%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO048-2 : 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 : 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 07:16:53 AM UTC 2026
% Result : Unsatisfiable 11.49s 2.10s
% Output : CNFRefutation 11.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 28 unt; 0 def)
% Number of atoms : 60 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 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(v1_between_u1_and_w,axiom,
between(u1,v1,w),
file('theBenchmark.p',v1_between_u1_and_w) ).
cnf(c_20,plain,
between(u1,v1,w),
inference(clausify,[status(thm)],[v1_between_u1_and_w]) ).
fof(x_between_u_and_u1,axiom,
between(u,x,u1),
file('theBenchmark.p',x_between_u_and_u1) ).
cnf(c_21,plain,
between(u,x,u1),
inference(clausify,[status(thm)],[x_between_u_and_u1]) ).
fof(prove_conclusion2,axiom,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
file('theBenchmark.p',prove_conclusion2) ).
cnf(c_23,plain,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
inference(clausify,[status(thm)],[prove_conclusion2]) ).
cnf(c_3522,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_3522]) ).
cnf(c_200,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_45,c_4]) ).
cnf(c_3523,plain,
( between(B,inner_pasch(u1,v1,w,B,A),u1)
| ~ between(A,B,w) ),
inference(resolve,[status(thm)],[c_9,c_20]) ).
cnf(c_279,plain,
between(w,inner_pasch(u1,v1,w,w,A),u1),
inference(resolve,[status(thm)],[c_3523,c_200]) ).
cnf(c_3524,plain,
( between(B,inner_pasch(u,v,w,B,A),u)
| ~ between(A,B,w) ),
inference(resolve,[status(thm)],[c_9,c_19]) ).
cnf(c_280,plain,
between(w,inner_pasch(u,v,w,w,A),u),
inference(resolve,[status(thm)],[c_3524,c_200]) ).
cnf(c_3525,plain,
( between(v1,inner_pasch(u1,v1,w,B,A),A)
| ~ between(A,B,w) ),
inference(resolve,[status(thm)],[c_8,c_20]) ).
cnf(c_288,plain,
between(v1,inner_pasch(u1,v1,w,w,A),A),
inference(resolve,[status(thm)],[c_3525,c_200]) ).
cnf(c_3526,plain,
( between(v,inner_pasch(u,v,w,B,A),A)
| ~ between(A,B,w) ),
inference(resolve,[status(thm)],[c_8,c_19]) ).
cnf(c_289,plain,
between(v,inner_pasch(u,v,w,w,A),A),
inference(resolve,[status(thm)],[c_3526,c_200]) ).
cnf(c_3527,plain,
v1 = inner_pasch(u1,v1,w,w,v1),
inference(resolve,[status(thm)],[c_288,c_7]) ).
cnf(c_2789,plain,
inner_pasch(u1,v1,w,w,v1) = v1,
inference(copy,[status(thm)],[c_3527]) ).
cnf(c_2990,plain,
between(w,v1,u1),
inference(paramod,[status(thm)],[c_2789,c_279]) ).
cnf(c_3528,plain,
( between(B,inner_pasch(u,x,u1,B,A),u)
| ~ between(A,B,u1) ),
inference(resolve,[status(thm)],[c_9,c_21]) ).
cnf(c_3101,plain,
between(v1,inner_pasch(u,x,u1,v1,w),u),
inference(resolve,[status(thm)],[c_3528,c_2990]) ).
cnf(c_3529,plain,
v = inner_pasch(u,v,w,w,v),
inference(resolve,[status(thm)],[c_289,c_7]) ).
cnf(c_3160,plain,
inner_pasch(u,v,w,w,v) = v,
inference(copy,[status(thm)],[c_3529]) ).
cnf(c_3352,plain,
between(w,v,u),
inference(paramod,[status(thm)],[c_3160,c_280]) ).
cnf(c_3530,plain,
( between(v,inner_pasch(A,B,u,v,w),A)
| ~ between(A,B,u) ),
inference(resolve,[status(thm)],[c_9,c_3352]) ).
cnf(c_3531,plain,
~ between(v1,inner_pasch(u,x,u1,v1,w),u),
inference(resolve,[status(thm)],[c_3530,c_23]) ).
cnf(c_3521,plain,
$false,
inference(resolve,[status(thm)],[c_3101,c_3531]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 12:36:14 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 1618480 was started by sandbox2 on n009,
% 0.19/0.45 % Fri Sep 25 12:36:14 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 11.49/2.10
% 11.49/2.10 % SZS status Unsatisfiable for theBenchmark
% 11.49/2.10
% 11.49/2.10 % Proof 1 at 1.39 (+ 0.24) seconds.
% 11.49/2.10 % Length of proof is 22.
% 11.49/2.10 % Level of proof is 7.
% 11.49/2.10 % Maximum clause weight is 29.000.
% 11.49/2.10 % Given clauses 85.
% 11.49/2.10
% 11.49/2.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------