain,
eq(extension(u,v,w,x),extension(u,v,y,z)) = false,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t45497,plain,
eq(sF0,extension(u,v,y,z)) = false,
inference(step,[status(thm)],[t28,t74]) ).
cnf(t45498,plain,
eq(sF0,sF1) = false,
inference(step,[status(thm)],[t45497,t75]) ).
cnf(t103,plain,
eq(sF0,sF1) = false,
inference(orient,[status(thm)],[t45498]) ).
cnf(t45529,plain,
sF2 = false,
inference(step,[status(thm)],[t45528,t103]) ).
cnf(t241,plain,
false = sF2,
inference(orient,[status(thm)],[t45529]) ).
cnf(t45558,plain,
sF3 = ifeq(sF0,sF1,sF2,true),
inference(step,[status(thm)],[t45557,t241]) ).
cnf(t38,plain,
ifeq(extension(u,v,w,x),extension(u,v,y,z),false,true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t45553,plain,
ifeq(sF0,extension(u,v,y,z),false,true) = true,
inference(step,[status(thm)],[t38,t74]) ).
cnf(t45554,plain,
ifeq(sF0,sF1,false,true) = true,
inference(step,[status(thm)],[t45553,t75]) ).
cnf(t45555,plain,
ifeq(sF0,sF1,sF2,true) = true,
inference(step,[status(thm)],[t45554,t241]) ).
cnf(t272,plain,
ifeq(sF0,sF1,sF2,true) = true,
inference(orient,[status(thm)],[t45555]) ).
cnf(t45559,plain,
sF3 = true,
inference(step,[status(thm)],[t45558,t272]) ).
cnf(t277,plain,
true = sF3,
inference(orient,[status(thm)],[t45559]) ).
cnf(f37,axiom,
( W = X
| U = V
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
fof(f37_nnf,plain,
! [U,V,W,X] :
( W = X
| U = V
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [U,V,W,X] :
( W = X
| U = V
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
( X2 = X3
| X0 = X1
| ~ equidistant(X1,X2,X1,X3)
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(t45,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X1,X2,X4),true,ifeq(equidistant(X2,X3,X2,X4),true,or(eq(X1,X2),eq(X3,X4)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t45725,plain,
ifeq(between(X1,X2,X3),sF3,ifeq(between(X1,X2,X4),true,ifeq(equidistant(X2,X3,X2,X4),true,or(eq(X1,X2),eq(X3,X4)),true),true),true) = true,
inference(step,[status(thm)],[t45,t277]) ).
cnf(t45726,plain,
ifeq(between(X1,X2,X3),sF3,ifeq(between(X1,X2,X4),sF3,ifeq(equidistant(X2,X3,X2,X4),true,or(eq(X1,X2),eq(X3,X4)),true),true),true) = true,
inference(step,[status(thm)],[t45725,t277]) ).
cnf(t45727,plain,
ifeq(between(X1,X2,X3),sF3,ifeq(between(X1,X2,X4),sF3,ifeq(equidistant(X2,X3,X2,X4),sF3,or(eq(X1,X2),eq(X3,X4)),true),true),true) = true,
inference(step,[status(thm)],[t45726,t277]) ).
cnf(t45728,plain,
ifeq(between(X1,X2,X3),sF3,ifeq(between(X1,X2,X4),sF3,ifeq(equidistant(X2,X3,X2,X4),sF3,or(eq(X1,X2),eq(X3,X4)),sF3),true),true) = true,
inference(step,[status(thm)],[t45727,t277]) ).
cnf(t45729,plain,
ifeq(between(X1,X2,X3),sF3,ifeq(between(X1,X2,X4),sF3,ifeq(equidistant(X2,X3,X2,X4),sF3,or(eq(X1,X2),eq(X3,X4)),sF3),sF3),true) = true,
inference(step,[status(thm)],[t45728,t277]) ).
cnf(t45730,plain,
ifeq(between(X1,X2,X3),sF3,ifeq(between(X1,X2,X4),sF3,ifeq(equidistant(X2,X3,X2,X4),sF3,or(eq(X1,X2),eq(X3,X4)),sF3),sF3),sF3) = true,
inference(step,[status(thm)],[t45729,t277]) ).
cnf(t45731,plain,
ifeq(between(X1,X2,X3),sF3,ifeq(between(X1,X2,X4),sF3,ifeq(equidistant(X2,X3,X2,X4),sF3,or(eq(X1,X2),eq(X3,X4)),sF3),sF3),sF3) = sF3,
inference(step,[status(thm)],[t45730,t277]) ).
