%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV405+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 09:07:38 AM UTC 2026
% Result : Theorem 0.16s 0.42s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 35 ( 14 ~; 11 |; 6 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 26 ( 4 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax22,axiom,
! [U,V] : ~ pair_in_list(create_slb,U,V),
file('theBenchmark.p',ax22) ).
fof(ax36,axiom,
! [U,V] : check_cpq(triple(U,create_slb,V)),
file('theBenchmark.p',ax36) ).
fof(l41_co,conjecture,
! [U,V] :
( check_cpq(triple(U,create_slb,V))
<=> ! [W,X] :
( pair_in_list(create_slb,W,X)
=> less_than(X,W) ) ),
file('theBenchmark.p',l41_co) ).
fof(l41_co_neg,negated_conjecture,
~ ! [U,V] :
( check_cpq(triple(U,create_slb,V))
<=> ! [W,X] :
( pair_in_list(create_slb,W,X)
=> less_than(X,W) ) ),
inference(assume_negation,[status(cth)],[l41_co]) ).
cnf(c_55,plain,
~ pair_in_list(create_slb,A,B),
inference(clausify,[status(thm)],[ax22]) ).
cnf(c_72,plain,
check_cpq(triple(A,create_slb,B)),
inference(clausify,[status(thm)],[ax36]) ).
fof(nnf_41,plain,
? [U,V] :
( ( ? [W,X] :
( ~ less_than(X,W)
& pair_in_list(create_slb,W,X) )
| ~ check_cpq(triple(U,create_slb,V)) )
& ( ! [X0,X1] :
( less_than(X1,X0)
| ~ pair_in_list(create_slb,X0,X1) )
| check_cpq(triple(U,create_slb,V)) ) ),
inference(fof_nnf,[status(thm)],[l41_co_neg]) ).
fof(sk_l41_co_neg_sk,plain,
( ( ( ~ less_than(sK3,sK2)
& pair_in_list(create_slb,sK2,sK3) )
| ~ check_cpq(triple(sK0,create_slb,sK1)) )
& ( ! [X0,X1] :
( less_than(X1,X0)
| ~ pair_in_list(create_slb,X0,X1) )
| check_cpq(triple(sK0,create_slb,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK3)],[nnf_41]) ).
fof(sk_l41_co_neg,plain,
( ( ~ less_than(sK3,sK2)
| ~ check_cpq(triple(sK0,create_slb,sK1)) )
& ( pair_in_list(create_slb,sK2,sK3)
| ~ check_cpq(triple(sK0,create_slb,sK1)) )
& ! [VAR_0,VAR_1] :
( less_than(VAR_1,VAR_0)
| ~ pair_in_list(create_slb,VAR_0,VAR_1)
| check_cpq(triple(sK0,create_slb,sK1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_l41_co_neg_sk]) ).
cnf(c_97,negated_conjecture,
( pair_in_list(create_slb,sK2,sK3)
| ~ check_cpq(triple(sK0,create_slb,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_l41_co_neg]) ).
cnf(c_99,negated_conjecture,
pair_in_list(create_slb,sK2,sK3),
inference(resolve,[status(thm)],[c_72,c_97]) ).
cnf(c_98,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_55,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV405+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 13:41:34 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.39 % Process 1461947 was started by sandbox2 on n019,
% 0.12/0.39 % Sat Sep 26 13:41:34 2026
% 0.12/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.41
% 0.16/0.41 % From the command line: assign(max_seconds, 300).
% 0.16/0.42
% 0.16/0.42 % SZS status Theorem for theBenchmark
% 0.16/0.42
% 0.16/0.42 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.42 % Length of proof is 7.
% 0.16/0.42 % Level of proof is 2.
% 0.16/0.42 % Maximum clause weight is 5.000.
% 0.16/0.42 % Given clauses 0.
% 0.16/0.42
% 0.16/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------