%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO066-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 07:16:57 AM UTC 2026
% Result : Unsatisfiable 2.97s 0.81s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 46 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 66 ( 7 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(identity_for_equidistance,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_2) ),
file('theBenchmark.p',identity_for_equidistance) ).
cnf(c_3,plain,
( A = B
| ~ equidistant(A,B,C,C) ),
inference(clausify,[status(thm)],[identity_for_equidistance]) ).
fof(segment_construction1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : between(VAR_0,VAR_1,extension(VAR_0,VAR_1,VAR_2,VAR_3)),
file('theBenchmark.p',segment_construction1) ).
cnf(c_4,plain,
between(A,B,extension(A,B,C,D)),
inference(clausify,[status(thm)],[segment_construction1]) ).
fof(segment_construction2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : equidistant(VAR_0,extension(VAR_1,VAR_0,VAR_2,VAR_3),VAR_2,VAR_3),
file('theBenchmark.p',segment_construction2) ).
cnf(c_5,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(clausify,[status(thm)],[segment_construction2]) ).
fof(identity_for_betweeness,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ between(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',identity_for_betweeness) ).
cnf(c_7,plain,
( A = B
| ~ between(A,B,A) ),
inference(clausify,[status(thm)],[identity_for_betweeness]) ).
fof(inner_pasch1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_1,inner_pasch(VAR_0,VAR_1,VAR_2,VAR_4,VAR_3),VAR_3)
| ~ between(VAR_3,VAR_4,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',inner_pasch1) ).
cnf(c_8,plain,
( between(B,inner_pasch(A,B,C,E,D),D)
| ~ between(D,E,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[inner_pasch1]) ).
fof(inner_pasch2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_4,inner_pasch(VAR_0,VAR_1,VAR_2,VAR_4,VAR_3),VAR_0)
| ~ between(VAR_3,VAR_4,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',inner_pasch2) ).
cnf(c_9,plain,
( between(E,inner_pasch(A,B,C,E,D),A)
| ~ between(D,E,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[inner_pasch2]) ).
fof(colinearity3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_1,VAR_2,VAR_0)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',colinearity3) ).
cnf(c_21,plain,
( colinear(B,C,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[colinearity3]) ).
fof(u_between_v_and_w,axiom,
between(v,u,w),
file('theBenchmark.p',u_between_v_and_w) ).
cnf(c_23,plain,
between(v,u,w),
inference(clausify,[status(thm)],[u_between_v_and_w]) ).
fof(prove_uvw_colinear,axiom,
~ colinear(u,v,w),
file('theBenchmark.p',prove_uvw_colinear) ).
cnf(c_24,plain,
~ colinear(u,v,w),
inference(clausify,[status(thm)],[prove_uvw_colinear]) ).
cnf(c_1176,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_47,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_1176]) ).
cnf(c_130,plain,
~ between(w,u,v),
inference(resolve,[status(thm)],[c_21,c_24]) ).
cnf(c_168,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_47,c_4]) ).
cnf(c_1177,plain,
( between(B,inner_pasch(v,u,w,B,A),v)
| ~ between(A,B,w) ),
inference(resolve,[status(thm)],[c_9,c_23]) ).
cnf(c_233,plain,
between(w,inner_pasch(v,u,w,w,A),v),
inference(resolve,[status(thm)],[c_1177,c_168]) ).
cnf(c_1178,plain,
( between(u,inner_pasch(v,u,w,B,A),A)
| ~ between(A,B,w) ),
inference(resolve,[status(thm)],[c_8,c_23]) ).
cnf(c_238,plain,
between(u,inner_pasch(v,u,w,w,A),A),
inference(resolve,[status(thm)],[c_1178,c_168]) ).
cnf(c_1179,plain,
u = inner_pasch(v,u,w,w,u),
inference(resolve,[status(thm)],[c_238,c_7]) ).
cnf(c_1047,plain,
inner_pasch(v,u,w,w,u) = u,
inference(copy,[status(thm)],[c_1179]) ).
cnf(c_1180,plain,
between(w,u,v),
inference(paramod,[status(thm)],[c_1047,c_233]) ).
cnf(c_1175,plain,
$false,
inference(resolve,[status(thm)],[c_130,c_1180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO066-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n007.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 12:36:08 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 1006804 was started by sandbox2 on n007,
% 0.15/0.43 % Fri Sep 25 12:36:08 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 2.97/0.81
% 2.97/0.81 % SZS status Unsatisfiable for theBenchmark
% 2.97/0.81
% 2.97/0.81 % Proof 1 at 0.31 (+ 0.06) seconds.
% 2.97/0.81 % Length of proof is 16.
% 2.97/0.81 % Level of proof is 5.
% 2.97/0.81 % Maximum clause weight is 27.000.
% 2.97/0.81 % Given clauses 83.
% 2.97/0.81
% 2.97/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------