cnf(t816,plain,
ifeq(between(X1,X2,X3),sF3,ifeq(between(X1,X2,X4),sF3,ifeq(equidistant(X2,X3,X2,X4),sF3,or(eq(X1,X2),eq(X3,X4)),sF3),sF3),sF3) = sF3,
inference(orient,[status(thm)],[t45731]) ).
cnf(f39,hypothesis,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
fof(f39_nnf,plain,
u != v,
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
u != v,
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
u != v,
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(t1,plain,
eq(u,v) = false,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t57,plain,
eq(u,v) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t45530,plain,
eq(u,v) = sF2,
inference(step,[status(thm)],[t57,t241]) ).
cnf(t242,plain,
eq(u,v) = sF2,
inference(orient,[status(thm)],[t45530]) ).
cnf(t819,plain,
sF3 = ifeq(between(u,v,X1),sF3,ifeq(between(u,v,X2),sF3,ifeq(equidistant(v,X1,v,X2),sF3,or(sF2,eq(X1,X2)),sF3),sF3),sF3),
inference(cp,[status(thm)],[t816,t242]) ).
cnf(t4,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t60,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t45533,plain,
or(sF2,X1) = X1,
inference(step,[status(thm)],[t60,t241]) ).
cnf(t245,plain,
or(sF2,X1) = X1,
inference(rw,[status(thm)],[t45533]) ).
cnf(t265,plain,
or(sF2,X1) = X1,
inference(orient,[status(thm)],[t245]) ).
cnf(t48191,plain,
sF3 = ifeq(between(u,v,X1),sF3,ifeq(between(u,v,X2),sF3,ifeq(equidistant(v,X1,v,X2),sF3,eq(X1,X2),sF3),sF3),sF3),
inference(step,[status(thm)],[t819,t265]) ).
cnf(t42335,plain,
ifeq(between(u,v,X1),sF3,ifeq(between(u,v,X2),sF3,ifeq(equidistant(v,X1,v,X2),sF3,eq(X1,X2),sF3),sF3),sF3) = sF3,
inference(orient,[status(thm)],[t48191]) ).
cnf(t45544,plain,
eq(sF0,sF1) = sF2,
inference(step,[status(thm)],[t103,t241]) ).
cnf(t255,plain,
eq(sF0,sF1) = sF2,
inference(orient,[status(thm)],[t45544]) ).
cnf(t42342,plain,
sF3 = ifeq(between(u,v,sF0),sF3,ifeq(between(u,v,sF1),sF3,ifeq(equidistant(v,sF0,v,sF1),sF3,sF2,sF3),sF3),sF3),
inference(cp,[status(thm)],[t42335,t255]) ).
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(t19,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t82,plain,
between(X1,X2,extension(X1,X2,X3,X4)) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t85,plain,
true = between(u,v,sF0),
inference(cp,[status(thm)],[t82,t74]) ).
cnf(t89,plain,
between(u,v,sF0) = true,
inference(orient,[status(thm)],[t85]) ).
cnf(t45575,plain,
between(u,v,sF0) = sF3,
inference(step,[status(thm)],[t89,t277]) ).
cnf(t295,plain,
between(u,v,sF0) = sF3,
inference(orient,[status(thm)],[t45575]) ).
cnf(t48192,plain,
sF3 = ifeq(sF3,sF3,ifeq(between(u,v,sF1),sF3,ifeq(equidistant(v,sF0,v,sF1),sF3,sF2,sF3),sF3),sF3),
inference(step,[status(thm)],[t42342,t295]) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t72,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t48193,plain,
sF3 = ifeq(between(u,v,sF1),sF3,ifeq(equidistant(v,sF0,v,sF1),sF3,sF2,sF3),sF3),
inference(step,[status(thm)],[t48192,t72]) ).
cnf(t86,plain,
true = between(u,v,sF1),
inference(cp,[status(thm)],[t82,t75]) ).
cnf(t90,plain,
between(u,v,sF1) = true,
inference(orient,[status(thm)],[t86]) ).
cnf(t45577,plain,
between(u,v,sF1) = sF3,
inference(step,[status(thm)],[t90,t277]) ).
cnf(t297,plain,
between(u,v,sF1) = sF3,
inference(orient,[status(thm)],[t45577]) ).
cnf(t48194,plain,
sF3 = ifeq(sF3,sF3,ifeq(equidistant(v,sF0,v,sF1),sF3,sF2,sF3),sF3),
inference(step,[status(thm)],[t48193,t297]) ).
