%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV392+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 : n004.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 09:07:37 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 4 unt; 0 def)
% Number of atoms : 20 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 19 ( 7 ~; 2 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 2 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax22,axiom,
! [U,V] : ~ pair_in_list(create_slb,U,V),
file('theBenchmark.p',ax22) ).
fof(l28_co,conjecture,
! [U,V] :
( pair_in_list(create_slb,U,V)
=> ! [W] :
( contains_slb(create_slb,W)
=> ( U = W
| pair_in_list(remove_slb(create_slb,W),U,V) ) ) ),
file('theBenchmark.p',l28_co) ).
fof(l28_co_neg,negated_conjecture,
~ ! [U,V] :
( pair_in_list(create_slb,U,V)
=> ! [W] :
( contains_slb(create_slb,W)
=> ( U = W
| pair_in_list(remove_slb(create_slb,W),U,V) ) ) ),
inference(assume_negation,[status(cth)],[l28_co]) ).
fof(nnf_18,plain,
? [U,V] :
( ? [W] :
( W != U
& ~ pair_in_list(remove_slb(create_slb,W),U,V)
& contains_slb(create_slb,W) )
& pair_in_list(create_slb,U,V) ),
inference(fof_nnf,[status(thm)],[l28_co_neg]) ).
fof(sk_l28_co_neg,plain,
( sK2 != sK0
& ~ pair_in_list(remove_slb(create_slb,sK2),sK0,sK1)
& contains_slb(create_slb,sK2)
& pair_in_list(create_slb,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2)],[nnf_18]) ).
cnf(c_27,negated_conjecture,
pair_in_list(create_slb,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_l28_co_neg]) ).
cnf(c_38,plain,
~ pair_in_list(create_slb,A,B),
inference(clausify,[status(thm)],[ax22]) ).
cnf(c_39,plain,
$false,
inference(resolve,[status(thm)],[c_38,c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV392+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 13:40:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1853315 was started by sandbox2 on n004,
% 0.09/0.37 % Sat Sep 26 13:40:51 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 5.
% 0.09/0.39 % Level of proof is 2.
% 0.09/0.39 % Maximum clause weight is 4.000.
% 0.09/0.39 % Given clauses 0.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------