%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO042-2 : 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 : n009.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 07:16:52 AM UTC 2026
% Result : Unsatisfiable 9.41s 2.90s
% Output : CNFRefutation 9.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 24 unt; 0 def)
% Number of atoms : 52 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 68 ( 8 sgn 23 !; 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(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(identity_for_betweeness,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ between(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',identity_for_betweeness) ).
cnf(c_7,plain,
( A = B
| ~ between(A,B,A) ),
inference(clausify,[status(thm)],[identity_for_betweeness]) ).
fof(inner_pasch1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_1,inner_pasch(VAR_0,VAR_1,VAR_2,VAR_4,VAR_3),VAR_3)
| ~ between(VAR_3,VAR_4,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',inner_pasch1) ).
cnf(c_8,plain,
( between(B,inner_pasch(A,B,C,E,D),D)
| ~ between(D,E,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[inner_pasch1]) ).
fof(inner_pasch2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_4,inner_pasch(VAR_0,VAR_1,VAR_2,VAR_4,VAR_3),VAR_0)
| ~ between(VAR_3,VAR_4,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',inner_pasch2) ).
cnf(c_9,plain,
( between(E,inner_pasch(A,B,C,E,D),A)
| ~ between(D,E,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[inner_pasch2]) ).
fof(v_between_u_and_x,axiom,
between(u,v,x),
file('theBenchmark.p',v_between_u_and_x) ).
cnf(c_19,plain,
between(u,v,x),
inference(clausify,[status(thm)],[v_between_u_and_x]) ).
fof(w_between_v_and_x,axiom,
between(v,w,x),
file('theBenchmark.p',w_between_v_and_x) ).
cnf(c_20,plain,
between(v,w,x),
inference(clausify,[status(thm)],[w_between_v_and_x]) ).
fof(prove_v_between_u_and_w,axiom,
~ between(u,v,w),
file('theBenchmark.p',prove_v_between_u_and_w) ).
cnf(c_21,plain,
~ between(u,v,w),
inference(clausify,[status(thm)],[prove_v_between_u_and_w]) ).
cnf(c_3232,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_43,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_3232]) ).
cnf(c_3233,plain,
( between(B,inner_pasch(v,w,x,B,A),v)
| ~ between(A,B,x) ),
inference(resolve,[status(thm)],[c_9,c_20]) ).
cnf(c_138,plain,
between(v,inner_pasch(v,w,x,v,u),v),
inference(resolve,[status(thm)],[c_3233,c_19]) ).
cnf(c_3234,plain,
( between(w,inner_pasch(v,w,x,B,A),A)
| ~ between(A,B,x) ),
inference(resolve,[status(thm)],[c_8,c_20]) ).
cnf(c_140,plain,
between(w,inner_pasch(v,w,x,v,u),u),
inference(resolve,[status(thm)],[c_3234,c_19]) ).
cnf(c_178,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_43,c_4]) ).
cnf(c_3235,plain,
v = inner_pasch(v,w,x,v,u),
inference(resolve,[status(thm)],[c_138,c_7]) ).
cnf(c_424,plain,
inner_pasch(v,w,x,v,u) = v,
inference(copy,[status(thm)],[c_3235]) ).
cnf(c_434,plain,
between(w,v,u),
inference(paramod,[status(thm)],[c_424,c_140]) ).
cnf(c_3236,plain,
( between(B,inner_pasch(D,C,C,B,A),D)
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_178]) ).
cnf(c_471,plain,
between(v,inner_pasch(A,u,u,v,w),A),
inference(resolve,[status(thm)],[c_3236,c_434]) ).
cnf(c_3237,plain,
( between(C,inner_pasch(D,C,C,B,A),A)
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_178]) ).
cnf(c_477,plain,
between(u,inner_pasch(A,u,u,v,w),w),
inference(resolve,[status(thm)],[c_3237,c_434]) ).
cnf(c_3238,plain,
v = inner_pasch(v,u,u,v,w),
inference(resolve,[status(thm)],[c_471,c_7]) ).
cnf(c_2802,plain,
inner_pasch(v,u,u,v,w) = v,
inference(copy,[status(thm)],[c_3238]) ).
cnf(c_3239,plain,
between(u,v,w),
inference(paramod,[status(thm)],[c_2802,c_477]) ).
cnf(c_3231,plain,
$false,
inference(resolve,[status(thm)],[c_21,c_3239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO042-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 12:35:43 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 1616782 was started by sandbox on n009,
% 0.08/0.36 % Fri Sep 25 12:35:43 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.36
% 0.14/0.36 % From the command line: assign(max_seconds, 300).
% 9.41/2.90
% 9.41/2.90 % SZS status Unsatisfiable for theBenchmark
% 9.41/2.90
% 9.41/2.90 % Proof 1 at 1.02 (+ 0.17) seconds.
% 9.41/2.90 % Length of proof is 19.
% 9.41/2.90 % Level of proof is 6.
% 9.41/2.90 % Maximum clause weight is 27.000.
% 9.41/2.90 % Given clauses 88.
% 9.41/2.90
% 9.41/2.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------