%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO025-3 : 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 : n001.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 2.50s 0.79s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 51 ( 29 unt; 0 def)
% Number of atoms : 104 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 105 ( 52 ~; 53 |; 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 : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 92 ( 0 sgn 41 !; 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(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(d4_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equidistant(VAR_1,VAR_0,VAR_3,VAR_2)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d4_2) ).
cnf(c_24,plain,
( equidistant(B,A,D,C)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d4_2]) ).
fof(d4_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equidistant(VAR_2,VAR_3,VAR_1,VAR_0)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d4_3) ).
cnf(c_25,plain,
( equidistant(C,D,B,A)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d4_3]) ).
fof(d4_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equidistant(VAR_3,VAR_2,VAR_1,VAR_0)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d4_5) ).
cnf(c_27,plain,
( equidistant(D,C,B,A)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d4_5]) ).
fof(d5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equidistant(VAR_0,VAR_1,VAR_4,VAR_5)
| ~ equidistant(VAR_2,VAR_3,VAR_4,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d5) ).
cnf(c_28,plain,
( equidistant(A,B,E,F)
| ~ equidistant(C,D,E,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d5]) ).
fof(d7,axiom,
! [VAR_0,VAR_1] : equidistant(VAR_0,VAR_0,VAR_1,VAR_1),
file('theBenchmark.p',d7) ).
cnf(c_40,plain,
equidistant(A,A,B,B),
inference(clausify,[status(thm)],[d7]) ).
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_41,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_42,plain,
equidistant(v,w,v1,w1),
inference(clausify,[status(thm)],[v_to_w_equals_v1_to_w1]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_43,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_44,plain,
between(u1,v1,w1),
inference(clausify,[status(thm)],[v1_between_u1_and_w1]) ).
fof(prove_equal_sums,axiom,
~ equidistant(u,w,u1,w1),
file('theBenchmark.p',prove_equal_sums) ).
cnf(c_45,plain,
~ equidistant(u,w,u1,w1),
inference(clausify,[status(thm)],[prove_equal_sums]) ).
cnf(c_147,plain,
equidistant(v,u,v1,u1),
inference(resolve,[status(thm)],[c_41,c_24]) ).
cnf(c_162,plain,
equidistant(v1,w1,w,v),
inference(resolve,[status(thm)],[c_42,c_25]) ).
cnf(c_223,plain,
~ equidistant(w1,u1,w,u),
inference(resolve,[status(thm)],[c_27,c_45]) ).
cnf(c_226,plain,
~ equidistant(w,u,w1,u1),
inference(resolve,[status(thm)],[c_24,c_45]) ).
cnf(c_547,plain,
( equidistant(A,C,B,D)
| u = v
| ~ between(u1,v1,B)
| ~ between(u,v,A)
| ~ equidistant(v,C,v1,D)
| ~ equidistant(u,C,u1,D)
| ~ equidistant(v,A,v1,B) ),
inference(resolve,[status(thm)],[c_6,c_41]) ).
cnf(c_548,plain,
( equidistant(w,A,w1,B)
| u = v
| ~ between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,A,v1,B)
| ~ equidistant(u,A,u1,B) ),
inference(resolve,[status(thm)],[c_547,c_42]) ).
cnf(c_549,plain,
( equidistant(w,u,w1,u1)
| u = v
| ~ between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,u,v1,u1) ),
inference(resolve,[status(thm)],[c_548,c_40]) ).
cnf(c_550,plain,
( equidistant(w,u,w1,u1)
| u = v
| ~ between(u1,v1,w1)
| ~ between(u,v,w) ),
inference(resolve,[status(thm)],[c_549,c_147]) ).
cnf(c_551,plain,
( equidistant(w,u,w1,u1)
| u = v
| ~ between(u1,v1,w1) ),
inference(resolve,[status(thm)],[c_550,c_43]) ).
cnf(c_552,plain,
( equidistant(w,u,w1,u1)
| u = v ),
inference(resolve,[status(thm)],[c_551,c_44]) ).
cnf(c_350,plain,
u = v,
inference(resolve,[status(thm)],[c_226,c_552]) ).
cnf(c_553,plain,
( equidistant(v1,u1,A,B)
| ~ equidistant(v,u,A,B) ),
inference(resolve,[status(thm)],[c_2,c_147]) ).
cnf(c_554,plain,
equidistant(v1,u1,v,u),
inference(resolve,[status(thm)],[c_553,c_20]) ).
cnf(c_352,plain,
equidistant(v1,u1,v,v),
inference(paramod,[status(thm)],[c_350,c_554]) ).
cnf(c_406,plain,
~ equidistant(w1,u1,w,v),
inference(paramod,[status(thm)],[c_350,c_223]) ).
cnf(c_555,plain,
( equidistant(A,B,w,v)
| ~ equidistant(A,B,v1,w1) ),
inference(resolve,[status(thm)],[c_28,c_162]) ).
cnf(c_516,plain,
~ equidistant(w1,u1,v1,w1),
inference(resolve,[status(thm)],[c_555,c_406]) ).
cnf(c_556,plain,
v1 = u1,
inference(resolve,[status(thm)],[c_352,c_3]) ).
cnf(c_541,plain,
u1 = v1,
inference(copy,[status(thm)],[c_556]) ).
cnf(c_557,plain,
~ equidistant(w1,v1,v1,w1),
inference(paramod,[status(thm)],[c_541,c_516]) ).
cnf(c_546,plain,
$false,
inference(resolve,[status(thm)],[c_1,c_557]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO025-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.34 % Computer : n001.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Fri Sep 25 12:38:40 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.34 % Process 3293449 was started by sandbox2 on n001,
% 0.06/0.34 % Fri Sep 25 12:38:40 2026
% 0.06/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.06/0.35
% 0.06/0.35 % From the command line: assign(max_seconds, 300).
% 2.50/0.79
% 2.50/0.79 % SZS status Unsatisfiable for theBenchmark
% 2.50/0.79
% 2.50/0.79 % Proof 1 at 0.36 (+ 0.05) seconds.
% 2.50/0.79 % Length of proof is 25.
% 2.50/0.79 % Level of proof is 5.
% 2.50/0.79 % Maximum clause weight is 41.000.
% 2.50/0.79 % Given clauses 75.
% 2.50/0.79
% 2.50/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------