%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV008-1 : 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 : n001.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 09:06:38 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 19 unt; 0 def)
% Number of atoms : 69 ( 15 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 69 ( 36 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(anti_symmetry_of_less_than,axiom,
! [VAR_0,VAR_1] :
( ~ less_than(VAR_1,VAR_0)
| ~ less_than(VAR_0,VAR_1) ),
file('theBenchmark.p',anti_symmetry_of_less_than) ).
cnf(c_10,plain,
( ~ less_than(B,A)
| ~ less_than(A,B) ),
inference(clausify,[status(thm)],[anti_symmetry_of_less_than]) ).
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_1,axiom,
~ less_than(n,l),
file('theBenchmark.p',clause_1) ).
cnf(c_13,plain,
~ less_than(n,l),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_2,axiom,
less_than(one,l),
file('theBenchmark.p',clause_2) ).
cnf(c_14,plain,
less_than(one,l),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_3,axiom,
less_than(a(l),a(predecessor(l))),
file('theBenchmark.p',clause_3) ).
cnf(c_15,plain,
less_than(a(l),a(predecessor(l))),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_4,axiom,
! [VAR_0] :
( ~ less_than(a(VAR_0),a(predecessor(n)))
| ~ less_than(one,n)
| less_than(n,VAR_0)
| less_than(VAR_0,n) ),
file('theBenchmark.p',clause_4) ).
cnf(c_16,plain,
( ~ less_than(a(A),a(predecessor(n)))
| ~ less_than(one,n)
| less_than(n,A)
| less_than(A,n) ),
inference(clausify,[status(thm)],[clause_4]) ).
fof(clause_5,axiom,
! [VAR_0] :
( ~ less_than(a(VAR_0),a(predecessor(VAR_0)))
| ~ less_than(VAR_0,n)
| ~ less_than(one,VAR_0) ),
file('theBenchmark.p',clause_5) ).
cnf(c_17,plain,
( ~ less_than(a(A),a(predecessor(A)))
| ~ less_than(A,n)
| ~ less_than(one,A) ),
inference(clausify,[status(thm)],[clause_5]) ).
cnf(c_41,plain,
( l = n
| less_than(l,n) ),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_56,plain,
~ less_than(a(predecessor(l)),a(l)),
inference(resolve,[status(thm)],[c_15,c_10]) ).
cnf(c_79,plain,
( ~ less_than(B,A)
| A != B ),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_59,plain,
a(predecessor(l)) != a(l),
inference(resolve,[status(thm)],[c_79,c_15]) ).
cnf(c_60,plain,
( a(predecessor(n)) = a(A)
| less_than(a(predecessor(n)),a(A))
| ~ less_than(one,n)
| less_than(n,A)
| less_than(A,n) ),
inference(resolve,[status(thm)],[c_16,c_8]) ).
cnf(c_80,plain,
( a(predecessor(n)) = a(n)
| less_than(a(predecessor(n)),a(n))
| ~ less_than(one,n)
| less_than(n,n) ),
inference(factor,[status(thm)],[c_60]) ).
cnf(c_61,plain,
( a(predecessor(n)) = a(n)
| less_than(a(predecessor(n)),a(n))
| ~ less_than(one,n) ),
inference(resolve,[status(thm)],[c_9,c_80]) ).
cnf(c_81,plain,
( ~ less_than(l,n)
| ~ less_than(one,l) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_62,plain,
~ less_than(l,n),
inference(resolve,[status(thm)],[c_14,c_81]) ).
cnf(c_65,plain,
l = n,
inference(resolve,[status(thm)],[c_62,c_41]) ).
cnf(c_82,plain,
a(predecessor(n)) != a(l),
inference(paramod,[status(thm)],[c_65,c_59]) ).
cnf(c_66,plain,
a(predecessor(n)) != a(n),
inference(paramod,[status(thm)],[c_65,c_82]) ).
cnf(c_83,plain,
~ less_than(a(predecessor(n)),a(l)),
inference(paramod,[status(thm)],[c_65,c_56]) ).
cnf(c_69,plain,
~ less_than(a(predecessor(n)),a(n)),
inference(paramod,[status(thm)],[c_65,c_83]) ).
cnf(c_77,plain,
less_than(one,n),
inference(paramod,[status(thm)],[c_65,c_14]) ).
cnf(c_84,plain,
( a(predecessor(n)) = a(n)
| less_than(a(predecessor(n)),a(n)) ),
inference(resolve,[status(thm)],[c_77,c_61]) ).
cnf(c_85,plain,
a(predecessor(n)) = a(n),
inference(resolve,[status(thm)],[c_69,c_84]) ).
cnf(c_78,plain,
$false,
inference(resolve,[status(thm)],[c_66,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 13:10:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1875404 was started by sandbox2 on n001,
% 0.09/0.37 % Sat Sep 26 13:10:28 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 20.
% 0.09/0.38 % Level of proof is 4.
% 0.09/0.38 % Maximum clause weight is 21.000.
% 0.09/0.38 % Given clauses 17.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------