cnf(t48195,plain,
sF3 = ifeq(equidistant(v,sF0,v,sF1),sF3,sF2,sF3),
inference(step,[status(thm)],[t48194,t72]) ).
cnf(f1,axiom,
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
fof(f1_nnf,plain,
! [X,Y,Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t39,plain,
ifeq(equidistant(X1,X2,X3,X4),true,ifeq(equidistant(X1,X2,X5,X6),true,equidistant(X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t45650,plain,
ifeq(equidistant(X1,X2,X3,X4),sF3,ifeq(equidistant(X1,X2,X5,X6),true,equidistant(X3,X4,X5,X6),true),true) = true,
inference(step,[status(thm)],[t39,t277]) ).
cnf(t45651,plain,
ifeq(equidistant(X1,X2,X3,X4),sF3,ifeq(equidistant(X1,X2,X5,X6),sF3,equidistant(X3,X4,X5,X6),true),true) = true,
inference(step,[status(thm)],[t45650,t277]) ).
cnf(t45652,plain,
ifeq(equidistant(X1,X2,X3,X4),sF3,ifeq(equidistant(X1,X2,X5,X6),sF3,equidistant(X3,X4,X5,X6),sF3),true) = true,
inference(step,[status(thm)],[t45651,t277]) ).
cnf(t45653,plain,
ifeq(equidistant(X1,X2,X3,X4),sF3,ifeq(equidistant(X1,X2,X5,X6),sF3,equidistant(X3,X4,X5,X6),sF3),sF3) = true,
inference(step,[status(thm)],[t45652,t277]) ).
cnf(t45654,plain,
ifeq(equidistant(X1,X2,X3,X4),sF3,ifeq(equidistant(X1,X2,X5,X6),sF3,equidistant(X3,X4,X5,X6),sF3),sF3) = sF3,
inference(step,[status(thm)],[t45653,t277]) ).
cnf(t402,plain,
ifeq(equidistant(X1,X2,X3,X4),sF3,ifeq(equidistant(X1,X2,X5,X6),sF3,equidistant(X3,X4,X5,X6),sF3),sF3) = sF3,
inference(orient,[status(thm)],[t45654]) ).
cnf(f20,axiom,
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f20_nnf,plain,
! [U,V,W,X] :
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [U,V,W,X] :
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t34,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t188,plain,
ifeq(equidistant(X1,X2,X3,X4),true,equidistant(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t34]) ).
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(t25,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t94,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t96,plain,
true = equidistant(v,sF0,w,x),
inference(cp,[status(thm)],[t94,t74]) ).
cnf(t98,plain,
equidistant(v,sF0,w,x) = true,
inference(orient,[status(thm)],[t96]) ).
cnf(t193,plain,
true = ifeq(true,true,equidistant(w,x,v,sF0),true),
inference(cp,[status(thm)],[t188,t98]) ).
cnf(t45511,plain,
true = equidistant(w,x,v,sF0),
inference(step,[status(thm)],[t193,t72]) ).
cnf(t220,plain,
equidistant(w,x,v,sF0) = true,
inference(orient,[status(thm)],[t45511]) ).
cnf(t45611,plain,
equidistant(w,x,v,sF0) = sF3,
inference(step,[status(thm)],[t220,t277]) ).
cnf(t351,plain,
equidistant(w,x,v,sF0) = sF3,
inference(orient,[status(thm)],[t45611]) ).
cnf(t460,plain,
sF3 = ifeq(sF3,sF3,ifeq(equidistant(w,x,X1,X2),sF3,equidistant(v,sF0,X1,X2),sF3),sF3),
inference(cp,[status(thm)],[t402,t351]) ).
cnf(t45911,plain,
sF3 = ifeq(equidistant(w,x,X1,X2),sF3,equidistant(v,sF0,X1,X2),sF3),
inference(step,[status(thm)],[t460,t72]) ).
cnf(t3646,plain,
ifeq(equidistant(w,x,X1,X2),sF3,equidistant(v,sF0,X1,X2),sF3) = sF3,
inference(orient,[status(thm)],[t45911]) ).
cnf(f38,hypothesis,
equidistant(w,x,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_to_x_equals_y_to_z) ).
fof(f38_nnf,plain,
equidistant(w,x,y,z),
inference(nnf_transformation,[status(thm)],[f38]) ).
