%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV403+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 : n016.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 0.49s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 13 unt; 0 def)
% Number of atoms : 107 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 88 ( 28 ~; 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 : 123 ( 13 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(l39_co,conjecture,
! [U] :
( ! [V,W,X] :
( ( strictly_less_than(W,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) )
=> ! [Y,Z,X1,X2,X3] :
( ( strictly_less_than(Z,X1)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
=> pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,X1) ) ),
file('theBenchmark.p',l39_co) ).
fof(l39_co_neg,negated_conjecture,
~ ! [U] :
( ! [V,W,X] :
( ( strictly_less_than(W,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) )
=> ! [Y,Z,X1,X2,X3] :
( ( strictly_less_than(Z,X1)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
=> pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,X1) ) ),
inference(assume_negation,[status(cth)],[l39_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]) ).
fof(nnf_18,plain,
? [U] :
( ? [Y,Z,X1,X2,X3] :
( ~ pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,X1)
& strictly_less_than(Z,X1)
& pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) )
& ! [V,W,X] :
( pair_in_list(update_slb(U,X),V,X)
| ~ strictly_less_than(W,X)
| ~ pair_in_list(U,V,W) ) ),
inference(fof_nnf,[status(thm)],[l39_co_neg]) ).
fof(sk_l39_co_neg,plain,
( ~ pair_in_list(update_slb(insert_slb(sK0,pair(sK3,sK4)),sK2),sK5,sK2)
& strictly_less_than(sK1,sK2)
& pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK1)
& ! [V,W,X] :
( pair_in_list(update_slb(sK0,X),V,X)
| ~ strictly_less_than(W,X)
| ~ pair_in_list(sK0,V,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK4,sK5,sK1,sK2]),skolemize(U,sK0),skolemize(Y,sK5),skolemize(Z,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[nnf_18]) ).
cnf(c_23,negated_conjecture,
( pair_in_list(update_slb(sK0,C),A,C)
| ~ strictly_less_than(B,C)
| ~ pair_in_list(sK0,A,B) ),
inference(split_conjunct,[status(thm)],[sk_l39_co_neg]) ).
cnf(c_24,negated_conjecture,
strictly_less_than(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_l39_co_neg]) ).
cnf(c_27,negated_conjecture,
update_slb(insert_slb(A,pair(B,sK1)),sK2) = insert_slb(update_slb(A,sK2),pair(B,sK2)),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_28,negated_conjecture,
( pair_in_list(update_slb(sK0,sK2),A,sK2)
| ~ pair_in_list(sK0,A,sK1) ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_30,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]) ).
cnf(c_31,negated_conjecture,
~ pair_in_list(update_slb(insert_slb(sK0,pair(sK3,sK4)),sK2),sK5,sK2),
inference(split_conjunct,[status(thm)],[sk_l39_co_neg]) ).
cnf(c_32,negated_conjecture,
pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK1),
inference(split_conjunct,[status(thm)],[sk_l39_co_neg]) ).
cnf(c_33,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_38,plain,
remove_slb(insert_slb(A,pair(B,C)),B) = A,
inference(clausify,[status(thm)],[ax24]) ).
cnf(c_39,plain,
( E != C
| D != B
| pair_in_list(insert_slb(A,pair(B,C)),D,E) ),
inference(clausify,[status(thm)],[ax23]) ).
cnf(c_40,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_41,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_42,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_52,plain,
( less_than(B,A)
| less_than(A,B) ),
inference(clausify,[status(thm)],[totality]) ).
cnf(c_410,plain,
( D != B
| pair_in_list(insert_slb(A,pair(B,C)),D,remove_slb(insert_slb(C,pair(E,F)),E)) ),
inference(resolve,[status(thm)],[c_39,c_38]) ).
cnf(c_57,plain,
( D != B
| pair_in_list(insert_slb(A,pair(B,C)),D,C) ),
inference(paramod,[status(thm)],[c_38,c_410]) ).
