%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO020-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 07:16:47 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_20,plain,
( equidistant(C,D,A,B)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d2]) ).
fof(d3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equidistant(VAR_1,VAR_0,VAR_2,VAR_3)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d3) ).
cnf(c_21,plain,
( equidistant(B,A,C,D)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d3]) ).
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_22,plain,
equidistant(u,v,w,x),
inference(clausify,[status(thm)],[u_to_v_equals_w_to_x]) ).
fof(prove_symmetry,axiom,
~ equidistant(x,w,u,v),
file('theBenchmark.p',prove_symmetry) ).
cnf(c_23,plain,
~ equidistant(x,w,u,v),
inference(clausify,[status(thm)],[prove_symmetry]) ).
cnf(c_100,plain,
equidistant(w,x,u,v),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_111,plain,
~ equidistant(w,x,u,v),
inference(resolve,[status(thm)],[c_21,c_23]) ).
cnf(c_110,plain,
$false,
inference(resolve,[status(thm)],[c_100,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO020-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 12:32:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 227954 was started by sandbox on n014,
% 0.10/0.36 % Fri Sep 25 12:32:47 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 6.
% 0.10/0.38 % Level of proof is 2.
% 0.10/0.38 % Maximum clause weight is 10.000.
% 0.10/0.38 % Given clauses 23.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------