%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO041-2 : 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 : n018.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 55.37s 10.43s
% Output : CNFRefutation 55.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 31 unt; 0 def)
% Number of atoms : 63 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 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 : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 70 ( 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_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(w_between_u_and_v,axiom,
between(u,w,v),
file('theBenchmark.p',w_between_u_and_v) ).
cnf(c_20,plain,
between(u,w,v),
inference(clausify,[status(thm)],[w_between_u_and_v]) ).
fof(prove_v_is_w,axiom,
v != w,
file('theBenchmark.p',prove_v_is_w) ).
cnf(c_21,plain,
v != w,
inference(clausify,[status(thm)],[prove_v_is_w]) ).
cnf(c_22,plain,
w != v,
inference(copy,[status(thm)],[c_21]) ).
cnf(c_2254,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_42,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_2254]) ).
cnf(c_109,plain,
( between(v,inner_pasch(A,B,w,v,u),A)
| ~ between(A,B,w) ),
inference(resolve,[status(thm)],[c_19,c_9]) ).
cnf(c_111,plain,
( between(B,inner_pasch(A,B,w,v,u),u)
| ~ between(A,B,w) ),
inference(resolve,[status(thm)],[c_19,c_8]) ).
cnf(c_129,plain,
( between(w,inner_pasch(A,B,v,w,u),A)
| ~ between(A,B,v) ),
inference(resolve,[status(thm)],[c_20,c_9]) ).
cnf(c_131,plain,
( between(B,inner_pasch(A,B,v,w,u),u)
| ~ between(A,B,v) ),
inference(resolve,[status(thm)],[c_20,c_8]) ).
cnf(c_139,plain,
~ between(w,v,w),
inference(resolve,[status(thm)],[c_7,c_22]) ).
cnf(c_202,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_42,c_4]) ).
cnf(c_568,plain,
between(v,inner_pasch(A,w,w,v,u),A),
inference(resolve,[status(thm)],[c_109,c_202]) ).
cnf(c_2255,plain,
v = inner_pasch(v,w,w,v,u),
inference(resolve,[status(thm)],[c_568,c_7]) ).
cnf(c_588,plain,
inner_pasch(v,w,w,v,u) = v,
inference(copy,[status(thm)],[c_2255]) ).
cnf(c_620,plain,
between(w,inner_pasch(A,w,w,v,u),u),
inference(resolve,[status(thm)],[c_111,c_202]) ).
cnf(c_641,plain,
between(w,v,u),
inference(paramod,[status(thm)],[c_588,c_620]) ).
cnf(c_658,plain,
( between(v,inner_pasch(A,B,u,v,w),A)
| ~ between(A,B,u) ),
inference(resolve,[status(thm)],[c_641,c_9]) ).
cnf(c_660,plain,
( between(B,inner_pasch(A,B,u,v,w),w)
| ~ between(A,B,u) ),
inference(resolve,[status(thm)],[c_641,c_8]) ).
cnf(c_772,plain,
between(w,inner_pasch(A,v,v,w,u),A),
inference(resolve,[status(thm)],[c_129,c_202]) ).
cnf(c_2256,plain,
w = inner_pasch(w,v,v,w,u),
inference(resolve,[status(thm)],[c_772,c_7]) ).
cnf(c_796,plain,
inner_pasch(w,v,v,w,u) = w,
inference(copy,[status(thm)],[c_2256]) ).
cnf(c_842,plain,
between(v,inner_pasch(A,v,v,w,u),u),
inference(resolve,[status(thm)],[c_131,c_202]) ).
cnf(c_863,plain,
between(v,w,u),
inference(paramod,[status(thm)],[c_796,c_842]) ).
cnf(c_2063,plain,
between(v,inner_pasch(v,w,u,v,w),v),
inference(resolve,[status(thm)],[c_658,c_863]) ).
cnf(c_2257,plain,
v = inner_pasch(v,w,u,v,w),
inference(resolve,[status(thm)],[c_2063,c_7]) ).
cnf(c_2131,plain,
inner_pasch(v,w,u,v,w) = v,
inference(copy,[status(thm)],[c_2257]) ).
cnf(c_2258,plain,
between(w,inner_pasch(v,w,u,v,w),w),
inference(resolve,[status(thm)],[c_660,c_863]) ).
cnf(c_2259,plain,
between(w,v,w),
inference(paramod,[status(thm)],[c_2131,c_2258]) ).
cnf(c_2253,plain,
$false,
inference(resolve,[status(thm)],[c_139,c_2259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO041-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 12:37:06 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1961139 was started by sandbox on n018,
% 0.10/0.36 % Fri Sep 25 12:37:06 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 55.37/10.43
% 55.37/10.43 % SZS status Unsatisfiable for theBenchmark
% 55.37/10.43
% 55.37/10.43 % Proof 1 at 1.97 (+ 0.05) seconds.
% 55.37/10.43 % Length of proof is 30.
% 55.37/10.43 % Level of proof is 9.
% 55.37/10.43 % Maximum clause weight is 27.000.
% 55.37/10.43 % Given clauses 241.
% 55.37/10.43
% 55.37/10.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------