%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV381+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 02:47:32 PM UTC 2026
% Result : Theorem 0.63s 0.74s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 116 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 124 ( 53 ~; 44 |; 18 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 121 ( 115 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [U,V] :
( issmallestelement_pq(U,V)
<=> ! [W] :
( contains_pq(U,W)
=> less_than(V,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_slb(V,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [U] : removemin_cpq_res(U) = findmin_cpq_res(U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,lemma,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_pq(i(triple(U,V,W)),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,lemma,
! [U,V,W] :
( ? [X] :
( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_cpq(triple(U,V,W),X) )
=> ~ phi(findmin_cpq_eff(triple(U,V,W))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,conjecture,
! [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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
~ ! [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))) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f70,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f72,plain,
! [U,V] :
( ( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f73,plain,
( ! [U,V] :
( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ! [U,V] :
( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f76,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f86,plain,
! [U,V] :
( issmallestelement_pq(U,V)
<=> ! [W] :
( less_than(V,W)
| ~ contains_pq(U,W) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f87,plain,
! [U,V] :
( ( ? [W] :
( ~ less_than(V,W)
& contains_pq(U,W) )
| issmallestelement_pq(U,V) )
& ( ! [W] :
( less_than(V,W)
| ~ contains_pq(U,W) )
| ~ issmallestelement_pq(U,V) ) ),
inference(NNF_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
( ! [U,V] :
( ? [W] :
( ~ less_than(V,W)
& contains_pq(U,W) )
| issmallestelement_pq(U,V) )
& ! [U,V] :
( ! [W] :
( less_than(V,W)
| ~ contains_pq(U,W) )
| ~ issmallestelement_pq(U,V) ) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f89,plain,
( ! [U,V] :
( ( ~ less_than(V,sK0_skl(V,U))
& contains_pq(U,sK0_skl(V,U)) )
| issmallestelement_pq(U,V) )
& ! [U,V] :
( ! [W] :
( less_than(V,W)
| ~ contains_pq(U,W) )
| ~ issmallestelement_pq(U,V) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W,sK0_skl(V,U))],[f88]) ).
fof(f91,plain,
! [X0,X1] :
( contains_pq(X0,sK0_skl(X1,X0))
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f92,plain,
! [X0,X1] :
( ~ less_than(X1,sK0_skl(X1,X0))
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f157,plain,
! [U,V,W,X] :
( ( ~ contains_slb(V,X)
| contains_cpq(triple(U,V,W),X) )
& ( contains_slb(V,X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(NNF_transformation,[status(thm)],[f39]) ).
fof(f158,plain,
( ! [V,X] :
( ~ contains_slb(V,X)
| ! [U,W] : contains_cpq(triple(U,V,W),X) )
& ! [V,X] :
( contains_slb(V,X)
| ! [U,W] : ~ contains_cpq(triple(U,V,W),X) ) ),
inference(miniscoping,[status(thm)],[f157]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f160,plain,
! [X0,X1,X2,X3] :
( ~ contains_slb(X1,X3)
| contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f193,plain,
! [X0] : removemin_cpq_res(X0) = findmin_cpq_res(X0),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f231,plain,
! [U,V,W,X] :
( ( ~ contains_pq(i(triple(U,V,W)),X)
| contains_cpq(triple(U,V,W),X) )
& ( contains_pq(i(triple(U,V,W)),X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(NNF_transformation,[status(thm)],[f63]) ).
fof(f232,plain,
( ! [U,V,W,X] :
( ~ contains_pq(i(triple(U,V,W)),X)
| contains_cpq(triple(U,V,W),X) )
& ! [U,V,W,X] :
( contains_pq(i(triple(U,V,W)),X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(miniscoping,[status(thm)],[f231]) ).
fof(f234,plain,
! [X0,X1,X2,X3] :
( ~ contains_pq(i(triple(X0,X1,X2)),X3)
| contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f235,plain,
! [U,V,W] :
( ~ phi(findmin_cpq_eff(triple(U,V,W)))
| ! [X] :
( ~ strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f236,plain,
! [X0,X1,X2,X3] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f237,plain,
? [U,V,W] :
( ~ issmallestelement_pq(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)],[f66]) ).
fof(f238,plain,
( ~ issmallestelement_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),findmin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)))
& phi(findmin_cpq_eff(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)],[f237]) ).
fof(f239,plain,
phi(findmin_cpq_eff(triple(sK4_skl,sK5_skl,sK6_skl))),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f240,plain,
~ issmallestelement_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),findmin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl))),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f252,plain,
~ issmallestelement_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),removemin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl))),
inference(backward_demodulation,[status(thm)],[f193,f240]) ).
fof(f255,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f70]) ).
fof(f262,plain,
contains_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK0_skl(removemin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)),i(triple(sK4_skl,sK5_skl,sK6_skl)))),
inference(resolution,[status(thm)],[f91,f252]) ).
fof(f351,plain,
~ less_than(removemin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)),sK0_skl(removemin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)),i(triple(sK4_skl,sK5_skl,sK6_skl)))),
inference(resolution,[status(thm)],[f252,f92]) ).
fof(f406,plain,
strictly_less_than(sK0_skl(removemin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)),i(triple(sK4_skl,sK5_skl,sK6_skl))),removemin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl))),
inference(resolution,[status(thm)],[f351,f255]) ).
fof(f970,plain,
! [X0,X1,X2,X3] :
( contains_slb(X1,X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(resolution,[status(thm)],[f234,f159]) ).
fof(f1082,plain,
contains_slb(sK5_skl,sK0_skl(removemin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)),i(triple(sK4_skl,sK5_skl,sK6_skl)))),
inference(resolution,[status(thm)],[f970,f262]) ).
fof(f1292,plain,
! [X0,X1,X2,X3] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ strictly_less_than(X3,removemin_cpq_res(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(forward_demodulation,[status(thm)],[f193,f236]) ).
fof(f1294,plain,
! [X0,X1,X2,X3] :
( ~ contains_slb(X2,X0)
| ~ phi(findmin_cpq_eff(triple(X1,X2,X3)))
| ~ strictly_less_than(X0,removemin_cpq_res(triple(X1,X2,X3))) ),
inference(resolution,[status(thm)],[f1292,f160]) ).
fof(f5543,plain,
! [X0] :
( ~ contains_slb(sK5_skl,X0)
| ~ strictly_less_than(X0,removemin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl))) ),
inference(resolution,[status(thm)],[f1294,f239]) ).
fof(f5553,plain,
~ strictly_less_than(sK0_skl(removemin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl)),i(triple(sK4_skl,sK5_skl,sK6_skl))),removemin_cpq_res(triple(sK4_skl,sK5_skl,sK6_skl))),
inference(resolution,[status(thm)],[f5543,f1082]) ).
fof(f5559,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5553,f406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV381+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n008.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 08:44:39 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.63/0.74 % Refutation found
% 0.63/0.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.63/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.63/0.79 % Elapsed time: 0.343829 seconds
% 0.63/0.79 % CPU time: 2.285169 seconds
% 0.63/0.79 % Total memory used: 135.017 MB
% 0.63/0.79 % Net memory used: 132.867 MB
%------------------------------------------------------------------------------