%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO026-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 31.52s 4.52s
% Output : Proof 31.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 80 ( 68 unt; 0 def)
% Number of atoms : 128 ( 50 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 114 ( 66 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-4 aty)
% Number of variables : 108 ( 2 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f41,negated_conjecture,
w != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_x) ).
fof(f41_nnf,plain,
w != x,
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
w != x,
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c41,plain,
w != x,
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(t2,plain,
eq(w,x) = false,
inference(equality_encoding,[status(esa)],[c41]) ).
cnf(t2913,plain,
eq(w,x) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(f2,axiom,
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/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(t101,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t262,plain,
ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
inference(orient,[status(thm)],[t101]) ).
cnf(f36,axiom,
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8) ).
fof(f36_nnf,plain,
! [U,V,U1,V1,W,W1] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [U,V,U1,V1,W,W1] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
( equidistant(X0,X4,X2,X5)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi33,axiom,
ifeq(equidistant(X0,X1,X2,X3),true,ifeq(equidistant(X1,X4,X3,X5),true,ifeq(between(X0,X1,X4),true,ifeq(between(X2,X3,X5),true,equidistant(X0,X4,X2,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(f19,axiom,
equidistant(U,V,U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f19_nnf,plain,
! [U,V] : equidistant(U,V,U,V),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [U,V] : equidistant(U,V,U,V),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
equidistant(X0,X1,X0,X1),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi15,axiom,
equidistant(X0,X1,X0,X1) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f39,hypothesis,
equidistant(v,w,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v_to_x) ).
fof(f39_nnf,plain,
equidistant(v,w,v,x),
inference(nnf_transformation,[status(thm)],[f39]) ).
cnf(c39,plain,
equidistant(v,w,v,x),
inference(cnf_transformation,[status(esa)],[f39_nnf]) ).
cnf(hi36,axiom,
equidistant(v,w,v,x) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(f37,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f37_nnf,plain,
between(u,v,w),
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c37,plain,
between(u,v,w),
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(hi34,axiom,
between(u,v,w) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(f38,hypothesis,
between(u,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_x) ).
fof(f38_nnf,plain,
between(u,v,x),
inference(nnf_transformation,[status(thm)],[f38]) ).
cnf(c38,plain,
between(u,v,x),
inference(cnf_transformation,[status(esa)],[f38_nnf]) ).
cnf(hi35,axiom,
between(u,v,x) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h214,plain,
equidistant(u,w,u,x) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi15,hi36,hi34,hi35]) ).
cnf(f5,axiom,
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
fof(f5_nnf,plain,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(equidistant(X0,X1,X2,X3),true,ifeq(equidistant(X1,X4,X3,X5),true,ifeq(equidistant(X0,X6,X2,X7),true,ifeq(equidistant(X1,X6,X3,X7),true,ifeq(between(X0,X1,X4),true,ifeq(between(X2,X3,X5),true,or(eq(X0,X1),equidistant(X4,X6,X5,X7)),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t119,plain,
or(eq(u,v),equidistant(x,w,x,x)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi15,hi15,h214,hi36,hi35,hi35]) ).
cnf(t1065,plain,
or(eq(u,v),equidistant(x,w,x,x)) = true,
inference(orient,[status(thm)],[t119]) ).
cnf(f40,hypothesis,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f40_nnf,plain,
u != v,
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
u != v,
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
u != v,
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t1,plain,
eq(u,v) = false,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t2920,plain,
eq(u,v) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t3014,plain,
or(false,equidistant(x,w,x,x)) = true,
inference(step,[status(thm)],[t1065,t2920]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t259,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t3015,plain,
equidistant(x,w,x,x) = true,
inference(step,[status(thm)],[t3014,t259]) ).
cnf(t2927,plain,
equidistant(x,w,x,x) = true,
inference(rw,[status(thm)],[t3015]) ).
cnf(t2957,plain,
equidistant(x,w,x,x) = true,
inference(orient,[status(thm)],[t2927]) ).
cnf(t2970,plain,
w = ifeq(true,true,x,w),
inference(cp,[status(thm)],[t262,t2957]) ).
cnf(t52,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t260,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t52]) ).
cnf(t3023,plain,
w = x,
inference(step,[status(thm)],[t2970,t260]) ).
cnf(t2992,plain,
w = x,
inference(orient,[status(thm)],[t3023]) ).
cnf(t3025,plain,
eq(x,x) = false,
inference(step,[status(thm)],[t2913,t2992]) ).
cnf(t0,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t1059,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t3026,plain,
true = false,
inference(step,[status(thm)],[t3025,t1059]) ).
cnf(t2994,plain,
true = false,
inference(rw,[status(thm)],[t3026]) ).
cnf(t2997,plain,
false = true,
inference(orient,[status(thm)],[t2994]) ).
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,c40,c41]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2997]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO026-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n002.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 10:29:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 31.52/4.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.52/4.52 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------