%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV408+2 : 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 : 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 09:07:39 AM UTC 2026
% Result : Theorem 0.23s 0.52s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 64 ( 24 ~; 21 |; 13 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn 28 !; 8 ?)
% 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(l45_li4647,axiom,
! [U,V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) ),
file('theBenchmark.p',l45_li4647) ).
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(l49_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',l49_li3637) ).
fof(l44_co,conjecture,
! [U,V,W,X] :
( ( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) )
=> ( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) ) ),
file('theBenchmark.p',l44_co) ).
fof(l44_co_neg,negated_conjecture,
~ ! [U,V,W,X] :
( ( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) )
=> ( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) ) ),
inference(assume_negation,[status(cth)],[l44_co]) ).
cnf(c_46,plain,
( less_than(B,A)
| less_than(A,B) ),
inference(clausify,[status(thm)],[totality]) ).
cnf(c_50,plain,
( less_than(B,A)
| ~ less_than(A,B)
| strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
fof(nnf_41,plain,
! [U,V] :
( ? [W] : pair_in_list(U,V,W)
| ~ contains_slb(U,V) ),
inference(fof_nnf,[status(thm)],[l45_li4647]) ).
fof(sk_l45_li4647,plain,
! [U,V] :
( pair_in_list(U,V,sK0(U,V))
| ~ contains_slb(U,V) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W,sK0(U,V))],[nnf_41]) ).
cnf(c_100,plain,
( pair_in_list(A,B,sK0(A,B))
| ~ contains_slb(A,B) ),
inference(split_conjunct,[status(thm)],[sk_l45_li4647]) ).
cnf(c_101,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]) ).
cnf(c_102,plain,
( pair_in_list(update_slb(A,D),B,C)
| ~ less_than(D,C)
| ~ pair_in_list(A,B,C) ),
inference(clausify,[status(thm)],[l49_li3637]) ).
fof(nnf_44,plain,
? [U,V,W,X] :
( ! [Y] :
( ~ less_than(findmin_pqp_res(U),Y)
| ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
& ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
& strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) ),
inference(fof_nnf,[status(thm)],[l44_co_neg]) ).
fof(sk_l44_co_neg,plain,
( ! [Y] :
( ~ less_than(findmin_pqp_res(sK3),Y)
| ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,Y) )
& ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,findmin_pqp_res(sK3))
& strictly_less_than(sK2,findmin_cpq_res(triple(sK3,sK1,sK4)))
& contains_slb(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(U,sK3),skolemize(V,sK1),skolemize(W,sK4),skolemize(X,sK2)],[nnf_44]) ).
cnf(c_103,negated_conjecture,
contains_slb(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_l44_co_neg]) ).
cnf(c_105,negated_conjecture,
~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,findmin_pqp_res(sK3)),
inference(split_conjunct,[status(thm)],[sk_l44_co_neg]) ).
cnf(c_106,negated_conjecture,
( ~ less_than(findmin_pqp_res(sK3),A)
| ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,A) ),
inference(split_conjunct,[status(thm)],[sk_l44_co_neg]) ).
cnf(c_314,plain,
( less_than(B,A)
| less_than(B,A)
| strictly_less_than(A,B) ),
inference(resolve,[status(thm)],[c_50,c_46]) ).
cnf(c_111,plain,
( less_than(B,A)
| strictly_less_than(A,B) ),
inference(copy,[status(thm)],[c_314]) ).
cnf(c_176,plain,
pair_in_list(sK1,sK2,sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_103,c_100]) ).
cnf(c_315,plain,
( pair_in_list(update_slb(sK1,A),sK2,A)
| ~ strictly_less_than(sK0(sK1,sK2),A) ),
inference(resolve,[status(thm)],[c_101,c_176]) ).
cnf(c_232,negated_conjecture,
~ strictly_less_than(sK0(sK1,sK2),findmin_pqp_res(sK3)),
inference(resolve,[status(thm)],[c_315,c_105]) ).
cnf(c_242,plain,
less_than(findmin_pqp_res(sK3),sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_232,c_111]) ).
cnf(c_288,negated_conjecture,
~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_106,c_242]) ).
cnf(c_316,plain,
( pair_in_list(update_slb(A,findmin_pqp_res(sK3)),B,sK0(sK1,sK2))
| ~ pair_in_list(A,B,sK0(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_102,c_242]) ).
cnf(c_317,plain,
~ pair_in_list(sK1,sK2,sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_316,c_288]) ).
cnf(c_313,plain,
$false,
inference(resolve,[status(thm)],[c_176,c_317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV408+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 13:37:19 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 847224 was started by sandbox on n017,
% 0.17/0.44 % Sat Sep 26 13:37:19 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.52
% 0.23/0.52 % SZS status Theorem for theBenchmark
% 0.23/0.52
% 0.23/0.52 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.23/0.52 % Length of proof is 20.
% 0.23/0.52 % Level of proof is 6.
% 0.23/0.52 % Maximum clause weight is 13.000.
% 0.23/0.52 % Given clauses 96.
% 0.23/0.52
% 0.23/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------