%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO025-2 : 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 : n008.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 2.02s 0.67s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 33 unt; 0 def)
% Number of atoms : 135 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 140 ( 67 ~; 73 |; 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 : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 100 ( 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(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_19,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_20,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_21,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_22,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_23,plain,
~ equidistant(u,w,u1,w1),
inference(clausify,[status(thm)],[prove_equal_sums]) ).
cnf(c_41,plain,
( equidistant(B,A,C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_663,plain,
( equidistant(B,A,C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_43,plain,
equidistant(A,B,A,B),
inference(resolve,[status(thm)],[c_663,c_1]) ).
cnf(c_664,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_45,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_664]) ).
cnf(c_665,plain,
( equidistant(u1,v1,A,B)
| ~ equidistant(u,v,A,B) ),
inference(resolve,[status(thm)],[c_2,c_19]) ).
cnf(c_106,plain,
equidistant(u1,v1,v,u),
inference(resolve,[status(thm)],[c_665,c_1]) ).
cnf(c_666,plain,
( equidistant(C,D,B,A)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_162,plain,
~ equidistant(w1,u1,u,w),
inference(resolve,[status(thm)],[c_666,c_23]) ).
cnf(c_667,plain,
( equidistant(B,A,C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_164,plain,
~ equidistant(w,u,u1,w1),
inference(resolve,[status(thm)],[c_667,c_23]) ).
cnf(c_668,plain,
( equidistant(C,D,B,A)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_182,plain,
~ equidistant(w,u,w1,u1),
inference(resolve,[status(thm)],[c_668,c_162]) ).
cnf(c_669,plain,
( equidistant(C,D,B,A)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_185,plain,
~ equidistant(w1,u1,w,u),
inference(resolve,[status(thm)],[c_669,c_164]) ).
cnf(c_670,plain,
( equidistant(v1,w1,A,B)
| ~ equidistant(v,w,A,B) ),
inference(resolve,[status(thm)],[c_2,c_20]) ).
cnf(c_214,plain,
equidistant(v1,w1,v,w),
inference(resolve,[status(thm)],[c_670,c_43]) ).
cnf(c_671,plain,
( equidistant(u1,v1,A,B)
| ~ equidistant(u,v,A,B) ),
inference(resolve,[status(thm)],[c_2,c_19]) ).
cnf(c_215,plain,
equidistant(u1,v1,u,v),
inference(resolve,[status(thm)],[c_671,c_43]) ).
cnf(c_228,plain,
equidistant(v1,u1,v,u),
inference(resolve,[status(thm)],[c_106,c_41]) ).
cnf(c_672,plain,
( equidistant(v,u,A,B)
| ~ equidistant(u1,v1,A,B) ),
inference(resolve,[status(thm)],[c_2,c_106]) ).
cnf(c_240,plain,
equidistant(v,u,v1,u1),
inference(resolve,[status(thm)],[c_672,c_1]) ).
cnf(c_396,plain,
equidistant(A,A,B,B),
inference(paramod,[status(thm)],[c_45,c_5]) ).
cnf(c_673,plain,
( equidistant(A,C,B,D)
| u1 = v1
| ~ between(u,v,B)
| ~ between(u1,v1,A)
| ~ equidistant(v1,C,v,D)
| ~ equidistant(u1,C,u,D)
| ~ equidistant(v1,A,v,B) ),
inference(resolve,[status(thm)],[c_6,c_215]) ).
cnf(c_674,plain,
( equidistant(w1,A,w,B)
| u1 = v1
| ~ between(u,v,w)
| ~ between(u1,v1,w1)
| ~ equidistant(v1,A,v,B)
| ~ equidistant(u1,A,u,B) ),
inference(resolve,[status(thm)],[c_673,c_214]) ).
cnf(c_675,plain,
( equidistant(w1,u1,w,u)
| u1 = v1
| ~ between(u,v,w)
| ~ between(u1,v1,w1)
| ~ equidistant(v1,u1,v,u) ),
inference(resolve,[status(thm)],[c_674,c_396]) ).
cnf(c_676,plain,
( equidistant(w1,u1,w,u)
| u1 = v1
| ~ between(u,v,w)
| ~ between(u1,v1,w1) ),
inference(resolve,[status(thm)],[c_675,c_228]) ).
cnf(c_677,plain,
( equidistant(w1,u1,w,u)
| u1 = v1
| ~ between(u,v,w) ),
inference(resolve,[status(thm)],[c_676,c_22]) ).
cnf(c_678,plain,
( equidistant(w1,u1,w,u)
| u1 = v1 ),
inference(resolve,[status(thm)],[c_677,c_21]) ).
cnf(c_544,plain,
u1 = v1,
inference(resolve,[status(thm)],[c_185,c_678]) ).
cnf(c_679,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_19]) ).
cnf(c_680,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_679,c_20]) ).
cnf(c_681,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_680,c_396]) ).
cnf(c_682,plain,
( equidistant(w,u,w1,u1)
| u = v
| ~ between(u1,v1,w1)
| ~ between(u,v,w) ),
inference(resolve,[status(thm)],[c_681,c_240]) ).
cnf(c_683,plain,
( equidistant(w,u,w1,u1)
| u = v
| ~ between(u1,v1,w1) ),
inference(resolve,[status(thm)],[c_682,c_21]) ).
cnf(c_684,plain,
( equidistant(w,u,w1,u1)
| u = v ),
inference(resolve,[status(thm)],[c_683,c_22]) ).
cnf(c_553,plain,
( equidistant(w,u,w1,v1)
| u = v ),
inference(paramod,[status(thm)],[c_544,c_684]) ).
cnf(c_641,plain,
~ equidistant(w,u,w1,v1),
inference(paramod,[status(thm)],[c_544,c_182]) ).
cnf(c_659,plain,
~ equidistant(u,w,v1,w1),
inference(paramod,[status(thm)],[c_544,c_23]) ).
cnf(c_661,plain,
u = v,
inference(resolve,[status(thm)],[c_641,c_553]) ).
cnf(c_685,plain,
~ equidistant(v,w,v1,w1),
inference(paramod,[status(thm)],[c_661,c_659]) ).
cnf(c_662,plain,
$false,
inference(resolve,[status(thm)],[c_20,c_685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO025-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 12:33:54 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1048904 was started by sandbox on n008,
% 0.08/0.36 % Fri Sep 25 12:33:54 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 2.02/0.67
% 2.02/0.67 % SZS status Unsatisfiable for theBenchmark
% 2.02/0.67
% 2.02/0.67 % Proof 1 at 0.26 (+ 0.04) seconds.
% 2.02/0.67 % Length of proof is 29.
% 2.02/0.67 % Level of proof is 6.
% 2.02/0.67 % Maximum clause weight is 41.000.
% 2.02/0.67 % Given clauses 77.
% 2.02/0.67
% 2.02/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------