%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV002-1 : 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 : n014.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 0.09s 0.62s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 51 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn 10 !; 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(all_related,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| less_than(VAR_1,VAR_0)
| less_than(VAR_0,VAR_1) ),
file('theBenchmark.p',all_related) ).
cnf(c_8,plain,
( A = B
| less_than(B,A)
| less_than(A,B) ),
inference(clausify,[status(thm)],[all_related]) ).
fof(x_not_less_than_x,axiom,
! [VAR_0] : ~ less_than(VAR_0,VAR_0),
file('theBenchmark.p',x_not_less_than_x) ).
cnf(c_9,plain,
~ less_than(A,A),
inference(clausify,[status(thm)],[x_not_less_than_x]) ).
fof(equal_and_less_than_transitivity2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_than(VAR_0,VAR_2)
| VAR_2 != VAR_1
| less_than(VAR_0,VAR_1) ),
file('theBenchmark.p',equal_and_less_than_transitivity2) ).
cnf(c_12,plain,
( ~ less_than(A,C)
| C != B
| less_than(A,B) ),
inference(clausify,[status(thm)],[equal_and_less_than_transitivity2]) ).
fof(clause_5,axiom,
less_than(a(j),a(k)),
file('theBenchmark.p',clause_5) ).
cnf(c_17,plain,
less_than(a(j),a(k)),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_6,axiom,
! [VAR_0] :
( ~ less_than(a(VAR_0),a(k))
| ~ less_than(VAR_0,j)
| less_than(VAR_0,i) ),
file('theBenchmark.p',clause_6) ).
cnf(c_18,plain,
( ~ less_than(a(A),a(k))
| ~ less_than(A,j)
| less_than(A,i) ),
inference(clausify,[status(thm)],[clause_6]) ).
fof(clause_9,axiom,
~ less_than(q,i),
file('theBenchmark.p',clause_9) ).
cnf(c_21,plain,
~ less_than(q,i),
inference(clausify,[status(thm)],[clause_9]) ).
fof(clause_10,axiom,
~ less_than(j,q),
file('theBenchmark.p',clause_10) ).
cnf(c_22,plain,
~ less_than(j,q),
inference(clausify,[status(thm)],[clause_10]) ).
fof(clause_11,axiom,
less_than(a(q),a(j)),
file('theBenchmark.p',clause_11) ).
cnf(c_23,plain,
less_than(a(q),a(j)),
inference(clausify,[status(thm)],[clause_11]) ).
cnf(c_75,plain,
( ~ less_than(A,a(j))
| less_than(A,a(k)) ),
inference(resolve,[status(thm)],[c_17,c_7]) ).
cnf(c_94,plain,
( q = j
| less_than(q,j) ),
inference(resolve,[status(thm)],[c_22,c_8]) ).
cnf(c_369,plain,
( ~ less_than(B,A)
| A != B ),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_370,plain,
a(j) != a(q),
inference(resolve,[status(thm)],[c_369,c_23]) ).
cnf(c_104,plain,
a(q) != a(j),
inference(copy,[status(thm)],[c_370]) ).
cnf(c_371,plain,
( ~ less_than(a(q),a(k))
| less_than(q,i)
| q = j ),
inference(resolve,[status(thm)],[c_94,c_18]) ).
cnf(c_223,plain,
( ~ less_than(a(q),a(k))
| q = j ),
inference(resolve,[status(thm)],[c_21,c_371]) ).
cnf(c_364,plain,
less_than(a(q),a(k)),
inference(resolve,[status(thm)],[c_75,c_23]) ).
cnf(c_365,plain,
q = j,
inference(resolve,[status(thm)],[c_364,c_223]) ).
cnf(c_372,plain,
a(j) != a(j),
inference(paramod,[status(thm)],[c_365,c_104]) ).
cnf(c_368,plain,
$false,
inference(copy,[status(thm)],[c_372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.51 % Computer : n014.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Sat Sep 26 13:04:33 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.52 % Process 3226285 was started by sandbox on n014,
% 0.09/0.52 % Sat Sep 26 13:04:33 2026
% 0.09/0.52 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.52
% 0.09/0.52 % From the command line: assign(max_seconds, 300).
% 0.09/0.62
% 0.09/0.62 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.62
% 0.09/0.62 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.09/0.62 % Length of proof is 16.
% 0.09/0.62 % Level of proof is 4.
% 0.09/0.62 % Maximum clause weight is 21.000.
% 0.09/0.62 % Given clauses 115.
% 0.09/0.62
% 0.09/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------