%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO070-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 : Sun Sep 27 07:16:58 AM UTC 2026
% Result : Unsatisfiable 21.43s 3.14s
% Output : CNFRefutation 21.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 88 ( 36 unt; 0 def)
% Number of atoms : 191 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 188 ( 85 ~; 103 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 117 ( 1 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_for_equidistance,axiom,
! [VAR_0,VAR_1] : equidistant(VAR_0,VAR_1,VAR_1,VAR_0),
file('theBenchmark.p',reflexivity_for_equidistance) ).
cnf(c_1,plain,
equidistant(A,B,B,A),
inference(clausify,[status(thm)],[reflexivity_for_equidistance]) ).
fof(colinearity4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( between(VAR_2,VAR_0,VAR_1)
| between(VAR_1,VAR_2,VAR_0)
| between(VAR_0,VAR_1,VAR_2)
| ~ colinear(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',colinearity4) ).
cnf(c_22,plain,
( between(C,A,B)
| between(B,C,A)
| between(A,B,C)
| ~ colinear(A,B,C) ),
inference(clausify,[status(thm)],[colinearity4]) ).
fof(d2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equidistant(VAR_2,VAR_3,VAR_0,VAR_1)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d2) ).
cnf(c_26,plain,
( equidistant(C,D,A,B)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d2]) ).
fof(d4_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equidistant(VAR_0,VAR_1,VAR_3,VAR_2)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d4_1) ).
cnf(c_28,plain,
( equidistant(A,B,D,C)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d4_1]) ).
fof(d4_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equidistant(VAR_3,VAR_2,VAR_0,VAR_1)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d4_4) ).
cnf(c_31,plain,
( equidistant(D,C,A,B)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d4_4]) ).
fof(t1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( between(VAR_2,VAR_1,VAR_0)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t1) ).
cnf(c_59,plain,
( between(C,B,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t1]) ).
fof(t2,axiom,
! [VAR_0,VAR_1] : between(VAR_0,VAR_0,VAR_1),
file('theBenchmark.p',t2) ).
cnf(c_60,plain,
between(A,A,B),
inference(clausify,[status(thm)],[t2]) ).
fof(b2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| ~ between(VAR_1,VAR_0,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b2) ).
cnf(c_61,plain,
( A = B
| ~ between(B,A,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b2]) ).
fof(b5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_1,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b5) ).
cnf(c_63,plain,
( between(B,C,D)
| ~ between(A,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b5]) ).
fof(b7,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_2
| between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_1,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b7) ).
cnf(c_65,plain,
( B = C
| between(A,B,D)
| ~ between(B,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b7]) ).
fof(b8,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_0,VAR_3,VAR_2)
| ~ between(VAR_1,VAR_3,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b8) ).
cnf(c_66,plain,
( between(A,D,C)
| ~ between(B,D,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b8]) ).
fof(b11,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( between(VAR_2,VAR_3,VAR_5)
| ~ between(VAR_0,VAR_1,VAR_4)
| ~ equidistant(VAR_0,VAR_4,VAR_2,VAR_5)
| ~ equidistant(VAR_1,VAR_4,VAR_3,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',b11) ).
cnf(c_93,plain,
( between(C,D,F)
| ~ between(A,B,E)
| ~ equidistant(A,E,C,F)
| ~ equidistant(B,E,D,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[b11]) ).
fof(t8,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_0,VAR_3,VAR_2)
| ~ between(VAR_0,VAR_4,VAR_2)
| ~ between(VAR_1,VAR_3,VAR_4)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t8) ).
cnf(c_99,plain,
( between(A,D,C)
| ~ between(A,E,C)
| ~ between(B,D,E)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t8]) ).
fof(u_to_v_equals_w_to_x,axiom,
equidistant(u,v,w,x),
file('theBenchmark.p',u_to_v_equals_w_to_x) ).
cnf(c_120,plain,
equidistant(u,v,w,x),
inference(clausify,[status(thm)],[u_to_v_equals_w_to_x]) ).
fof(v_to_w_equals_x_to_u,axiom,
equidistant(v,w,x,u),
file('theBenchmark.p',v_to_w_equals_x_to_u) ).
cnf(c_121,plain,
equidistant(v,w,x,u),
inference(clausify,[status(thm)],[v_to_w_equals_x_to_u]) ).
fof(u_to_w_equals_v_to_x,axiom,
equidistant(u,w,v,x),
file('theBenchmark.p',u_to_w_equals_v_to_x) ).
