%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV399+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 : n017.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 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 74 ( 31 ~; 25 |; 12 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 63 ( 0 sgn 23 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity,axiom,
! [U,V,W] :
( ( less_than(V,W)
& less_than(U,V) )
=> less_than(U,W) ),
file('theBenchmark.p',transitivity) ).
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(l35_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',l35_li3637) ).
fof(l35_li3839,axiom,
! [U,V,W,X] :
( ( strictly_less_than(W,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) ),
file('theBenchmark.p',l35_li3839) ).
fof(l35_co,conjecture,
! [U] :
( ? [V,W] :
( strictly_less_than(V,W)
& pair_in_list(U,V,W) )
=> ! [X] :
? [Y,Z] :
( strictly_less_than(Y,Z)
& pair_in_list(update_slb(U,X),Y,Z) ) ),
file('theBenchmark.p',l35_co) ).
fof(l35_co_neg,negated_conjecture,
~ ! [U] :
( ? [V,W] :
( strictly_less_than(V,W)
& pair_in_list(U,V,W) )
=> ! [X] :
? [Y,Z] :
( strictly_less_than(Y,Z)
& pair_in_list(update_slb(U,X),Y,Z) ) ),
inference(assume_negation,[status(cth)],[l35_co]) ).
cnf(c_21,plain,
( less_than(B,A)
| ~ less_than(A,B)
| strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_23,plain,
( less_than(A,B)
| ~ strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_25,plain,
( pair_in_list(update_slb(A,D),B,D)
| ~ strictly_less_than(C,D)
| ~ pair_in_list(A,B,C) ),
inference(clausify,[status(thm)],[l35_li3839]) ).
fof(nnf_20,plain,
? [U] :
( ? [X] :
! [Y,Z] :
( ~ strictly_less_than(Y,Z)
| ~ pair_in_list(update_slb(U,X),Y,Z) )
& ? [V,W] :
( strictly_less_than(V,W)
& pair_in_list(U,V,W) ) ),
inference(fof_nnf,[status(thm)],[l35_co_neg]) ).
fof(sk_l35_co_neg,plain,
( ! [Y,Z] :
( ~ strictly_less_than(Y,Z)
| ~ pair_in_list(update_slb(sK2,sK3),Y,Z) )
& strictly_less_than(sK0,sK1)
& pair_in_list(sK2,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1,sK3]),skolemize(U,sK2),skolemize(V,sK0),skolemize(W,sK1),skolemize(X,sK3)],[nnf_20]) ).
cnf(c_26,negated_conjecture,
strictly_less_than(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_l35_co_neg]) ).
cnf(c_27,negated_conjecture,
( ~ strictly_less_than(A,B)
| ~ pair_in_list(update_slb(sK2,sK3),A,B) ),
inference(split_conjunct,[status(thm)],[sk_l35_co_neg]) ).
cnf(c_28,negated_conjecture,
( less_than(B,A)
| ~ less_than(A,B)
| ~ pair_in_list(update_slb(sK2,sK3),A,B) ),
inference(resolve,[status(thm)],[c_27,c_21]) ).
cnf(c_29,negated_conjecture,
~ pair_in_list(update_slb(sK2,sK3),sK0,sK1),
inference(resolve,[status(thm)],[c_27,c_26]) ).
cnf(c_30,negated_conjecture,
less_than(sK0,sK1),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_34,plain,
( less_than(D,C)
| ~ less_than(C,D)
| pair_in_list(update_slb(A,D),B,D)
| ~ pair_in_list(A,B,C) ),
inference(resolve,[status(thm)],[c_25,c_21]) ).
cnf(c_36,negated_conjecture,
pair_in_list(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_l35_co_neg]) ).
cnf(c_37,plain,
( pair_in_list(update_slb(A,D),B,C)
| ~ less_than(D,C)
| ~ pair_in_list(A,B,C) ),
inference(clausify,[status(thm)],[l35_li3637]) ).
cnf(c_57,plain,
( less_than(B,A)
| less_than(A,B) ),
inference(clausify,[status(thm)],[totality]) ).
cnf(c_58,plain,
( less_than(A,C)
| ~ less_than(B,C)
| ~ less_than(A,B) ),
inference(clausify,[status(thm)],[transitivity]) ).
cnf(c_303,negated_conjecture,
( pair_in_list(update_slb(sK2,A),sK0,sK1)
| ~ less_than(A,sK1) ),
inference(resolve,[status(thm)],[c_37,c_36]) ).
cnf(c_63,negated_conjecture,
~ less_than(sK3,sK1),
inference(resolve,[status(thm)],[c_303,c_29]) ).
cnf(c_130,plain,
less_than(sK1,sK3),
inference(resolve,[status(thm)],[c_63,c_57]) ).
cnf(c_304,negated_conjecture,
( less_than(A,sK1)
| ~ less_than(A,sK0) ),
inference(resolve,[status(thm)],[c_58,c_30]) ).
cnf(c_132,negated_conjecture,
~ less_than(sK3,sK0),
inference(resolve,[status(thm)],[c_304,c_63]) ).
cnf(c_135,plain,
less_than(sK0,sK3),
inference(resolve,[status(thm)],[c_132,c_57]) ).
cnf(c_305,negated_conjecture,
( less_than(sK3,sK0)
| ~ pair_in_list(update_slb(sK2,sK3),sK0,sK3) ),
inference(resolve,[status(thm)],[c_28,c_135]) ).
cnf(c_143,negated_conjecture,
~ pair_in_list(update_slb(sK2,sK3),sK0,sK3),
inference(resolve,[status(thm)],[c_305,c_132]) ).
cnf(c_306,plain,
( less_than(sK3,A)
| ~ less_than(A,sK3)
| ~ pair_in_list(sK2,sK0,A) ),
inference(resolve,[status(thm)],[c_34,c_143]) ).
cnf(c_307,plain,
( less_than(sK3,sK1)
| ~ pair_in_list(sK2,sK0,sK1) ),
inference(resolve,[status(thm)],[c_306,c_130]) ).
cnf(c_308,plain,
~ pair_in_list(sK2,sK0,sK1),
inference(resolve,[status(thm)],[c_307,c_63]) ).
cnf(c_302,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_36,c_308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV399+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n017.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 13:36:33 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 845811 was started by sandbox2 on n017,
% 0.16/0.43 % Sat Sep 26 13:36:33 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.47
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47
% 0.16/0.47 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.16/0.47 % Length of proof is 25.
% 0.16/0.47 % Level of proof is 7.
% 0.16/0.47 % Maximum clause weight is 26.000.
% 0.16/0.47 % Given clauses 75.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------