%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV373+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 : n002.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 09:07:35 AM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 36 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 19 ~; 6 |; 4 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 35 ( 9 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax39,axiom,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_slb(V,X) ),
file('theBenchmark.p',ax39) ).
fof(ax51,axiom,
! [U,V,W,X] :
( V != create_slb
=> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U) ),
file('theBenchmark.p',ax51) ).
fof(l9_l10,axiom,
! [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
=> ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb ) ),
file('theBenchmark.p',l9_l10) ).
fof(l9_co,conjecture,
! [U,V,W] :
( ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W)))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
file('theBenchmark.p',l9_co) ).
fof(l9_co_neg,negated_conjecture,
~ ! [U,V,W] :
( ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W)))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(assume_negation,[status(cth)],[l9_co]) ).
cnf(c_78,plain,
( ~ contains_slb(B,D)
| contains_cpq(triple(A,B,C),D) ),
inference(clausify,[status(thm)],[ax39]) ).
cnf(c_90,plain,
( findmin_cpq_res(triple(B,A,C)) = findmin_pqp_res(B)
| create_slb = A ),
inference(clausify,[status(thm)],[ax51]) ).
cnf(c_93,plain,
( create_slb != B
| ~ ok(findmin_cpq_eff(triple(A,B,C))) ),
inference(clausify,[status(thm)],[l9_l10]) ).
cnf(c_94,plain,
( contains_slb(B,findmin_pqp_res(A))
| ~ ok(findmin_cpq_eff(triple(A,B,C))) ),
inference(clausify,[status(thm)],[l9_l10]) ).
fof(nnf_42,plain,
? [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
& ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W))) ),
inference(fof_nnf,[status(thm)],[l9_co_neg]) ).
fof(sk_l9_co_neg,plain,
( ok(findmin_cpq_eff(triple(sK0,sK1,sK2)))
& ~ contains_cpq(triple(sK0,sK1,sK2),findmin_cpq_res(triple(sK0,sK1,sK2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2)],[nnf_42]) ).
cnf(c_96,negated_conjecture,
~ contains_cpq(triple(sK0,sK1,sK2),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l9_co_neg]) ).
cnf(c_97,negated_conjecture,
ok(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l9_co_neg]) ).
cnf(c_200,plain,
( ~ contains_cpq(triple(sK0,sK1,sK2),findmin_pqp_res(sK0))
| create_slb = sK1 ),
inference(paramod,[status(thm)],[c_90,c_96]) ).
cnf(c_170,plain,
( ~ contains_cpq(triple(sK0,sK1,sK2),findmin_pqp_res(sK0))
| sK1 = create_slb ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_172,plain,
contains_slb(sK1,findmin_pqp_res(sK0)),
inference(resolve,[status(thm)],[c_97,c_94]) ).
cnf(c_201,negated_conjecture,
create_slb != sK1,
inference(resolve,[status(thm)],[c_97,c_93]) ).
cnf(c_173,negated_conjecture,
sK1 != create_slb,
inference(copy,[status(thm)],[c_201]) ).
cnf(c_174,plain,
~ contains_cpq(triple(sK0,sK1,sK2),findmin_pqp_res(sK0)),
inference(resolve,[status(thm)],[c_173,c_170]) ).
cnf(c_198,plain,
contains_cpq(triple(A,sK1,B),findmin_pqp_res(sK0)),
inference(resolve,[status(thm)],[c_172,c_78]) ).
cnf(c_199,plain,
$false,
inference(resolve,[status(thm)],[c_198,c_174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV373+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n002.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 13:42:20 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 1869976 was started by sandbox on n002,
% 0.18/0.43 % Sat Sep 26 13:42:20 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.49
% 0.18/0.49 % SZS status Theorem for theBenchmark
% 0.18/0.49
% 0.18/0.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/0.49 % Length of proof is 16.
% 0.18/0.49 % Level of proof is 4.
% 0.18/0.49 % Maximum clause weight is 11.000.
% 0.18/0.49 % Given clauses 63.
% 0.18/0.49
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------