%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV390+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 09:07:37 AM UTC 2026
% Result : Theorem 0.58s 0.58s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 59 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 59 ( 27 ~; 18 |; 8 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 82 ( 11 sgn 44 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bottom_smallest,axiom,
! [U] : less_than(bottom,U),
file('theBenchmark.p',bottom_smallest) ).
fof(ax37,axiom,
! [U,V,W,X,Y] :
( less_than(Y,X)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) ) ),
file('theBenchmark.p',ax37) ).
fof(ax42,axiom,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
file('theBenchmark.p',ax42) ).
fof(l26_li4142,axiom,
! [U,V,W] :
( check_cpq(triple(U,V,W))
<=> ! [X,Y] :
( pair_in_list(V,X,Y)
=> less_than(Y,X) ) ),
file('theBenchmark.p',l26_li4142) ).
fof(l26_co,conjecture,
! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ! [X] : ~ check_cpq(insert_cpq(triple(U,V,W),X)) ),
file('theBenchmark.p',l26_co) ).
fof(l26_co_neg,negated_conjecture,
~ ! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ! [X] : ~ check_cpq(insert_cpq(triple(U,V,W),X)) ),
inference(assume_negation,[status(cth)],[l26_co]) ).
cnf(c_49,plain,
less_than(bottom,A),
inference(clausify,[status(thm)],[bottom_smallest]) ).
cnf(c_74,plain,
( check_cpq(triple(C,D,E))
| ~ check_cpq(triple(C,insert_slb(D,pair(B,A)),E))
| ~ less_than(A,B) ),
inference(clausify,[status(thm)],[ax37]) ).
cnf(c_81,plain,
triple(insert_pqp(A,B),insert_slb(C,pair(B,bottom)),D) = insert_cpq(triple(A,C,D),B),
inference(clausify,[status(thm)],[ax42]) ).
fof(nnf_41,plain,
! [U,V,W] :
( ( ? [X,Y] :
( ~ less_than(Y,X)
& pair_in_list(V,X,Y) )
| check_cpq(triple(U,V,W)) )
& ( ! [X0,X1] :
( less_than(X1,X0)
| ~ pair_in_list(V,X0,X1) )
| ~ check_cpq(triple(U,V,W)) ) ),
inference(fof_nnf,[status(thm)],[l26_li4142]) ).
fof(sk_l26_li4142_sk,plain,
! [U,V,W] :
( ( ( ~ less_than(sK1(U,V,W),sK0(U,V,W))
& pair_in_list(V,sK0(U,V,W),sK1(U,V,W)) )
| check_cpq(triple(U,V,W)) )
& ( ! [X0,X1] :
( less_than(X1,X0)
| ~ pair_in_list(V,X0,X1) )
| ~ check_cpq(triple(U,V,W)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0(U,V,W)),skolemize(Y,sK1(U,V,W))],[nnf_41]) ).
fof(sk_l26_li4142,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ less_than(sK1(VAR_0,VAR_1,VAR_2),sK0(VAR_0,VAR_1,VAR_2))
| check_cpq(triple(VAR_0,VAR_1,VAR_2)) )
& ! [VAR_0,VAR_1,VAR_2] :
( pair_in_list(VAR_1,sK0(VAR_0,VAR_1,VAR_2),sK1(VAR_0,VAR_1,VAR_2))
| check_cpq(triple(VAR_0,VAR_1,VAR_2)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( less_than(VAR_4,VAR_3)
| ~ pair_in_list(VAR_1,VAR_3,VAR_4)
| ~ check_cpq(triple(VAR_0,VAR_1,VAR_2)) ) ),
inference(cnf_transformation,[status(thm)],[sk_l26_li4142_sk]) ).
cnf(c_98,plain,
( less_than(E,D)
| ~ pair_in_list(B,D,E)
| ~ check_cpq(triple(A,B,C)) ),
inference(split_conjunct,[status(thm)],[sk_l26_li4142]) ).
cnf(c_99,plain,
( pair_in_list(B,sK0(A,B,C),sK1(A,B,C))
| check_cpq(triple(A,B,C)) ),
inference(split_conjunct,[status(thm)],[sk_l26_li4142]) ).
cnf(c_100,plain,
( ~ less_than(sK1(A,B,C),sK0(A,B,C))
| check_cpq(triple(A,B,C)) ),
inference(split_conjunct,[status(thm)],[sk_l26_li4142]) ).
fof(nnf_42,plain,
? [U,V,W] :
( ? [X] : check_cpq(insert_cpq(triple(U,V,W),X))
& ~ check_cpq(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[l26_co_neg]) ).
fof(sk_l26_co_neg,plain,
( check_cpq(insert_cpq(triple(sK2,sK3,sK4),sK5))
& ~ check_cpq(triple(sK2,sK3,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK4),skolemize(X,sK5)],[nnf_42]) ).
cnf(c_101,negated_conjecture,
~ check_cpq(triple(sK2,sK3,sK4)),
inference(split_conjunct,[status(thm)],[sk_l26_co_neg]) ).
cnf(c_102,negated_conjecture,
check_cpq(insert_cpq(triple(sK2,sK3,sK4),sK5)),
inference(split_conjunct,[status(thm)],[sk_l26_co_neg]) ).
cnf(c_246,plain,
pair_in_list(sK3,sK0(sK2,sK3,sK4),sK1(sK2,sK3,sK4)),
inference(resolve,[status(thm)],[c_101,c_99]) ).
cnf(c_247,negated_conjecture,
~ less_than(sK1(sK2,sK3,sK4),sK0(sK2,sK3,sK4)),
inference(resolve,[status(thm)],[c_100,c_101]) ).
cnf(c_250,plain,
check_cpq(triple(insert_pqp(sK2,sK5),insert_slb(sK3,pair(sK5,bottom)),sK4)),
inference(paramod,[status(thm)],[c_81,c_102]) ).
cnf(c_898,plain,
( less_than(sK1(sK2,sK3,sK4),sK0(sK2,sK3,sK4))
| ~ check_cpq(triple(A,sK3,B)) ),
inference(resolve,[status(thm)],[c_246,c_98]) ).
cnf(c_886,plain,
~ check_cpq(triple(A,sK3,B)),
inference(resolve,[status(thm)],[c_247,c_898]) ).
cnf(c_899,plain,
( check_cpq(triple(A,B,D))
| ~ check_cpq(triple(A,insert_slb(B,pair(C,bottom)),D)) ),
inference(resolve,[status(thm)],[c_74,c_49]) ).
cnf(c_896,plain,
~ check_cpq(triple(A,insert_slb(sK3,pair(B,bottom)),C)),
inference(resolve,[status(thm)],[c_899,c_886]) ).
cnf(c_897,plain,
$false,
inference(resolve,[status(thm)],[c_896,c_250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV390+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n017.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 13:36:03 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 844567 was started by sandbox2 on n017,
% 0.17/0.43 % Sat Sep 26 13:36:03 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.58/0.58
% 0.58/0.58 % SZS status Theorem for theBenchmark
% 0.58/0.58
% 0.58/0.58 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.58/0.58 % Length of proof is 19.
% 0.58/0.58 % Level of proof is 5.
% 0.58/0.58 % Maximum clause weight is 37.000.
% 0.58/0.58 % Given clauses 139.
% 0.58/0.58
% 0.58/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------