%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV401+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 09:07:38 AM UTC 2026
% Result : Theorem 0.85s 0.76s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 15 unt; 0 def)
% Number of atoms : 108 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 29 ~; 38 |; 12 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 125 ( 14 sgn 44 !; 6 ?)
% 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(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(ax29,axiom,
! [U,V,W,X] :
( strictly_less_than(X,W)
=> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W)) ),
file('theBenchmark.p',ax29) ).
fof(ax30,axiom,
! [U,V,W,X] :
( less_than(W,X)
=> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X)) ),
file('theBenchmark.p',ax30) ).
fof(l37_co,conjecture,
! [U] :
( ! [V,W,X] :
( ( less_than(X,W)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,W) )
=> ! [Y,Z,X1,X2,X3] :
( ( less_than(X1,Z)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
=> pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,Z) ) ),
file('theBenchmark.p',l37_co) ).
fof(l37_co_neg,negated_conjecture,
~ ! [U] :
( ! [V,W,X] :
( ( less_than(X,W)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,W) )
=> ! [Y,Z,X1,X2,X3] :
( ( less_than(X1,Z)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
=> pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,Z) ) ),
inference(assume_negation,[status(cth)],[l37_co]) ).
cnf(c_19,plain,
( less_than(B,A)
| ~ less_than(A,B)
| strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_22,plain,
( update_slb(insert_slb(C,pair(D,A)),B) = insert_slb(update_slb(C,B),pair(D,B))
| ~ strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[ax29]) ).
cnf(c_23,plain,
( less_than(D,C)
| ~ less_than(C,D)
| update_slb(insert_slb(A,pair(B,C)),D) = insert_slb(update_slb(A,D),pair(B,D)) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
fof(nnf_18,plain,
? [U] :
( ? [Y,Z,X1,X2,X3] :
( ~ pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,Z)
& less_than(X1,Z)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
& ! [V,W,X] :
( pair_in_list(update_slb(U,X),V,W)
| ~ less_than(X,W)
| ~ pair_in_list(U,V,W) ) ),
inference(fof_nnf,[status(thm)],[l37_co_neg]) ).
fof(sk_l37_co_neg,plain,
( ~ pair_in_list(update_slb(insert_slb(sK0,pair(sK1,sK2)),sK3),sK4,sK5)
& less_than(sK3,sK5)
& pair_in_list(insert_slb(sK0,pair(sK1,sK2)),sK4,sK5)
& ! [V,W,X] :
( pair_in_list(update_slb(sK0,X),V,W)
| ~ less_than(X,W)
| ~ pair_in_list(sK0,V,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK4,sK5,sK3]),skolemize(U,sK0),skolemize(Y,sK4),skolemize(Z,sK5),skolemize(X1,sK3),skolemize(X2,sK1),skolemize(X3,sK2)],[nnf_18]) ).
cnf(c_24,negated_conjecture,
~ pair_in_list(update_slb(insert_slb(sK0,pair(sK1,sK2)),sK3),sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_l37_co_neg]) ).
cnf(c_25,negated_conjecture,
less_than(sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_l37_co_neg]) ).
cnf(c_26,negated_conjecture,
pair_in_list(insert_slb(sK0,pair(sK1,sK2)),sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_l37_co_neg]) ).
cnf(c_27,negated_conjecture,
( pair_in_list(update_slb(sK0,C),A,B)
| ~ less_than(C,B)
| ~ pair_in_list(sK0,A,B) ),
inference(split_conjunct,[status(thm)],[sk_l37_co_neg]) ).
cnf(c_28,plain,
( update_slb(insert_slb(C,pair(D,B)),A) = insert_slb(update_slb(C,A),pair(D,B))
| ~ less_than(A,B) ),
inference(clausify,[status(thm)],[ax30]) ).
cnf(c_33,plain,
remove_slb(insert_slb(A,pair(B,C)),B) = A,
inference(clausify,[status(thm)],[ax24]) ).
cnf(c_34,plain,
( E != C
| D != B
| pair_in_list(insert_slb(A,pair(B,C)),D,E) ),
inference(clausify,[status(thm)],[ax23]) ).
cnf(c_35,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_36,plain,
( E = C
| pair_in_list(A,D,E)
| ~ pair_in_list(insert_slb(A,pair(B,C)),D,E) ),
inference(clausify,[status(thm)],[ax23]) ).
cnf(c_37,plain,
( D = B
| pair_in_list(A,D,E)
| ~ pair_in_list(insert_slb(A,pair(B,C)),D,E) ),
inference(clausify,[status(thm)],[ax23]) ).
cnf(c_47,plain,
( less_than(B,A)
| less_than(A,B) ),
inference(clausify,[status(thm)],[totality]) ).
cnf(c_51,plain,
( pair_in_list(update_slb(sK0,sK3),A,sK5)
| ~ pair_in_list(sK0,A,sK5) ),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_52,plain,
update_slb(insert_slb(A,pair(B,sK5)),sK3) = insert_slb(update_slb(A,sK3),pair(B,sK5)),
inference(resolve,[status(thm)],[c_28,c_25]) ).
cnf(c_523,plain,
( F != C
| pair_in_list(insert_slb(A,pair(B,C)),remove_slb(insert_slb(B,pair(D,E)),D),F) ),
inference(resolve,[status(thm)],[c_34,c_33]) ).
cnf(c_53,plain,
( D != C
| pair_in_list(insert_slb(A,pair(B,C)),B,D) ),
inference(paramod,[status(thm)],[c_33,c_523]) ).
