%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV409+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 : n007.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 0.15s 5.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 117 ( 47 ~; 45 |; 19 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 77 ( 0 sgn 42 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(totality,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('theBenchmark.p',totality) ).
fof(stricly_smaller_definition,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('theBenchmark.p',stricly_smaller_definition) ).
fof(l45_li4647,axiom,
! [U,V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) ),
file('theBenchmark.p',l45_li4647) ).
fof(l45_l48,axiom,
! [U,V,W,X] :
( ( strictly_less_than(W,X)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) ),
file('theBenchmark.p',l45_l48) ).
fof(l45_l49,axiom,
! [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',l45_l49) ).
fof(l45_co,conjecture,
! [U,V,W] :
( ( strictly_less_than(V,W)
& contains_slb(U,V) )
=> ( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W) ) ),
file('theBenchmark.p',l45_co) ).
fof(l45_co_neg,negated_conjecture,
~ ! [U,V,W] :
( ( strictly_less_than(V,W)
& contains_slb(U,V) )
=> ( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W) ) ),
inference(assume_negation,[status(cth)],[l45_co]) ).
cnf(c_23,plain,
( less_than(B,A)
| less_than(A,B) ),
inference(clausify,[status(thm)],[totality]) ).
cnf(c_27,plain,
( less_than(B,A)
| ~ less_than(A,B)
| strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
fof(nnf_18,plain,
! [U,V] :
( ? [W] : pair_in_list(U,V,W)
| ~ contains_slb(U,V) ),
inference(fof_nnf,[status(thm)],[l45_li4647]) ).
fof(sk_l45_li4647,plain,
! [U,V] :
( pair_in_list(U,V,sK0(U,V))
| ~ contains_slb(U,V) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W,sK0(U,V))],[nnf_18]) ).
cnf(c_47,plain,
( pair_in_list(A,B,sK0(A,B))
| ~ contains_slb(A,B) ),
inference(split_conjunct,[status(thm)],[sk_l45_li4647]) ).
cnf(c_48,plain,
( pair_in_list(update_slb(A,D),B,D)
| ~ strictly_less_than(C,D)
| ~ strictly_less_than(B,D)
| ~ pair_in_list(A,B,C) ),
inference(clausify,[status(thm)],[l45_l48]) ).
fof(nnf_20,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)],[l45_l49]) ).
fof(sk_l45_l49_sk,plain,
! [U,V,W,X] :
( ( less_than(X,sK1(U,V,W,X))
& pair_in_list(update_slb(U,X),V,sK1(U,V,W,X)) )
| ~ less_than(X,W)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y,sK1(U,V,W,X))],[nnf_20]) ).
fof(sk_l45_l49,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( less_than(VAR_3,sK1(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ less_than(VAR_3,VAR_2)
| ~ strictly_less_than(VAR_1,VAR_3)
| ~ pair_in_list(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( pair_in_list(update_slb(VAR_0,VAR_3),VAR_1,sK1(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ less_than(VAR_3,VAR_2)
| ~ strictly_less_than(VAR_1,VAR_3)
| ~ pair_in_list(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_l45_l49_sk]) ).
cnf(c_49,plain,
( pair_in_list(update_slb(A,D),B,sK1(A,B,C,D))
| ~ less_than(D,C)
| ~ strictly_less_than(B,D)
| ~ pair_in_list(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_l45_l49]) ).
cnf(c_50,plain,
( less_than(D,sK1(A,B,C,D))
| ~ less_than(D,C)
| ~ strictly_less_than(B,D)
| ~ pair_in_list(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_l45_l49]) ).
fof(nnf_21,plain,
? [U,V,W] :
( ! [X] :
( ~ less_than(W,X)
| ~ pair_in_list(update_slb(U,W),V,X) )
& ~ pair_in_list(update_slb(U,W),V,W)
& strictly_less_than(V,W)
& contains_slb(U,V) ),
inference(fof_nnf,[status(thm)],[l45_co_neg]) ).
fof(sk_l45_co_neg,plain,
( ! [X] :
( ~ less_than(sK4,X)
| ~ pair_in_list(update_slb(sK2,sK4),sK3,X) )
& ~ pair_in_list(update_slb(sK2,sK4),sK3,sK4)
& strictly_less_than(sK3,sK4)
& contains_slb(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK4)],[nnf_21]) ).