cnf(c_122,plain,
equidistant(u,w,v,x),
inference(clausify,[status(thm)],[u_to_w_equals_v_to_x]) ).
fof(y_between_u_and_w,axiom,
between(u,y,w),
file('theBenchmark.p',y_between_u_and_w) ).
cnf(c_123,plain,
between(u,y,w),
inference(clausify,[status(thm)],[y_between_u_and_w]) ).
fof(y_between_v_and_x,axiom,
between(v,y,x),
file('theBenchmark.p',y_between_v_and_x) ).
cnf(c_124,plain,
between(v,y,x),
inference(clausify,[status(thm)],[y_between_v_and_x]) ).
fof(u_not_v,axiom,
u != v,
file('theBenchmark.p',u_not_v) ).
cnf(c_125,plain,
u != v,
inference(clausify,[status(thm)],[u_not_v]) ).
cnf(c_126,plain,
v != u,
inference(copy,[status(thm)],[c_125]) ).
fof(x_not_u,axiom,
x != u,
file('theBenchmark.p',x_not_u) ).
cnf(c_127,plain,
x != u,
inference(clausify,[status(thm)],[x_not_u]) ).
fof(prove_uvw_not_colinear,axiom,
colinear(u,v,w),
file('theBenchmark.p',prove_uvw_not_colinear) ).
cnf(c_128,plain,
colinear(u,v,w),
inference(clausify,[status(thm)],[prove_uvw_not_colinear]) ).
cnf(c_436,plain,
( between(A,C,D)
| ~ between(C,A,B)
| ~ equidistant(C,B,A,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_93,c_1]) ).
cnf(c_457,plain,
( between(A,D,C)
| ~ between(B,D,A)
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_99,c_60]) ).
cnf(c_509,plain,
equidistant(x,w,u,v),
inference(resolve,[status(thm)],[c_120,c_31]) ).
cnf(c_548,plain,
equidistant(u,x,v,w),
inference(resolve,[status(thm)],[c_121,c_31]) ).
cnf(c_551,plain,
equidistant(v,w,u,x),
inference(resolve,[status(thm)],[c_121,c_28]) ).
cnf(c_587,plain,
equidistant(x,v,u,w),
inference(resolve,[status(thm)],[c_122,c_31]) ).
cnf(c_590,plain,
equidistant(u,w,x,v),
inference(resolve,[status(thm)],[c_122,c_28]) ).
cnf(c_592,plain,
equidistant(v,x,u,w),
inference(resolve,[status(thm)],[c_122,c_26]) ).
cnf(c_637,plain,
( between(y,w,A)
| ~ between(u,w,A) ),
inference(resolve,[status(thm)],[c_123,c_63]) ).
cnf(c_640,plain,
between(w,y,u),
inference(resolve,[status(thm)],[c_123,c_59]) ).
cnf(c_707,plain,
between(x,y,v),
inference(resolve,[status(thm)],[c_124,c_59]) ).
cnf(c_752,plain,
( between(w,u,v)
| between(v,w,u)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_128,c_22]) ).
cnf(c_910,plain,
( between(y,u,A)
| ~ between(w,u,A) ),
inference(resolve,[status(thm)],[c_640,c_63]) ).
cnf(c_1120,plain,
( between(x,A,v)
| ~ between(y,A,v) ),
inference(resolve,[status(thm)],[c_707,c_66]) ).
cnf(c_9045,plain,
( between(v,A,x)
| ~ between(y,A,v) ),
inference(resolve,[status(thm)],[c_457,c_124]) ).
cnf(c_9508,plain,
( between(y,u,v)
| between(v,w,u)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_752,c_910]) ).
cnf(c_11029,plain,
( between(v,u,x)
| between(v,w,u)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_9508,c_9045]) ).
cnf(c_12349,plain,
( between(u,w,v)
| between(v,u,x)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_11029,c_59]) ).
cnf(c_14766,plain,
( between(A,B,C)
| ~ equidistant(v,x,A,C)
| ~ equidistant(u,x,B,C)
| ~ equidistant(v,u,A,B)
| between(u,w,v)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_12349,c_93]) ).
cnf(c_20677,plain,
( ~ equidistant(v,x,u,w)
| ~ equidistant(u,x,v,w)
| ~ equidistant(v,u,u,v)
| between(u,w,v)
| between(u,v,w) ),
inference(factor,[status(thm)],[c_14766]) ).
cnf(c_20678,plain,
( ~ equidistant(v,x,u,w)
| ~ equidistant(u,x,v,w)
| between(u,w,v)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_1,c_20677]) ).
