%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 09:02:18 AM UTC 2026
% Result : Theorem 25.22s 4.06s
% Output : CNFRefutation 25.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 49 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 54 ( 26 ~; 17 |; 4 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 32 ( 0 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(main4_l7,lemma,
! [X0,X1,X2] :
( phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
=> 'pi$usharp$ufind$umin'(i(triple(X0,X1,X2)),'findmin$ucpq$ures'(triple(X0,X1,X2))) ) ).
fof(ax14,axiom,
! [X0,X1] :
( ( 'issmallestelement$upq'(X0,X1)
& 'contains$upq'(X0,X1) )
=> 'findmin$upq$ures'(X0,X1) = X1 ) ).
fof(ax58,axiom,
! [X0,X1] :
( 'pi$usharp$ufind$umin'(X0,X1)
<=> ( 'issmallestelement$upq'(X0,X1)
& 'contains$upq'(X0,X1) ) ) ).
fof(co4,conjecture,
! [X0,X1,X2] :
( 'pi$ufind$umin'(triple(X0,X1,X2))
=> ( phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
=> ? [X3] :
( 'findmin$ucpq$ures'(triple(X0,X1,X2)) = 'findmin$upq$ures'(i(triple(X0,X1,X2)),X3)
& 'pi$usharp$ufind$umin'(i(triple(X0,X1,X2)),X3) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( 'pi$ufind$umin'(triple(X0,X1,X2))
=> ( phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
=> ? [X3] :
( 'findmin$ucpq$ures'(triple(X0,X1,X2)) = 'findmin$upq$ures'(i(triple(X0,X1,X2)),X3)
& 'pi$usharp$ufind$umin'(i(triple(X0,X1,X2)),X3) ) ) ),
inference(negate_conjecture,[status(cth)],[co4]) ).
cnf(c0,plain,
( 'pi$usharp$ufind$umin'(i(triple(X0,X1,X2)),'findmin$ucpq$ures'(triple(X0,X1,X2)))
| ~ phi('findmin$ucpq$ueff'(triple(X0,X1,X2))) ),
inference(clausification,[status(esa)],[main4_l7]) ).
cnf(c20,plain,
( 'findmin$upq$ures'(X0,X1) = X1
| ~ 'issmallestelement$upq'(X0,X1)
| ~ 'contains$upq'(X0,X1) ),
inference(clausification,[status(esa)],[ax14]) ).
cnf(c73,plain,
( 'contains$upq'(X0,X1)
| ~ 'pi$usharp$ufind$umin'(X0,X1) ),
inference(clausification,[status(esa)],[ax58]) ).
cnf(c74,plain,
( 'issmallestelement$upq'(X0,X1)
| ~ 'pi$usharp$ufind$umin'(X0,X1) ),
inference(clausification,[status(esa)],[ax58]) ).
cnf(c88,plain,
phi('findmin$ucpq$ueff'(triple(sK170,sK171,sK172))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c89,plain,
( 'findmin$ucpq$ures'(triple(sK170,sK171,sK172)) != 'findmin$upq$ures'(i(triple(sK170,sK171,sK172)),X0)
| ~ 'pi$usharp$ufind$umin'(i(triple(sK170,sK171,sK172)),X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
| 'contains$upq'(i(triple(X0,X1,X2)),'findmin$ucpq$ures'(triple(X0,X1,X2))) ),
inference(resolution,[status(thm)],[c73,c0]) ).
cnf(d1,plain,
( ~ 'issmallestelement$upq'(i(triple(sK170,sK171,sK172)),X0)
| ~ 'contains$upq'(i(triple(sK170,sK171,sK172)),X0)
| ~ 'pi$usharp$ufind$umin'(i(triple(sK170,sK171,sK172)),X0)
| 'findmin$ucpq$ures'(triple(sK170,sK171,sK172)) != X0 ),
inference(superposition,[status(thm)],[c20,c89]) ).
cnf(d2,plain,
( ~ 'issmallestelement$upq'(i(triple(sK170,sK171,sK172)),'findmin$ucpq$ures'(triple(sK170,sK171,sK172)))
| ~ 'contains$upq'(i(triple(sK170,sK171,sK172)),'findmin$ucpq$ures'(triple(sK170,sK171,sK172)))
| ~ 'pi$usharp$ufind$umin'(i(triple(sK170,sK171,sK172)),'findmin$ucpq$ures'(triple(sK170,sK171,sK172))) ),
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
( ~ phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
| 'issmallestelement$upq'(i(triple(X0,X1,X2)),'findmin$ucpq$ures'(triple(X0,X1,X2))) ),
inference(resolution,[status(thm)],[c74,c0]) ).
cnf(d4,plain,
( ~ 'contains$upq'(i(triple(sK170,sK171,sK172)),'findmin$ucpq$ures'(triple(sK170,sK171,sK172)))
| ~ 'pi$usharp$ufind$umin'(i(triple(sK170,sK171,sK172)),'findmin$ucpq$ures'(triple(sK170,sK171,sK172)))
| ~ phi('findmin$ucpq$ueff'(triple(sK170,sK171,sK172))) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ 'contains$upq'(i(triple(sK170,sK171,sK172)),'findmin$ucpq$ures'(triple(sK170,sK171,sK172)))
| ~ 'pi$usharp$ufind$umin'(i(triple(sK170,sK171,sK172)),'findmin$ucpq$ures'(triple(sK170,sK171,sK172))) ),
inference(resolution,[status(thm)],[c88,d4]) ).
cnf(d6,plain,
( ~ phi('findmin$ucpq$ueff'(triple(sK170,sK171,sK172)))
| ~ 'pi$usharp$ufind$umin'(i(triple(sK170,sK171,sK172)),'findmin$ucpq$ures'(triple(sK170,sK171,sK172))) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
~ 'pi$usharp$ufind$umin'(i(triple(sK170,sK171,sK172)),'findmin$ucpq$ures'(triple(sK170,sK171,sK172))),
inference(resolution,[status(thm)],[c88,d6]) ).
cnf(d8,plain,
~ phi('findmin$ucpq$ueff'(triple(sK170,sK171,sK172))),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c88,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 13:42:03 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.22/4.06 % SZS status Theorem for theBenchmark.p
% 25.22/4.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------