%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO029-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:16:49 AM UTC 2026
% Result : Unsatisfiable 6.71s 1.33s
% Output : CNFRefutation 6.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 81 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 93 ( 48 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 119 ( 9 sgn 27 !; 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_construction1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : between(VAR_0,VAR_1,extension(VAR_0,VAR_1,VAR_2,VAR_3)),
file('theBenchmark.p',segment_construction1) ).
cnf(c_4,plain,
between(A,B,extension(A,B,C,D)),
inference(clausify,[status(thm)],[segment_construction1]) ).
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(u_not_v,axiom,
u != v,
file('theBenchmark.p',u_not_v) ).
cnf(c_19,plain,
u != v,
inference(clausify,[status(thm)],[u_not_v]) ).
cnf(c_20,plain,
v != u,
inference(copy,[status(thm)],[c_19]) ).
fof(prove_equal_extensions,axiom,
extension(u,v,u,v) != extension(u,v,v,u),
file('theBenchmark.p',prove_equal_extensions) ).
cnf(c_21,plain,
extension(u,v,u,v) != extension(u,v,v,u),
inference(clausify,[status(thm)],[prove_equal_extensions]) ).
cnf(c_22,plain,
extension(u,v,v,u) != extension(u,v,u,v),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_23,plain,
( equidistant(C,D,C,D)
| ~ equidistant(A,B,C,D) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_40,plain,
( equidistant(B,A,C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_44,plain,
( equidistant(C,D,E,F)
| ~ equidistant(A,extension(B,A,C,D),E,F) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_66,plain,
~ equidistant(extension(u,v,v,u),extension(u,v,u,v),A,A),
inference(resolve,[status(thm)],[c_3,c_22]) ).
cnf(c_69,plain,
equidistant(A,B,A,B),
inference(resolve,[status(thm)],[c_23,c_5]) ).
cnf(c_139,plain,
equidistant(A,B,C,extension(D,C,A,B)),
inference(resolve,[status(thm)],[c_44,c_69]) ).
cnf(c_175,plain,
equidistant(A,B,C,extension(D,C,B,A)),
inference(resolve,[status(thm)],[c_139,c_40]) ).
cnf(c_217,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_69]) ).
cnf(c_218,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_217,c_69]) ).
cnf(c_219,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_218,c_69]) ).
cnf(c_220,plain,
( equidistant(extension(B,A,C,D),F,E,F)
| B = A
| ~ between(B,A,E)
| ~ equidistant(A,extension(B,A,C,D),A,E) ),
inference(resolve,[status(thm)],[c_219,c_4]) ).
cnf(c_221,plain,
( equidistant(extension(B,A,C,D),V6,extension(B,A,E,F),V6)
| B = A
| ~ equidistant(A,extension(B,A,C,D),A,extension(B,A,E,F)) ),
inference(resolve,[status(thm)],[c_220,c_4]) ).
cnf(c_222,plain,
u != v,
inference(copy,[status(thm)],[c_20]) ).
cnf(c_223,plain,
( equidistant(extension(u,v,A,B),E,extension(u,v,C,D),E)
| ~ equidistant(v,extension(u,v,A,B),v,extension(u,v,C,D)) ),
inference(resolve,[status(thm)],[c_221,c_222]) ).
cnf(c_189,plain,
~ equidistant(v,extension(u,v,v,u),v,extension(u,v,u,v)),
inference(resolve,[status(thm)],[c_223,c_66]) ).
cnf(c_224,plain,
( equidistant(C,D,E,extension(F,E,B,A))
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_175]) ).
cnf(c_225,plain,
~ equidistant(v,u,v,extension(u,v,v,u)),
inference(resolve,[status(thm)],[c_224,c_189]) ).
cnf(c_216,plain,
$false,
inference(resolve,[status(thm)],[c_139,c_225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO029-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 12:34:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 180465 was started by sandbox2 on n003,
% 0.11/0.37 % Fri Sep 25 12:34:52 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 6.71/1.33
% 6.71/1.33 % SZS status Unsatisfiable for theBenchmark
% 6.71/1.33
% 6.71/1.33 % Proof 1 at 0.70 (+ 0.02) seconds.
% 6.71/1.33 % Length of proof is 19.
% 6.71/1.33 % Level of proof is 5.
% 6.71/1.33 % Maximum clause weight is 38.000.
% 6.71/1.33 % Given clauses 83.
% 6.71/1.33
% 6.71/1.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------