%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO026-2 : 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 : 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 07:16:48 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 21 unt; 0 def)
% Number of atoms : 80 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 88 ( 44 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 81 ( 3 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_for_equidistance,axiom,
! [VAR_0,VAR_1] : equidistant(VAR_0,VAR_1,VAR_1,VAR_0),
file('theBenchmark.p',reflexivity_for_equidistance) ).
cnf(c_1,plain,
equidistant(A,B,B,A),
inference(clausify,[status(thm)],[reflexivity_for_equidistance]) ).
fof(transitivity_for_equidistance,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equidistant(VAR_2,VAR_3,VAR_4,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_4,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',transitivity_for_equidistance) ).
cnf(c_2,plain,
( equidistant(C,D,E,F)
| ~ equidistant(A,B,E,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[transitivity_for_equidistance]) ).
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_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(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(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_19,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(v_between_u_and_x,axiom,
between(u,v,x),
file('theBenchmark.p',v_between_u_and_x) ).
cnf(c_20,plain,
between(u,v,x),
inference(clausify,[status(thm)],[v_between_u_and_x]) ).
fof(v_to_w_equals_v_to_x,axiom,
equidistant(v,w,v,x),
file('theBenchmark.p',v_to_w_equals_v_to_x) ).
cnf(c_21,plain,
equidistant(v,w,v,x),
inference(clausify,[status(thm)],[v_to_w_equals_v_to_x]) ).
fof(u_not_v,axiom,
u != v,
file('theBenchmark.p',u_not_v) ).
cnf(c_22,plain,
u != v,
inference(clausify,[status(thm)],[u_not_v]) ).
fof(prove_w_is_x,axiom,
w != x,
file('theBenchmark.p',prove_w_is_x) ).
cnf(c_23,plain,
w != x,
inference(clausify,[status(thm)],[prove_w_is_x]) ).
cnf(c_24,plain,
x != w,
inference(copy,[status(thm)],[c_23]) ).
cnf(c_25,plain,
( equidistant(C,D,C,D)
| ~ equidistant(A,B,C,D) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_42,plain,
( equidistant(B,A,C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_43,plain,
( equidistant(C,D,B,A)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_166,plain,
~ equidistant(x,w,A,A),
inference(resolve,[status(thm)],[c_3,c_24]) ).
cnf(c_170,plain,
equidistant(A,B,A,B),
inference(resolve,[status(thm)],[c_25,c_5]) ).
cnf(c_206,plain,
equidistant(w,v,v,x),
inference(resolve,[status(thm)],[c_42,c_21]) ).
cnf(c_273,plain,
equidistant(v,x,v,w),
inference(resolve,[status(thm)],[c_206,c_43]) ).
cnf(c_316,plain,
( equidistant(B,E,C,F)
| D = A
| ~ between(D,A,C)
| ~ between(D,A,B)
| ~ equidistant(A,E,A,F)
| ~ equidistant(D,E,D,F)
| ~ equidistant(A,B,A,C) ),
inference(resolve,[status(thm)],[c_6,c_170]) ).
cnf(c_317,plain,
( equidistant(B,D,C,D)
| E = A
| ~ between(E,A,C)
| ~ between(E,A,B)
| ~ equidistant(A,D,A,D)
| ~ equidistant(A,B,A,C) ),
inference(resolve,[status(thm)],[c_316,c_170]) ).
cnf(c_318,plain,
( equidistant(B,E,C,E)
| D = A
| ~ between(D,A,C)
| ~ between(D,A,B)
| ~ equidistant(A,B,A,C) ),
inference(resolve,[status(thm)],[c_317,c_170]) ).
cnf(c_319,plain,
( equidistant(x,B,A,B)
| u = v
| ~ between(u,v,A)
| ~ equidistant(v,x,v,A) ),
inference(resolve,[status(thm)],[c_318,c_20]) ).
cnf(c_320,plain,
( equidistant(x,A,w,A)
| u = v
| ~ equidistant(v,x,v,w) ),
inference(resolve,[status(thm)],[c_319,c_19]) ).
cnf(c_321,plain,
( equidistant(x,A,w,A)
| ~ equidistant(v,x,v,w) ),
inference(resolve,[status(thm)],[c_320,c_22]) ).
cnf(c_322,plain,
~ equidistant(v,x,v,w),
inference(resolve,[status(thm)],[c_321,c_166]) ).
cnf(c_315,plain,
$false,
inference(resolve,[status(thm)],[c_273,c_322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO026-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n007.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 12:30:53 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.41 % Process 995645 was started by sandbox on n007,
% 0.16/0.41 % Fri Sep 25 12:30:53 2026
% 0.16/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.42
% 0.16/0.42 % From the command line: assign(max_seconds, 300).
% 0.16/0.50
% 0.16/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.50
% 0.16/0.50 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.16/0.50 % Length of proof is 19.
% 0.16/0.50 % Level of proof is 4.
% 0.16/0.50 % Maximum clause weight is 41.000.
% 0.16/0.50 % Given clauses 55.
% 0.16/0.50
% 0.16/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------