%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV413+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:07:40 AM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 34 ( 12 ~; 6 |; 13 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 14 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l49_li3637,axiom,
! [U,V,W,X] :
( ( less_than(X,W)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,W) ),
file('theBenchmark.p',l49_li3637) ).
fof(l49_co,conjecture,
! [U,V,W,X] :
( ( less_than(X,W)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) ) ),
file('theBenchmark.p',l49_co) ).
fof(l49_co_neg,negated_conjecture,
~ ! [U,V,W,X] :
( ( less_than(X,W)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) ) ),
inference(assume_negation,[status(cth)],[l49_co]) ).
fof(nnf_19,plain,
? [U,V,W,X] :
( ! [Y] :
( ~ less_than(X,Y)
| ~ pair_in_list(update_slb(U,X),V,Y) )
& less_than(X,W)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) ),
inference(fof_nnf,[status(thm)],[l49_co_neg]) ).
fof(sk_l49_co_neg,plain,
( ! [Y] :
( ~ less_than(sK1,Y)
| ~ pair_in_list(update_slb(sK0,sK1),sK2,Y) )
& less_than(sK1,sK3)
& strictly_less_than(sK2,sK1)
& pair_in_list(sK0,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK3,sK1]),skolemize(U,sK0),skolemize(V,sK2),skolemize(W,sK3),skolemize(X,sK1)],[nnf_19]) ).
cnf(c_29,negated_conjecture,
( ~ less_than(sK1,A)
| ~ pair_in_list(update_slb(sK0,sK1),sK2,A) ),
inference(split_conjunct,[status(thm)],[sk_l49_co_neg]) ).
cnf(c_30,negated_conjecture,
less_than(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_l49_co_neg]) ).
cnf(c_31,negated_conjecture,
pair_in_list(sK0,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_l49_co_neg]) ).
cnf(c_32,plain,
( pair_in_list(update_slb(A,D),B,C)
| ~ less_than(D,C)
| ~ pair_in_list(A,B,C) ),
inference(clausify,[status(thm)],[l49_li3637]) ).
cnf(c_56,negated_conjecture,
~ pair_in_list(update_slb(sK0,sK1),sK2,sK3),
inference(resolve,[status(thm)],[c_29,c_30]) ).
cnf(c_80,negated_conjecture,
( pair_in_list(update_slb(A,sK1),B,sK3)
| ~ pair_in_list(A,B,sK3) ),
inference(resolve,[status(thm)],[c_32,c_30]) ).
cnf(c_81,negated_conjecture,
~ pair_in_list(sK0,sK2,sK3),
inference(resolve,[status(thm)],[c_80,c_56]) ).
cnf(c_79,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_31,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV413+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 13:47:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1940213 was started by sandbox on n001,
% 0.11/0.37 % Sat Sep 26 13:47:27 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 8.
% 0.15/0.39 % Level of proof is 3.
% 0.15/0.39 % Maximum clause weight is 13.000.
% 0.15/0.39 % Given clauses 31.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------