cnf(c_20679,plain,
( ~ equidistant(v,x,u,w)
| between(u,w,v)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_548,c_20678]) ).
cnf(c_14805,plain,
( between(u,w,v)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_592,c_20679]) ).
cnf(c_14806,plain,
( between(y,w,v)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_14805,c_637]) ).
cnf(c_15019,plain,
( between(x,w,v)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_14806,c_1120]) ).
cnf(c_16032,plain,
( between(A,B,C)
| ~ equidistant(x,v,A,C)
| ~ equidistant(w,v,B,C)
| ~ equidistant(x,w,A,B)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_15019,c_93]) ).
cnf(c_20680,plain,
( ~ equidistant(x,v,u,w)
| ~ equidistant(w,v,v,w)
| ~ equidistant(x,w,u,v)
| between(u,v,w) ),
inference(factor,[status(thm)],[c_16032]) ).
cnf(c_20681,plain,
( ~ equidistant(x,v,u,w)
| ~ equidistant(w,v,v,w)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_509,c_20680]) ).
cnf(c_20682,plain,
( ~ equidistant(x,v,u,w)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_1,c_20681]) ).
cnf(c_16071,plain,
between(u,v,w),
inference(resolve,[status(thm)],[c_587,c_20682]) ).
cnf(c_20683,plain,
( u = v
| between(A,u,w)
| ~ between(A,u,v) ),
inference(resolve,[status(thm)],[c_16071,c_65]) ).
cnf(c_20684,plain,
( v = u
| between(A,u,w)
| ~ between(A,u,v) ),
inference(copy,[status(thm)],[c_20683]) ).
cnf(c_16272,plain,
( between(A,u,w)
| ~ between(A,u,v) ),
inference(resolve,[status(thm)],[c_126,c_20684]) ).
cnf(c_20685,plain,
( between(u,x,v)
| ~ between(x,u,w)
| ~ equidistant(x,w,u,v) ),
inference(resolve,[status(thm)],[c_436,c_590]) ).
cnf(c_17249,plain,
( between(u,x,v)
| ~ between(x,u,w) ),
inference(resolve,[status(thm)],[c_509,c_20685]) ).
cnf(c_20686,plain,
( between(v,u,x)
| ~ between(u,v,w)
| ~ equidistant(u,w,v,x) ),
inference(resolve,[status(thm)],[c_436,c_551]) ).
cnf(c_20687,plain,
( between(v,u,x)
| ~ between(u,v,w) ),
inference(resolve,[status(thm)],[c_122,c_20686]) ).
cnf(c_17256,plain,
between(v,u,x),
inference(resolve,[status(thm)],[c_16071,c_20687]) ).
cnf(c_17474,plain,
between(x,u,v),
inference(resolve,[status(thm)],[c_17256,c_59]) ).
cnf(c_20688,plain,
( u = x
| ~ between(u,x,v) ),
inference(resolve,[status(thm)],[c_17474,c_61]) ).
cnf(c_20689,plain,
( x = u
| ~ between(u,x,v) ),
inference(copy,[status(thm)],[c_20688]) ).
cnf(c_17919,plain,
~ between(u,x,v),
inference(resolve,[status(thm)],[c_127,c_20689]) ).
cnf(c_17936,plain,
~ between(x,u,w),
inference(resolve,[status(thm)],[c_17919,c_17249]) ).
cnf(c_20690,plain,
between(x,u,w),
inference(resolve,[status(thm)],[c_16272,c_17474]) ).
cnf(c_20676,plain,
$false,
inference(resolve,[status(thm)],[c_17936,c_20690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO070-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 12:38:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3187284 was started by sandbox on n004,
% 0.09/0.35 % Fri Sep 25 12:38:51 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 21.43/3.14
% 21.43/3.14 % given #500 (W,wt=16): 1035 -colinear(A,y,w) | colinear(A,u,y) | y = w. [resolve(649,a,118,a),flip(c)].
% 21.43/3.14
% 21.43/3.14 % given #1000 (T,wt=12): 17700 colinear(x,y,w) | w = u. [resolve(17445,a,9223,a)].
% 21.43/3.14
% 21.43/3.14 % SZS status Unsatisfiable for theBenchmark
% 21.43/3.14
% 21.43/3.14 % Proof 1 at 2.33 (+ 0.43) seconds.
% 21.43/3.14 % Length of proof is 53.
% 21.43/3.14 % Level of proof is 16.
% 21.43/3.14 % Maximum clause weight is 32.000.
% 21.43/3.14 % Given clauses 1108.
% 21.43/3.14
% 21.43/3.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------