%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO030-3 : 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 : 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 07:16:50 AM UTC 2026
% Result : Unsatisfiable 6.45s 1.53s
% Output : CNFRefutation 6.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 21 unt; 0 def)
% Number of atoms : 72 ( 17 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 81 ( 42 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 52 ( 0 sgn 17 !; 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(outer_five_segment,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( equidistant(VAR_4,VAR_6,VAR_5,VAR_7)
| VAR_0 = VAR_1
| ~ between(VAR_2,VAR_3,VAR_5)
| ~ between(VAR_0,VAR_1,VAR_4)
| ~ equidistant(VAR_1,VAR_6,VAR_3,VAR_7)
| ~ equidistant(VAR_0,VAR_6,VAR_2,VAR_7)
| ~ equidistant(VAR_1,VAR_4,VAR_3,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',outer_five_segment) ).
cnf(c_6,plain,
( equidistant(E,V6,F,V7)
| A = B
| ~ between(C,D,F)
| ~ between(A,B,E)
| ~ equidistant(B,V6,D,V7)
| ~ equidistant(A,V6,C,V7)
| ~ equidistant(B,E,D,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[outer_five_segment]) ).
fof(d1,axiom,
! [VAR_0,VAR_1] : equidistant(VAR_0,VAR_1,VAR_0,VAR_1),
file('theBenchmark.p',d1) ).
cnf(c_20,plain,
equidistant(A,B,A,B),
inference(clausify,[status(thm)],[d1]) ).
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_21,plain,
( equidistant(C,D,A,B)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d2]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_73,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(u_to_w_equals_u_to_w1,axiom,
equidistant(u,w,u,w1),
file('theBenchmark.p',u_to_w_equals_u_to_w1) ).
cnf(c_74,plain,
equidistant(u,w,u,w1),
inference(clausify,[status(thm)],[u_to_w_equals_u_to_w1]) ).
fof(v_to_w_equals_v_to_w1,axiom,
equidistant(v,w,v,w1),
file('theBenchmark.p',v_to_w_equals_v_to_w1) ).
cnf(c_75,plain,
equidistant(v,w,v,w1),
inference(clausify,[status(thm)],[v_to_w_equals_v_to_w1]) ).
fof(u_not_v,axiom,
u != v,
file('theBenchmark.p',u_not_v) ).
cnf(c_76,plain,
u != v,
inference(clausify,[status(thm)],[u_not_v]) ).
cnf(c_77,plain,
v != u,
inference(copy,[status(thm)],[c_76]) ).
fof(prove_w_is_w1,axiom,
w != w1,
file('theBenchmark.p',prove_w_is_w1) ).
cnf(c_78,plain,
w != w1,
inference(clausify,[status(thm)],[prove_w_is_w1]) ).
cnf(c_79,plain,
w1 != w,
inference(copy,[status(thm)],[c_78]) ).
cnf(c_804,plain,
( equidistant(C,D,C,E)
| A = B
| ~ between(A,B,C)
| ~ equidistant(B,D,B,E)
| ~ equidistant(A,D,A,E)
| ~ equidistant(B,C,B,C)
| ~ equidistant(A,B,A,B) ),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_805,plain,
( equidistant(B,D,B,E)
| C = A
| ~ between(C,A,B)
| ~ equidistant(A,D,A,E)
| ~ equidistant(C,D,C,E)
| ~ equidistant(A,B,A,B) ),
inference(resolve,[status(thm)],[c_20,c_804]) ).
cnf(c_80,plain,
( equidistant(E,B,E,C)
| A = D
| ~ between(A,D,E)
| ~ equidistant(D,B,D,C)
| ~ equidistant(A,B,A,C) ),
inference(resolve,[status(thm)],[c_20,c_805]) ).
cnf(c_311,plain,
equidistant(u,w1,u,w),
inference(resolve,[status(thm)],[c_74,c_21]) ).
cnf(c_333,plain,
equidistant(v,w1,v,w),
inference(resolve,[status(thm)],[c_75,c_21]) ).
cnf(c_806,plain,
w != w1,
inference(copy,[status(thm)],[c_79]) ).
cnf(c_363,plain,
~ equidistant(w,w1,A,A),
inference(resolve,[status(thm)],[c_3,c_806]) ).
cnf(c_807,plain,
( equidistant(B,w1,B,w)
| A = v
| ~ between(A,v,B)
| ~ equidistant(A,w1,A,w) ),
inference(resolve,[status(thm)],[c_80,c_333]) ).
cnf(c_808,plain,
( equidistant(w,w1,w,w)
| u = v
| ~ equidistant(u,w1,u,w) ),
inference(resolve,[status(thm)],[c_807,c_73]) ).
cnf(c_809,plain,
u != v,
inference(copy,[status(thm)],[c_77]) ).
cnf(c_810,plain,
( equidistant(w,w1,w,w)
| ~ equidistant(u,w1,u,w) ),
inference(resolve,[status(thm)],[c_808,c_809]) ).
cnf(c_811,plain,
~ equidistant(u,w1,u,w),
inference(resolve,[status(thm)],[c_810,c_363]) ).
cnf(c_803,plain,
$false,
inference(resolve,[status(thm)],[c_311,c_811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO030-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 12:33:52 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3176635 was started by sandbox on n004,
% 0.09/0.37 % Fri Sep 25 12:33:52 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 6.45/1.53
% 6.45/1.53 % SZS status Unsatisfiable for theBenchmark
% 6.45/1.53
% 6.45/1.53 % Proof 1 at 0.81 (+ 0.03) seconds.
% 6.45/1.53 % Length of proof is 16.
% 6.45/1.53 % Level of proof is 3.
% 6.45/1.53 % Maximum clause weight is 38.000.
% 6.45/1.53 % Given clauses 168.
% 6.45/1.53
% 6.45/1.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------