%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV416+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : 7
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 5 unt; 2 def)
% Number of atoms : 75 ( 13 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 71 ( 28 ~; 24 |; 10 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 52 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,axiom,
! [U,V] :
( pi_sharp_remove(U,V)
<=> contains_pq(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U,V] :
( pi_remove(U,V)
<=> pi_sharp_remove(i(U),V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,lemma,
! [U,V,W,X,Y] : i(triple(U,W,X)) = i(triple(V,W,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,lemma,
! [U,V,W,X] :
( contains_pq(i(triple(U,V,W)),X)
=> i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,conjecture,
! [U,V,W,X] :
( pi_remove(triple(U,V,W),X)
=> ( phi(remove_cpq(triple(U,V,W),X))
=> ( i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X)
& pi_sharp_remove(i(triple(U,V,W)),X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
~ ! [U,V,W,X] :
( pi_remove(triple(U,V,W),X)
=> ( phi(remove_cpq(triple(U,V,W),X))
=> ( i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X)
& pi_sharp_remove(i(triple(U,V,W)),X) ) ) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f196,plain,
! [U,V] :
( ( ~ contains_pq(U,V)
| pi_sharp_remove(U,V) )
& ( contains_pq(U,V)
| ~ pi_sharp_remove(U,V) ) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f197,plain,
( ! [U,V] :
( ~ contains_pq(U,V)
| pi_sharp_remove(U,V) )
& ! [U,V] :
( contains_pq(U,V)
| ~ pi_sharp_remove(U,V) ) ),
inference(miniscoping,[status(thm)],[f196]) ).
fof(f198,plain,
! [X0,X1] :
( contains_pq(X0,X1)
| ~ pi_sharp_remove(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f200,plain,
! [U,V] :
( ( ~ pi_sharp_remove(i(U),V)
| pi_remove(U,V) )
& ( pi_sharp_remove(i(U),V)
| ~ pi_remove(U,V) ) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f201,plain,
( ! [U,V] :
( ~ pi_sharp_remove(i(U),V)
| pi_remove(U,V) )
& ! [U,V] :
( pi_sharp_remove(i(U),V)
| ~ pi_remove(U,V) ) ),
inference(miniscoping,[status(thm)],[f200]) ).
fof(f202,plain,
! [X0,X1] :
( pi_sharp_remove(i(X0),X1)
| ~ pi_remove(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f231,plain,
! [X0,X1,X2,X3,X4] : i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f232,plain,
! [U,V,W,X] :
( i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X)
| ~ contains_pq(i(triple(U,V,W)),X) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f233,plain,
! [X0,X1,X2,X3] :
( i(remove_cpq(triple(X0,X1,X2),X3)) = remove_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f234,plain,
? [U,V,W,X] :
( ( i(remove_cpq(triple(U,V,W),X)) != remove_pq(i(triple(U,V,W)),X)
| ~ pi_sharp_remove(i(triple(U,V,W)),X) )
& phi(remove_cpq(triple(U,V,W),X))
& pi_remove(triple(U,V,W),X) ),
inference(pre_NNF_transformation,[status(thm)],[f66]) ).
fof(f235,plain,
( ( i(remove_cpq(triple(sK4_skl,sK5_skl,sK6_skl),sK7_skl)) != remove_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK7_skl)
| ~ pi_sharp_remove(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK7_skl) )
& phi(remove_cpq(triple(sK4_skl,sK5_skl,sK6_skl),sK7_skl))
& pi_remove(triple(sK4_skl,sK5_skl,sK6_skl),sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(U,sK4_skl),skolemize(V,sK5_skl),skolemize(W,sK6_skl),skolemize(X,sK7_skl)],[f234]) ).
fof(f236,plain,
pi_remove(triple(sK4_skl,sK5_skl,sK6_skl),sK7_skl),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f238,plain,
( i(remove_cpq(triple(sK4_skl,sK5_skl,sK6_skl),sK7_skl)) != remove_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK7_skl)
| ~ pi_sharp_remove(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK7_skl) ),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f239,definition,
( sQ0_spl
<=> pi_sharp_remove(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ0_spl
| ~ pi_sharp_remove(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK7_skl) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,definition,
( sQ1_spl
<=> i(remove_cpq(triple(sK4_skl,sK5_skl,sK6_skl),sK7_skl)) = remove_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( sQ1_spl
| i(remove_cpq(triple(sK4_skl,sK5_skl,sK6_skl),sK7_skl)) != remove_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK7_skl) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f238,f239,f242]) ).
fof(f256,plain,
( sQ0_spl
| ~ pi_remove(triple(sK4_skl,sK5_skl,sK6_skl),sK7_skl) ),
inference(resolution,[status(thm)],[f202,f241]) ).
fof(f257,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f236]) ).
fof(f258,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f264,plain,
! [X0,X1] :
( sQ1_spl
| i(remove_cpq(triple(sK4_skl,sK5_skl,sK6_skl),sK7_skl)) != remove_pq(i(triple(X0,sK5_skl,X1)),sK7_skl) ),
inference(paramodulation,[status(thm)],[f231,f244]) ).
fof(f275,plain,
( sQ1_spl
| ~ contains_pq(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK7_skl) ),
inference(resolution,[status(thm)],[f233,f264]) ).
fof(f279,plain,
( sQ1_spl
| ~ pi_sharp_remove(i(triple(sK4_skl,sK5_skl,sK6_skl)),sK7_skl) ),
inference(resolution,[status(thm)],[f275,f198]) ).
fof(f282,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f279,f239,f242]) ).
fof(f283,plain,
$false,
inference(sat_refutation,[status(thm)],[f245,f258,f282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV416+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 08:45:27 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % 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: 0.062889 seconds
% 0.12/0.42 % CPU time: 0.150314 seconds
% 0.12/0.42 % Total memory used: 104.980 MB
% 0.12/0.42 % Net memory used: 104.891 MB
%------------------------------------------------------------------------------