%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 : Thu Sep 24 02:47:37 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 5 unt; 0 def)
% Number of atoms : 62 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 64 ( 25 ~; 20 |; 12 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 40 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [U,V] :
( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
=> findmin_pq_res(U,V) = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U,V] :
( pi_sharp_find_min(U,V)
<=> ( issmallestelement_pq(U,V)
& contains_pq(U,V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,lemma,
! [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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,conjecture,
! [U,V,W] :
( pi_find_min(triple(U,V,W))
=> ( phi(findmin_cpq_eff(triple(U,V,W)))
=> ? [X] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pq_res(i(triple(U,V,W)),X)
& pi_sharp_find_min(i(triple(U,V,W)),X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,negated_conjecture,
~ ! [U,V,W] :
( pi_find_min(triple(U,V,W))
=> ( phi(findmin_cpq_eff(triple(U,V,W)))
=> ? [X] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pq_res(i(triple(U,V,W)),X)
& pi_sharp_find_min(i(triple(U,V,W)),X) ) ) ),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f97,plain,
! [U,V] :
( findmin_pq_res(U,V) = V
| ~ issmallestelement_pq(U,V)
| ~ contains_pq(U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f98,plain,
! [X0,X1] :
( findmin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f203,plain,
! [U,V] :
( ( ~ issmallestelement_pq(U,V)
| ~ contains_pq(U,V)
| pi_sharp_find_min(U,V) )
& ( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
| ~ pi_sharp_find_min(U,V) ) ),
inference(NNF_transformation,[status(thm)],[f58]) ).
fof(f204,plain,
( ! [U,V] :
( ~ issmallestelement_pq(U,V)
| ~ contains_pq(U,V)
| pi_sharp_find_min(U,V) )
& ! [U,V] :
( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
| ~ pi_sharp_find_min(U,V) ) ),
inference(miniscoping,[status(thm)],[f203]) ).
fof(f205,plain,
! [X0,X1] :
( contains_pq(X0,X1)
| ~ pi_sharp_find_min(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f206,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ~ pi_sharp_find_min(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f230,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(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f231,plain,
! [X0,X1,X2] :
( pi_sharp_find_min(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f232,plain,
? [U,V,W] :
( ! [X] :
( findmin_cpq_res(triple(U,V,W)) != findmin_pq_res(i(triple(U,V,W)),X)
| ~ pi_sharp_find_min(i(triple(U,V,W)),X) )
& phi(findmin_cpq_eff(triple(U,V,W)))
& pi_find_min(triple(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f233,plain,
( ! [X] :
( findmin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)) != findmin_pq_res(i(triple(sK4_skl,sK5_skl,sK6_skl)),X)
| ~ pi_sharp_find_min(i(triple(sK4_skl,sK5_skl,sK6_skl)),X) )
& phi(findmin_cpq_eff(triple(sK4_skl,sK5_skl,sK6_skl)))
& pi_find_min(triple(sK4_skl,sK5_skl,sK6_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(U,sK4_skl),skolemize(V,sK5_skl),skolemize(W,sK6_skl)],[f232]) ).
fof(f235,plain,
phi(findmin_cpq_eff(triple(sK4_skl,sK5_skl,sK6_skl))),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f236,plain,
! [X0] :
( findmin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)) != findmin_pq_res(i(triple(sK4_skl,sK5_skl,sK6_skl)),X0)
| ~ pi_sharp_find_min(i(triple(sK4_skl,sK5_skl,sK6_skl)),X0) ),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f240,plain,
! [X0,X1] :
( ~ pi_sharp_find_min(X0,X1)
| findmin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1) ),
inference(resolution,[status(thm)],[f98,f205]) ).
fof(f241,plain,
! [X0,X1] :
( ~ pi_sharp_find_min(X0,X1)
| findmin_pq_res(X0,X1) = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f206]) ).
fof(f244,plain,
pi_sharp_find_min(i(triple(sK4_skl,sK5_skl,sK6_skl)),findmin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl))),
inference(resolution,[status(thm)],[f231,f235]) ).
fof(f245,plain,
findmin_pq_res(i(triple(sK4_skl,sK5_skl,sK6_skl)),findmin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl))) = findmin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)),
inference(resolution,[status(thm)],[f244,f241]) ).
fof(f248,plain,
~ pi_sharp_find_min(i(triple(sK4_skl,sK5_skl,sK6_skl)),findmin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl))),
inference(resolution,[status(thm)],[f245,f236]) ).
fof(f251,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f248,f244]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.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 : Mon Sep 21 08:46:09 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.051120 seconds
% 0.12/0.42 % CPU time: 0.131150 seconds
% 0.12/0.42 % Total memory used: 62.341 MB
% 0.12/0.42 % Net memory used: 62.279 MB
%------------------------------------------------------------------------------