cnf(c38,plain,
equidistant(w,x,y,z),
inference(cnf_transformation,[status(esa)],[f38_nnf]) ).
cnf(t12,plain,
equidistant(w,x,y,z) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t68,plain,
equidistant(w,x,y,z) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t189,plain,
true = ifeq(true,true,equidistant(y,z,w,x),true),
inference(cp,[status(thm)],[t188,t68]) ).
cnf(t45510,plain,
true = equidistant(y,z,w,x),
inference(step,[status(thm)],[t189,t72]) ).
cnf(t219,plain,
equidistant(y,z,w,x) = true,
inference(orient,[status(thm)],[t45510]) ).
cnf(t45609,plain,
equidistant(y,z,w,x) = sF3,
inference(step,[status(thm)],[t219,t277]) ).
cnf(t349,plain,
equidistant(y,z,w,x) = sF3,
inference(orient,[status(thm)],[t45609]) ).
cnf(t457,plain,
sF3 = ifeq(sF3,sF3,ifeq(equidistant(y,z,X1,X2),sF3,equidistant(w,x,X1,X2),sF3),sF3),
inference(cp,[status(thm)],[t402,t349]) ).
cnf(t45867,plain,
sF3 = ifeq(equidistant(y,z,X1,X2),sF3,equidistant(w,x,X1,X2),sF3),
inference(step,[status(thm)],[t457,t72]) ).
cnf(t2622,plain,
ifeq(equidistant(y,z,X1,X2),sF3,equidistant(w,x,X1,X2),sF3) = sF3,
inference(orient,[status(thm)],[t45867]) ).
cnf(t97,plain,
true = equidistant(v,sF1,y,z),
inference(cp,[status(thm)],[t94,t75]) ).
cnf(t99,plain,
equidistant(v,sF1,y,z) = true,
inference(orient,[status(thm)],[t97]) ).
cnf(t195,plain,
true = ifeq(true,true,equidistant(y,z,v,sF1),true),
inference(cp,[status(thm)],[t188,t99]) ).
cnf(t45512,plain,
true = equidistant(y,z,v,sF1),
inference(step,[status(thm)],[t195,t72]) ).
cnf(t221,plain,
equidistant(y,z,v,sF1) = true,
inference(orient,[status(thm)],[t45512]) ).
cnf(t45613,plain,
equidistant(y,z,v,sF1) = sF3,
inference(step,[status(thm)],[t221,t277]) ).
cnf(t353,plain,
equidistant(y,z,v,sF1) = sF3,
inference(orient,[status(thm)],[t45613]) ).
cnf(t2623,plain,
sF3 = ifeq(sF3,sF3,equidistant(w,x,v,sF1),sF3),
inference(cp,[status(thm)],[t2622,t353]) ).
cnf(t45868,plain,
sF3 = equidistant(w,x,v,sF1),
inference(step,[status(thm)],[t2623,t72]) ).
cnf(t2633,plain,
equidistant(w,x,v,sF1) = sF3,
inference(orient,[status(thm)],[t45868]) ).
cnf(t3651,plain,
sF3 = ifeq(sF3,sF3,equidistant(v,sF0,v,sF1),sF3),
inference(cp,[status(thm)],[t3646,t2633]) ).
cnf(t45912,plain,
sF3 = equidistant(v,sF0,v,sF1),
inference(step,[status(thm)],[t3651,t72]) ).
cnf(t3661,plain,
equidistant(v,sF0,v,sF1) = sF3,
inference(orient,[status(thm)],[t45912]) ).
cnf(t48196,plain,
sF3 = ifeq(sF3,sF3,sF2,sF3),
inference(step,[status(thm)],[t48195,t3661]) ).
cnf(t48197,plain,
sF3 = sF2,
inference(step,[status(thm)],[t48196,t72]) ).
cnf(t42545,plain,
sF3 = sF2,
inference(orient,[status(thm)],[t48197]) ).
cnf(t48278,plain,
true = sF2,
inference(step,[status(thm)],[t277,t42545]) ).
cnf(t42626,plain,
true = sF2,
inference(orient,[status(thm)],[t48278]) ).
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,c39,c40]) ).
cnf(g0_0,plain,
sF2 != false,
inference(rw,[status(thm)],[goal_0,t42626]) ).
cnf(g0_1,plain,
sF2 != sF2,
inference(rw,[status(thm)],[g0_0,t241]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO028-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/10.39 % Computer : n016.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Wed Sep 23 10:32:37 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 176.05/36.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 176.05/36.47 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------