%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV411+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 : n009.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 09:07:39 AM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 49 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 43 ( 17 ~; 13 |; 5 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 8 sgn 26 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax21,axiom,
! [U,V,W,X] :
( contains_slb(insert_slb(U,pair(V,X)),W)
<=> ( V = W
| contains_slb(U,W) ) ),
file('theBenchmark.p',ax21) ).
fof(ax23,axiom,
! [U,V,W,X,Y] :
( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( ( X = Y
& V = W )
| pair_in_list(U,W,Y) ) ),
file('theBenchmark.p',ax23) ).
fof(ax24,axiom,
! [U,V,W] : remove_slb(insert_slb(U,pair(V,W)),V) = U,
file('theBenchmark.p',ax24) ).
fof(l47_co,conjecture,
! [U] :
( ! [V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) )
=> ! [X,Y,Z] :
( contains_slb(insert_slb(U,pair(Y,Z)),X)
=> ? [X1] : pair_in_list(insert_slb(U,pair(Y,Z)),X,X1) ) ),
file('theBenchmark.p',l47_co) ).
fof(l47_co_neg,negated_conjecture,
~ ! [U] :
( ! [V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) )
=> ! [X,Y,Z] :
( contains_slb(insert_slb(U,pair(Y,Z)),X)
=> ? [X1] : pair_in_list(insert_slb(U,pair(Y,Z)),X,X1) ) ),
inference(assume_negation,[status(cth)],[l47_co]) ).
fof(nnf_18,plain,
? [U] :
( ? [X,Y,Z] :
( ! [X1] : ~ pair_in_list(insert_slb(U,pair(Y,Z)),X,X1)
& contains_slb(insert_slb(U,pair(Y,Z)),X) )
& ! [V] :
( ? [W] : pair_in_list(U,V,W)
| ~ contains_slb(U,V) ) ),
inference(fof_nnf,[status(thm)],[l47_co_neg]) ).
fof(sk_l47_co_neg,plain,
( ! [X1] : ~ pair_in_list(insert_slb(sK0,pair(sK1,sK2)),sK3,X1)
& contains_slb(insert_slb(sK0,pair(sK1,sK2)),sK3)
& ! [V] :
( pair_in_list(sK0,V,sK4(V))
| ~ contains_slb(sK0,V) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4,sK1,sK2,sK3]),skolemize(U,sK0),skolemize(W,sK4(V)),skolemize(X,sK3),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_18]) ).
cnf(c_24,negated_conjecture,
~ pair_in_list(insert_slb(sK0,pair(sK1,sK2)),sK3,A),
inference(split_conjunct,[status(thm)],[sk_l47_co_neg]) ).
cnf(c_25,negated_conjecture,
contains_slb(insert_slb(sK0,pair(sK1,sK2)),sK3),
inference(split_conjunct,[status(thm)],[sk_l47_co_neg]) ).
cnf(c_26,negated_conjecture,
( pair_in_list(sK0,A,sK4(A))
| ~ contains_slb(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_l47_co_neg]) ).
cnf(c_32,plain,
remove_slb(insert_slb(A,pair(B,C)),B) = A,
inference(clausify,[status(thm)],[ax24]) ).
cnf(c_33,plain,
( E != C
| D != B
| pair_in_list(insert_slb(A,pair(B,C)),D,E) ),
inference(clausify,[status(thm)],[ax23]) ).
cnf(c_34,plain,
( ~ pair_in_list(A,D,E)
| pair_in_list(insert_slb(A,pair(B,C)),D,E) ),
inference(clausify,[status(thm)],[ax23]) ).
cnf(c_40,plain,
( D = B
| contains_slb(A,D)
| ~ contains_slb(insert_slb(A,pair(B,C)),D) ),
inference(clausify,[status(thm)],[ax21]) ).
cnf(c_87,negated_conjecture,
( A != sK2
| sK3 != sK1 ),
inference(resolve,[status(thm)],[c_33,c_24]) ).
cnf(c_88,negated_conjecture,
sK3 != sK1,
inference(resolve,[status(thm)],[c_87,c_32]) ).
cnf(c_53,negated_conjecture,
sK1 != sK3,
inference(copy,[status(thm)],[c_88]) ).
cnf(c_54,negated_conjecture,
~ pair_in_list(sK0,sK3,A),
inference(resolve,[status(thm)],[c_34,c_24]) ).
cnf(c_89,negated_conjecture,
( sK3 = sK1
| contains_slb(sK0,sK3) ),
inference(resolve,[status(thm)],[c_40,c_25]) ).
cnf(c_90,negated_conjecture,
( sK1 = sK3
| contains_slb(sK0,sK3) ),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_57,negated_conjecture,
contains_slb(sK0,sK3),
inference(resolve,[status(thm)],[c_53,c_90]) ).
cnf(c_91,negated_conjecture,
~ contains_slb(sK0,sK3),
inference(resolve,[status(thm)],[c_26,c_54]) ).
cnf(c_86,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_57,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV411+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 13:41:45 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 295279 was started by sandbox2 on n009,
% 0.08/0.36 % Sat Sep 26 13:41:45 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.14/0.38 % Length of proof is 15.
% 0.14/0.38 % Level of proof is 4.
% 0.14/0.38 % Maximum clause weight is 14.000.
% 0.14/0.38 % Given clauses 29.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------