cnf(c_51,negated_conjecture,
contains_slb(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_l45_co_neg]) ).
cnf(c_52,negated_conjecture,
strictly_less_than(sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_l45_co_neg]) ).
cnf(c_53,negated_conjecture,
~ pair_in_list(update_slb(sK2,sK4),sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_l45_co_neg]) ).
cnf(c_54,negated_conjecture,
( ~ less_than(sK4,A)
| ~ pair_in_list(update_slb(sK2,sK4),sK3,A) ),
inference(split_conjunct,[status(thm)],[sk_l45_co_neg]) ).
cnf(c_311,plain,
( less_than(B,A)
| less_than(B,A)
| strictly_less_than(A,B) ),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_59,plain,
( less_than(B,A)
| strictly_less_than(A,B) ),
inference(copy,[status(thm)],[c_311]) ).
cnf(c_68,plain,
pair_in_list(sK2,sK3,sK0(sK2,sK3)),
inference(resolve,[status(thm)],[c_51,c_47]) ).
cnf(c_86,plain,
( less_than(A,sK1(sK2,sK3,sK0(sK2,sK3),A))
| ~ less_than(A,sK0(sK2,sK3))
| ~ strictly_less_than(sK3,A) ),
inference(resolve,[status(thm)],[c_68,c_50]) ).
cnf(c_87,plain,
( pair_in_list(update_slb(sK2,A),sK3,sK1(sK2,sK3,sK0(sK2,sK3),A))
| ~ less_than(A,sK0(sK2,sK3))
| ~ strictly_less_than(sK3,A) ),
inference(resolve,[status(thm)],[c_68,c_49]) ).
cnf(c_312,plain,
( pair_in_list(update_slb(sK2,A),sK3,A)
| ~ strictly_less_than(sK0(sK2,sK3),A)
| ~ strictly_less_than(sK3,A) ),
inference(resolve,[status(thm)],[c_48,c_68]) ).
cnf(c_313,negated_conjecture,
( pair_in_list(update_slb(sK2,sK4),sK3,sK4)
| ~ strictly_less_than(sK0(sK2,sK3),sK4) ),
inference(resolve,[status(thm)],[c_312,c_52]) ).
cnf(c_90,negated_conjecture,
~ strictly_less_than(sK0(sK2,sK3),sK4),
inference(resolve,[status(thm)],[c_313,c_53]) ).
cnf(c_95,plain,
less_than(sK4,sK0(sK2,sK3)),
inference(resolve,[status(thm)],[c_90,c_59]) ).
cnf(c_314,negated_conjecture,
( less_than(sK4,sK1(sK2,sK3,sK0(sK2,sK3),sK4))
| ~ less_than(sK4,sK0(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_86,c_52]) ).
cnf(c_280,negated_conjecture,
less_than(sK4,sK1(sK2,sK3,sK0(sK2,sK3),sK4)),
inference(resolve,[status(thm)],[c_95,c_314]) ).
cnf(c_289,negated_conjecture,
~ pair_in_list(update_slb(sK2,sK4),sK3,sK1(sK2,sK3,sK0(sK2,sK3),sK4)),
inference(resolve,[status(thm)],[c_54,c_280]) ).
cnf(c_315,negated_conjecture,
( pair_in_list(update_slb(sK2,sK4),sK3,sK1(sK2,sK3,sK0(sK2,sK3),sK4))
| ~ less_than(sK4,sK0(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_87,c_52]) ).
cnf(c_316,negated_conjecture,
pair_in_list(update_slb(sK2,sK4),sK3,sK1(sK2,sK3,sK0(sK2,sK3),sK4)),
inference(resolve,[status(thm)],[c_95,c_315]) ).
cnf(c_310,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_289,c_316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n007.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 13:39:44 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3873006 was started by sandbox on n007,
% 0.10/5.38 % Sat Sep 26 13:39:44 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.47
% 0.15/5.47 % SZS status Theorem for theBenchmark
% 0.15/5.47
% 0.15/5.47 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.15/5.47 % Length of proof is 25.
% 0.15/5.47 % Level of proof is 7.
% 0.15/5.47 % Maximum clause weight is 20.000.
% 0.15/5.47 % Given clauses 112.
% 0.15/5.47
% 0.15/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------