%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV371+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 : n005.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 09:07:34 AM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 5 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 12 ~; 7 |; 3 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax58,axiom,
! [U,V] :
( pi_sharp_find_min(U,V)
<=> ( issmallestelement_pq(U,V)
& contains_pq(U,V) ) ),
file('theBenchmark.p',ax58) ).
fof(l7_l8,axiom,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('theBenchmark.p',l7_l8) ).
fof(l7_lX,axiom,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('theBenchmark.p',l7_lX) ).
fof(l7_co,conjecture,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('theBenchmark.p',l7_co) ).
fof(l7_co_neg,negated_conjecture,
~ ! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
inference(assume_negation,[status(cth)],[l7_co]) ).
cnf(c_72,plain,
( ~ issmallestelement_pq(A,B)
| ~ contains_pq(A,B)
| pi_sharp_find_min(A,B) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_75,plain,
( issmallestelement_pq(i(triple(A,B,C)),findmin_cpq_res(triple(A,B,C)))
| ~ phi(findmin_cpq_eff(triple(A,B,C))) ),
inference(clausify,[status(thm)],[l7_lX]) ).
cnf(c_163,plain,
( contains_pq(i(triple(A,B,C)),findmin_cpq_res(triple(A,B,C)))
| ~ phi(findmin_cpq_eff(triple(A,B,C))) ),
inference(clausify,[status(thm)],[l7_l8]) ).
fof(nnf_63,plain,
? [U,V,W] :
( ~ pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W)))
& phi(findmin_cpq_eff(triple(U,V,W))) ),
inference(fof_nnf,[status(thm)],[l7_co_neg]) ).
fof(sk_l7_co_neg,plain,
( ~ pi_sharp_find_min(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
& phi(findmin_cpq_eff(triple(sK0,sK1,sK2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2)],[nnf_63]) ).
cnf(c_164,negated_conjecture,
phi(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l7_co_neg]) ).
cnf(c_165,negated_conjecture,
~ pi_sharp_find_min(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l7_co_neg]) ).
cnf(c_183,plain,
( ~ contains_pq(i(triple(A,B,C)),findmin_cpq_res(triple(A,B,C)))
| pi_sharp_find_min(i(triple(A,B,C)),findmin_cpq_res(triple(A,B,C)))
| ~ phi(findmin_cpq_eff(triple(A,B,C))) ),
inference(resolve,[status(thm)],[c_75,c_72]) ).
cnf(c_306,plain,
contains_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(resolve,[status(thm)],[c_164,c_163]) ).
cnf(c_323,negated_conjecture,
( ~ contains_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
| pi_sharp_find_min(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))) ),
inference(resolve,[status(thm)],[c_183,c_164]) ).
cnf(c_324,negated_conjecture,
~ contains_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(resolve,[status(thm)],[c_165,c_323]) ).
cnf(c_322,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_306,c_324]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV371+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 13:39:02 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2286865 was started by sandbox2 on n005,
% 0.07/0.35 % Sat Sep 26 13:39:02 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.43
% 0.13/0.43 % SZS status Theorem for theBenchmark
% 0.13/0.43
% 0.13/0.43 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.13/0.43 % Length of proof is 12.
% 0.13/0.43 % Level of proof is 3.
% 0.13/0.43 % Maximum clause weight is 43.000.
% 0.13/0.43 % Given clauses 88.
% 0.13/0.43
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------