%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO032-3 : 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 : 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 07:16:50 AM UTC 2026
% Result : Unsatisfiable 2.14s 0.68s
% Output : CNFRefutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 57 ( 30 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 29 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7,axiom,
! [VAR_0,VAR_1] : equidistant(VAR_0,VAR_0,VAR_1,VAR_1),
file('theBenchmark.p',d7) ).
cnf(c_41,plain,
equidistant(A,A,B,B),
inference(clausify,[status(thm)],[d7]) ).
fof(d12,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( equidistant(VAR_1,VAR_6,VAR_3,VAR_7)
| ~ between(VAR_2,VAR_3,VAR_5)
| ~ between(VAR_0,VAR_1,VAR_4)
| ~ equidistant(VAR_4,VAR_6,VAR_5,VAR_7)
| ~ equidistant(VAR_0,VAR_6,VAR_2,VAR_7)
| ~ equidistant(VAR_0,VAR_4,VAR_2,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d12) ).
cnf(c_74,plain,
( equidistant(B,V6,D,V7)
| ~ between(C,D,F)
| ~ between(A,B,E)
| ~ equidistant(E,V6,F,V7)
| ~ equidistant(A,V6,C,V7)
| ~ equidistant(A,E,C,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d12]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_75,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(v1_between_u1_and_w1,axiom,
between(u1,v1,w1),
file('theBenchmark.p',v1_between_u1_and_w1) ).
cnf(c_76,plain,
between(u1,v1,w1),
inference(clausify,[status(thm)],[v1_between_u1_and_w1]) ).
fof(u_to_v_equals_u1_to_v1,axiom,
equidistant(u,v,u1,v1),
file('theBenchmark.p',u_to_v_equals_u1_to_v1) ).
cnf(c_77,plain,
equidistant(u,v,u1,v1),
inference(clausify,[status(thm)],[u_to_v_equals_u1_to_v1]) ).
fof(u_to_w_equals_u1_to_w1,axiom,
equidistant(u,w,u1,w1),
file('theBenchmark.p',u_to_w_equals_u1_to_w1) ).
cnf(c_78,plain,
equidistant(u,w,u1,w1),
inference(clausify,[status(thm)],[u_to_w_equals_u1_to_w1]) ).
fof(v_to_w_equals_v1_to_w1,axiom,
~ equidistant(v,w,v1,w1),
file('theBenchmark.p',v_to_w_equals_v1_to_w1) ).
cnf(c_79,plain,
~ equidistant(v,w,v1,w1),
inference(clausify,[status(thm)],[v_to_w_equals_v1_to_w1]) ).
cnf(c_587,plain,
( equidistant(A,C,B,D)
| ~ between(u1,B,w1)
| ~ between(u,A,w)
| ~ equidistant(w,C,w1,D)
| ~ equidistant(u,C,u1,D)
| ~ equidistant(u,A,u1,B) ),
inference(resolve,[status(thm)],[c_74,c_78]) ).
cnf(c_588,plain,
( equidistant(A,w,B,w1)
| ~ between(u1,B,w1)
| ~ between(u,A,w)
| ~ equidistant(w,w,w1,w1)
| ~ equidistant(u,A,u1,B) ),
inference(resolve,[status(thm)],[c_587,c_78]) ).
cnf(c_589,plain,
( equidistant(A,w,B,w1)
| ~ between(u1,B,w1)
| ~ between(u,A,w)
| ~ equidistant(u,A,u1,B) ),
inference(resolve,[status(thm)],[c_588,c_41]) ).
cnf(c_590,plain,
( equidistant(v,w,A,w1)
| ~ between(u1,A,w1)
| ~ equidistant(u,v,u1,A) ),
inference(resolve,[status(thm)],[c_589,c_75]) ).
cnf(c_591,plain,
( equidistant(v,w,v1,w1)
| ~ equidistant(u,v,u1,v1) ),
inference(resolve,[status(thm)],[c_590,c_76]) ).
cnf(c_592,plain,
~ equidistant(u,v,u1,v1),
inference(resolve,[status(thm)],[c_591,c_79]) ).
cnf(c_586,plain,
$false,
inference(resolve,[status(thm)],[c_77,c_592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO032-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n007.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Sep 25 12:32:23 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 998215 was started by sandbox on n007,
% 0.12/0.36 % Fri Sep 25 12:32:23 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 2.14/0.68
% 2.14/0.68 % SZS status Unsatisfiable for theBenchmark
% 2.14/0.68
% 2.14/0.68 % Proof 1 at 0.30 (+ 0.01) seconds.
% 2.14/0.68 % Length of proof is 8.
% 2.14/0.68 % Level of proof is 1.
% 2.14/0.68 % Maximum clause weight is 38.000.
% 2.14/0.68 % Given clauses 66.
% 2.14/0.68
% 2.14/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------