%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV412+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 : 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 09:07:39 AM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 46 ( 18 ~; 12 |; 12 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 33 ( 0 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(l48_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',l48_li3839) ).
fof(l48_co,conjecture,
! [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',l48_co) ).
fof(l48_co_neg,negated_conjecture,
~ ! [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) ),
inference(assume_negation,[status(cth)],[l48_co]) ).
cnf(c_20,plain,
( less_than(B,A)
| ~ less_than(A,B)
| strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_21,plain,
( ~ less_than(B,A)
| ~ strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_22,plain,
( less_than(A,B)
| ~ strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_24,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)],[l48_li3839]) ).
fof(nnf_19,plain,
? [U,V,W,X] :
( ~ pair_in_list(update_slb(U,X),V,X)
& strictly_less_than(W,X)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) ),
inference(fof_nnf,[status(thm)],[l48_co_neg]) ).
fof(sk_l48_co_neg,plain,
( ~ pair_in_list(update_slb(sK2,sK1),sK3,sK1)
& strictly_less_than(sK0,sK1)
& strictly_less_than(sK3,sK1)
& pair_in_list(sK2,sK3,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0,sK1]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK1)],[nnf_19]) ).
cnf(c_26,negated_conjecture,
strictly_less_than(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_l48_co_neg]) ).
cnf(c_27,negated_conjecture,
less_than(sK0,sK1),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_28,negated_conjecture,
~ less_than(sK1,sK0),
inference(resolve,[status(thm)],[c_26,c_21]) ).
cnf(c_35,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_24,c_20]) ).
cnf(c_37,negated_conjecture,
~ pair_in_list(update_slb(sK2,sK1),sK3,sK1),
inference(split_conjunct,[status(thm)],[sk_l48_co_neg]) ).
cnf(c_38,negated_conjecture,
pair_in_list(sK2,sK3,sK0),
inference(split_conjunct,[status(thm)],[sk_l48_co_neg]) ).
cnf(c_63,negated_conjecture,
( less_than(sK1,A)
| ~ less_than(A,sK1)
| ~ pair_in_list(sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_35,c_37]) ).
cnf(c_64,negated_conjecture,
( less_than(sK1,sK0)
| ~ pair_in_list(sK2,sK3,sK0) ),
inference(resolve,[status(thm)],[c_63,c_27]) ).
cnf(c_65,negated_conjecture,
~ pair_in_list(sK2,sK3,sK0),
inference(resolve,[status(thm)],[c_64,c_28]) ).
cnf(c_62,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_38,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV412+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 13:47:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1940223 was started by sandbox2 on n001,
% 0.11/0.37 % Sat Sep 26 13:47:28 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Theorem for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 14.
% 0.11/0.39 % Level of proof is 3.
% 0.11/0.39 % Maximum clause weight is 16.000.
% 0.11/0.39 % Given clauses 11.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------