cnf(c_411,negated_conjecture,
( sK1 = sK4
| pair_in_list(sK0,sK5,sK1) ),
inference(resolve,[status(thm)],[c_41,c_32]) ).
cnf(c_59,negated_conjecture,
( sK4 = sK1
| pair_in_list(sK0,sK5,sK1) ),
inference(copy,[status(thm)],[c_411]) ).
cnf(c_412,negated_conjecture,
( sK5 = sK3
| pair_in_list(sK0,sK5,sK1) ),
inference(resolve,[status(thm)],[c_42,c_32]) ).
cnf(c_60,negated_conjecture,
( sK3 = sK5
| pair_in_list(sK0,sK5,sK1) ),
inference(copy,[status(thm)],[c_412]) ).
cnf(c_413,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_52,c_30]) ).
cnf(c_67,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_413]) ).
cnf(c_414,plain,
( ~ pair_in_list(update_slb(insert_slb(sK0,pair(sK3,sK1)),sK2),sK5,sK2)
| pair_in_list(sK0,sK5,sK1) ),
inference(paramod,[status(thm)],[c_59,c_31]) ).
cnf(c_95,plain,
( ~ pair_in_list(insert_slb(update_slb(sK0,sK2),pair(sK3,sK2)),sK5,sK2)
| pair_in_list(sK0,sK5,sK1) ),
inference(paramod,[status(thm)],[c_27,c_414]) ).
cnf(c_415,plain,
( B != D
| pair_in_list(insert_slb(A,pair(B,C)),D,C) ),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_109,plain,
( pair_in_list(insert_slb(A,pair(sK3,B)),sK5,B)
| pair_in_list(sK0,sK5,sK1) ),
inference(resolve,[status(thm)],[c_60,c_415]) ).
cnf(c_184,plain,
( ~ pair_in_list(insert_slb(update_slb(sK0,sK2),pair(sK3,sK2)),sK5,sK2)
| less_than(sK2,sK4) ),
inference(paramod,[status(thm)],[c_67,c_31]) ).
cnf(c_416,plain,
( pair_in_list(sK0,sK5,sK1)
| pair_in_list(sK0,sK5,sK1) ),
inference(resolve,[status(thm)],[c_95,c_109]) ).
cnf(c_389,plain,
pair_in_list(sK0,sK5,sK1),
inference(copy,[status(thm)],[c_416]) ).
cnf(c_392,plain,
pair_in_list(update_slb(sK0,sK2),sK5,sK2),
inference(resolve,[status(thm)],[c_389,c_28]) ).
cnf(c_393,plain,
pair_in_list(insert_slb(update_slb(sK0,sK2),pair(A,B)),sK5,sK2),
inference(resolve,[status(thm)],[c_392,c_40]) ).
cnf(c_395,plain,
less_than(sK2,sK4),
inference(resolve,[status(thm)],[c_393,c_184]) ).
cnf(c_406,plain,
update_slb(insert_slb(A,pair(B,sK4)),sK2) = insert_slb(update_slb(A,sK2),pair(B,sK4)),
inference(resolve,[status(thm)],[c_395,c_33]) ).
cnf(c_417,negated_conjecture,
~ pair_in_list(insert_slb(update_slb(sK0,sK2),pair(sK3,sK4)),sK5,sK2),
inference(paramod,[status(thm)],[c_406,c_31]) ).
cnf(c_409,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_393,c_417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV403+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 13:46:00 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1002039 was started by sandbox on n016,
% 0.09/0.35 % Sat Sep 26 13:46:00 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.85/0.49
% 0.85/0.49 % SZS status Theorem for theBenchmark
% 0.85/0.49
% 0.85/0.49 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.85/0.49 % Length of proof is 36.
% 0.85/0.49 % Level of proof is 9.
% 0.85/0.49 % Maximum clause weight is 29.000.
% 0.85/0.49 % Given clauses 106.
% 0.85/0.49
% 0.85/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------