%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO033-3 : 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 : n017.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 6.78s 1.37s
% Output : CNFRefutation 6.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 85 ( 44 ~; 41 |; 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 : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 36 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equidistant(VAR_0,VAR_4,VAR_2,VAR_5)
| ~ between(VAR_2,VAR_3,VAR_5)
| ~ between(VAR_0,VAR_1,VAR_4)
| ~ equidistant(VAR_1,VAR_4,VAR_3,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d8) ).
cnf(c_41,plain,
( equidistant(A,E,C,F)
| ~ between(C,D,F)
| ~ between(A,B,E)
| ~ equidistant(B,E,D,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d8]) ).
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(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_76,plain,
equidistant(u,v,u1,v1),
inference(clausify,[status(thm)],[u_to_v_equals_u1_to_v1]) ).
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_77,plain,
equidistant(v,w,v1,w1),
inference(clausify,[status(thm)],[v_to_w_equals_v1_to_w1]) ).
fof(u_to_x_equals_u1_to_x1,axiom,
equidistant(u,x,u1,x1),
file('theBenchmark.p',u_to_x_equals_u1_to_x1) ).
cnf(c_78,plain,
equidistant(u,x,u1,x1),
inference(clausify,[status(thm)],[u_to_x_equals_u1_to_x1]) ).
fof(w_to_x_equals_w1_to_x1,axiom,
equidistant(w,x,w1,x1),
file('theBenchmark.p',w_to_x_equals_w1_to_x1) ).
cnf(c_79,plain,
equidistant(w,x,w1,x1),
inference(clausify,[status(thm)],[w_to_x_equals_w1_to_x1]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_80,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_81,plain,
between(u1,v1,w1),
inference(clausify,[status(thm)],[v1_between_u1_and_w1]) ).
fof(prove_v_to_x_equals_v1_to_x1,axiom,
~ equidistant(v,x,v1,x1),
file('theBenchmark.p',prove_v_to_x_equals_v1_to_x1) ).
cnf(c_82,plain,
~ equidistant(v,x,v1,x1),
inference(clausify,[status(thm)],[prove_v_to_x_equals_v1_to_x1]) ).
cnf(c_794,plain,
( equidistant(u,A,u1,B)
| ~ between(u1,v1,B)
| ~ between(u,v,A)
| ~ equidistant(v,A,v1,B) ),
inference(resolve,[status(thm)],[c_41,c_76]) ).
cnf(c_795,plain,
( equidistant(u,w,u1,w1)
| ~ between(u1,v1,w1)
| ~ between(u,v,w) ),
inference(resolve,[status(thm)],[c_794,c_77]) ).
cnf(c_796,plain,
( equidistant(u,w,u1,w1)
| ~ between(u1,v1,w1) ),
inference(resolve,[status(thm)],[c_795,c_80]) ).
cnf(c_745,plain,
equidistant(u,w,u1,w1),
inference(resolve,[status(thm)],[c_796,c_81]) ).
cnf(c_797,plain,
( equidistant(v,C,v1,D)
| ~ between(u1,v1,B)
| ~ between(u,v,A)
| ~ equidistant(A,C,B,D)
| ~ equidistant(u,C,u1,D)
| ~ equidistant(u,A,u1,B) ),
inference(resolve,[status(thm)],[c_74,c_76]) ).
cnf(c_798,plain,
( equidistant(v,x,v1,x1)
| ~ between(u1,v1,B)
| ~ between(u,v,A)
| ~ equidistant(A,x,B,x1)
| ~ equidistant(u,A,u1,B) ),
inference(resolve,[status(thm)],[c_797,c_78]) ).
cnf(c_799,plain,
( equidistant(v,x,v1,x1)
| ~ between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(u,w,u1,w1) ),
inference(resolve,[status(thm)],[c_798,c_79]) ).
cnf(c_800,plain,
( equidistant(v,x,v1,x1)
| ~ between(u1,v1,w1)
| ~ equidistant(u,w,u1,w1) ),
inference(resolve,[status(thm)],[c_799,c_80]) ).
cnf(c_801,plain,
( equidistant(v,x,v1,x1)
| ~ equidistant(u,w,u1,w1) ),
inference(resolve,[status(thm)],[c_800,c_81]) ).
cnf(c_802,plain,
~ equidistant(u,w,u1,w1),
inference(resolve,[status(thm)],[c_801,c_82]) ).
cnf(c_793,plain,
$false,
inference(resolve,[status(thm)],[c_745,c_802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO033-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n017.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Fri Sep 25 12:29:32 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 2267612 was started by sandbox on n017,
% 0.15/0.44 % Fri Sep 25 12:29:32 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.45
% 0.15/0.45 % From the command line: assign(max_seconds, 300).
% 6.78/1.37
% 6.78/1.37 % SZS status Unsatisfiable for theBenchmark
% 6.78/1.37
% 6.78/1.37 % Proof 1 at 0.81 (+ 0.10) seconds.
% 6.78/1.37 % Length of proof is 11.
% 6.78/1.37 % Level of proof is 2.
% 6.78/1.37 % Maximum clause weight is 38.000.
% 6.78/1.37 % Given clauses 65.
% 6.78/1.37
% 6.78/1.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------