cnf(c_524,negated_conjecture,
( sK5 = sK2
| pair_in_list(sK0,sK4,sK5) ),
inference(resolve,[status(thm)],[c_36,c_26]) ).
cnf(c_56,negated_conjecture,
( sK2 = sK5
| pair_in_list(sK0,sK4,sK5) ),
inference(copy,[status(thm)],[c_524]) ).
cnf(c_525,negated_conjecture,
( sK4 = sK1
| pair_in_list(sK0,sK4,sK5) ),
inference(resolve,[status(thm)],[c_37,c_26]) ).
cnf(c_57,negated_conjecture,
( sK1 = sK4
| pair_in_list(sK0,sK4,sK5) ),
inference(copy,[status(thm)],[c_525]) ).
cnf(c_526,plain,
( less_than(A,B)
| update_slb(insert_slb(C,pair(D,B)),A) = insert_slb(update_slb(C,A),pair(D,A))
| less_than(A,B) ),
inference(resolve,[status(thm)],[c_47,c_23]) ).
cnf(c_66,plain,
( update_slb(insert_slb(C,pair(D,B)),A) = insert_slb(update_slb(C,A),pair(D,A))
| less_than(A,B) ),
inference(copy,[status(thm)],[c_526]) ).
cnf(c_527,plain,
( ~ pair_in_list(update_slb(insert_slb(sK0,pair(sK1,sK5)),sK3),sK4,sK5)
| pair_in_list(sK0,sK4,sK5) ),
inference(paramod,[status(thm)],[c_56,c_24]) ).
cnf(c_91,plain,
( ~ pair_in_list(insert_slb(update_slb(sK0,sK3),pair(sK1,sK5)),sK4,sK5)
| pair_in_list(sK0,sK4,sK5) ),
inference(paramod,[status(thm)],[c_52,c_527]) ).
cnf(c_528,plain,
pair_in_list(insert_slb(A,pair(B,C)),B,remove_slb(insert_slb(C,pair(D,E)),D)),
inference(resolve,[status(thm)],[c_53,c_33]) ).
cnf(c_95,plain,
pair_in_list(insert_slb(A,pair(B,C)),B,C),
inference(paramod,[status(thm)],[c_33,c_528]) ).
cnf(c_260,plain,
( ~ pair_in_list(insert_slb(update_slb(sK0,sK3),pair(sK1,sK3)),sK4,sK5)
| less_than(sK3,sK2) ),
inference(paramod,[status(thm)],[c_66,c_24]) ).
cnf(c_529,plain,
( ~ pair_in_list(insert_slb(update_slb(sK0,sK3),pair(sK4,sK5)),sK4,sK5)
| pair_in_list(sK0,sK4,sK5)
| pair_in_list(sK0,sK4,sK5) ),
inference(paramod,[status(thm)],[c_57,c_91]) ).
cnf(c_530,plain,
( ~ pair_in_list(insert_slb(update_slb(sK0,sK3),pair(sK4,sK5)),sK4,sK5)
| pair_in_list(sK0,sK4,sK5) ),
inference(copy,[status(thm)],[c_529]) ).
cnf(c_493,plain,
pair_in_list(sK0,sK4,sK5),
inference(resolve,[status(thm)],[c_95,c_530]) ).
cnf(c_498,plain,
pair_in_list(update_slb(sK0,sK3),sK4,sK5),
inference(resolve,[status(thm)],[c_493,c_51]) ).
cnf(c_503,plain,
pair_in_list(insert_slb(update_slb(sK0,sK3),pair(A,B)),sK4,sK5),
inference(resolve,[status(thm)],[c_498,c_35]) ).
cnf(c_505,plain,
less_than(sK3,sK2),
inference(resolve,[status(thm)],[c_503,c_260]) ).
cnf(c_520,plain,
update_slb(insert_slb(A,pair(B,sK2)),sK3) = insert_slb(update_slb(A,sK3),pair(B,sK2)),
inference(resolve,[status(thm)],[c_505,c_28]) ).
cnf(c_531,negated_conjecture,
~ pair_in_list(insert_slb(update_slb(sK0,sK3),pair(sK1,sK2)),sK4,sK5),
inference(paramod,[status(thm)],[c_520,c_24]) ).
cnf(c_522,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_503,c_531]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV401+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.46 % Computer : n001.cluster.edu
% 0.10/0.46 % Model : x86_64 x86_64
% 0.10/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.46 % Memory : 8046.5625MB
% 0.10/0.46 % OS : Linux 6.8.0-71-generic
% 0.10/0.46 % CPULimit : 300
% 0.10/0.46 % WCLimit : 300
% 0.10/0.46 % DateTime : Sat Sep 26 13:47:13 UTC 2026
% 0.10/0.47 % CPUTime :
% 0.10/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.47 % Process 1938868 was started by sandbox on n001,
% 0.10/0.47 % Sat Sep 26 13:47:13 2026
% 0.10/0.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.48
% 0.10/0.48 % From the command line: assign(max_seconds, 300).
% 0.85/0.76
% 0.85/0.76 % SZS status Theorem for theBenchmark
% 0.85/0.76
% 0.85/0.76 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.85/0.76 % Length of proof is 36.
% 0.85/0.76 % Level of proof is 9.
% 0.85/0.76 % Maximum clause weight is 29.000.
% 0.85/0.76 % Given clauses 107.
% 0.85/0.76
% 0.85/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------