%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO048-3 : 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 : n012.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 07:16:54 AM UTC 2026
% Result : Unsatisfiable 1.14s 0.50s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-5 aty)
% Number of variables : 20 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( between(VAR_2,VAR_1,VAR_0)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t1) ).
cnf(c_54,plain,
( between(C,B,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t1]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_72,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_73,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_74,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_76,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_401,plain,
between(w,v,u),
inference(resolve,[status(thm)],[c_72,c_54]) ).
cnf(c_470,plain,
between(w,v1,u1),
inference(resolve,[status(thm)],[c_73,c_54]) ).
cnf(c_770,plain,
( between(v,inner_pasch(A,B,u,v,w),A)
| ~ between(A,B,u) ),
inference(resolve,[status(thm)],[c_9,c_401]) ).
cnf(c_709,plain,
~ between(v1,inner_pasch(u,x,u1,v1,w),u),
inference(resolve,[status(thm)],[c_770,c_76]) ).
cnf(c_771,plain,
( between(B,inner_pasch(u,x,u1,B,A),u)
| ~ between(A,B,u1) ),
inference(resolve,[status(thm)],[c_9,c_74]) ).
cnf(c_772,plain,
between(v1,inner_pasch(u,x,u1,v1,w),u),
inference(resolve,[status(thm)],[c_771,c_470]) ).
cnf(c_769,plain,
$false,
inference(resolve,[status(thm)],[c_709,c_772]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO048-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 25 12:35:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 2097484 was started by sandbox on n012,
% 0.03/0.30 % Fri Sep 25 12:35:50 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 1.14/0.50
% 1.14/0.50 % SZS status Unsatisfiable for theBenchmark
% 1.14/0.50
% 1.14/0.50 % Proof 1 at 0.16 (+ 0.03) seconds.
% 1.14/0.50 % Length of proof is 10.
% 1.14/0.50 % Level of proof is 3.
% 1.14/0.50 % Maximum clause weight is 29.000.
% 1.14/0.50 % Given clauses 76.
% 1.14/0.50
% 1.14/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------