%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV003-1 : 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 : n010.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 09:06:37 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 7 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_of_less_than,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_than(VAR_2,VAR_1)
| ~ less_than(VAR_0,VAR_2)
| less_than(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_less_than) ).
cnf(c_7,plain,
( ~ less_than(C,B)
| ~ less_than(A,C)
| less_than(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less_than]) ).
fof(clause_2,axiom,
less_than(k,j),
file('theBenchmark.p',clause_2) ).
cnf(c_14,plain,
less_than(k,j),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_3,axiom,
~ less_than(k,i),
file('theBenchmark.p',clause_3) ).
cnf(c_15,plain,
~ less_than(k,i),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_9,axiom,
less_than(j,i),
file('theBenchmark.p',clause_9) ).
cnf(c_21,plain,
less_than(j,i),
inference(clausify,[status(thm)],[clause_9]) ).
cnf(c_63,plain,
( ~ less_than(A,i)
| ~ less_than(k,A) ),
inference(resolve,[status(thm)],[c_7,c_15]) ).
cnf(c_64,plain,
~ less_than(j,i),
inference(resolve,[status(thm)],[c_63,c_14]) ).
cnf(c_62,plain,
$false,
inference(resolve,[status(thm)],[c_21,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 13:05:04 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3388596 was started by sandbox2 on n010,
% 0.13/0.36 % Sat Sep 26 13:05:04 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 5.
% 0.13/0.37 % Level of proof is 1.
% 0.13/0.37 % Maximum clause weight is 9.000.
% 0.13/0.37 % Given clauses 15.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------