%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV371+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 : n006.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 09:02:12 AM UTC 2026
% Result : Theorem 30.34s 4.30s
% Output : CNFRefutation 30.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 18 unt; 0 def)
% Number of atoms : 155 ( 53 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 124 ( 40 ~; 70 |; 2 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 124 ( 14 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l7_l8,lemma,
! [X0,X1,X2] :
( phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
=> 'contains$upq'(i(triple(X0,X1,X2)),'findmin$ucpq$ures'(triple(X0,X1,X2))) ) ).
fof(l7_lX,lemma,
! [X0,X1,X2] :
( phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
=> 'issmallestelement$upq'(i(triple(X0,X1,X2)),'findmin$ucpq$ures'(triple(X0,X1,X2))) ) ).
fof(ax8,axiom,
! [X0] : ~ 'contains$upq'('create$upq',X0) ).
fof(ax9,axiom,
! [X0,X1,X2] :
( 'contains$upq'('insert$upq'(X0,X1),X2)
<=> ( X1 = X2
| 'contains$upq'(X0,X2) ) ) ).
fof(ax10,axiom,
! [X0,X1] :
( 'issmallestelement$upq'(X0,X1)
<=> ! [X2] :
( 'contains$upq'(X0,X2)
=> 'less$uthan'(X1,X2) ) ) ).
fof(ax11,axiom,
! [X0,X1] : 'remove$upq'('insert$upq'(X0,X1),X1) = X0 ).
fof(ax12,axiom,
! [X0,X1,X2] :
( ( X1 != X2
& 'contains$upq'(X0,X2) )
=> 'remove$upq'('insert$upq'(X0,X1),X2) = 'insert$upq'('remove$upq'(X0,X2),X1) ) ).
fof(ax46,axiom,
! [X0,X1] : 'findmin$ucpq$ueff'(triple(X0,'create$uslb',X1)) = triple(X0,'create$uslb',bad) ).
fof(ax50,axiom,
! [X0,X1] : 'findmin$ucpq$ures'(triple(X0,'create$uslb',X1)) = bottom ).
fof(ax51,axiom,
! [X0,X1,X2,X3] :
( X1 != 'create$uslb'
=> 'findmin$ucpq$ures'(triple(X0,X1,X2)) = 'findmin$upqp$ures'(X0) ) ).
fof(ax54,axiom,
! [X0,X1] : i(triple(X0,'create$uslb',X1)) = 'create$upq' ).
fof(ax56,axiom,
! [X0,X1] :
( 'pi$usharp$uremove'(X0,X1)
<=> 'contains$upq'(X0,X1) ) ).
fof(ax57,axiom,
! [X0,X1] :
( 'pi$uremove'(X0,X1)
<=> 'pi$usharp$uremove'(i(X0),X1) ) ).
fof(ax58,axiom,
! [X0,X1] :
( 'pi$usharp$ufind$umin'(X0,X1)
<=> ( 'issmallestelement$upq'(X0,X1)
& 'contains$upq'(X0,X1) ) ) ).
fof(l7_co,conjecture,
! [X0,X1,X2] :
( phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
=> 'pi$usharp$ufind$umin'(i(triple(X0,X1,X2)),'findmin$ucpq$ures'(triple(X0,X1,X2))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
=> 'pi$usharp$ufind$umin'(i(triple(X0,X1,X2)),'findmin$ucpq$ures'(triple(X0,X1,X2))) ),
inference(negate_conjecture,[status(cth)],[l7_co]) ).
cnf(c0,plain,
( 'contains$upq'(i(triple(X0,X1,X2)),'findmin$ucpq$ures'(triple(X0,X1,X2)))
| ~ phi('findmin$ucpq$ueff'(triple(X0,X1,X2))) ),
inference(clausification,[status(esa)],[l7_l8]) ).
cnf(c1,plain,
( 'issmallestelement$upq'(i(triple(X0,X1,X2)),'findmin$ucpq$ures'(triple(X0,X1,X2)))
| ~ phi('findmin$ucpq$ueff'(triple(X0,X1,X2))) ),
inference(clausification,[status(esa)],[l7_lX]) ).
cnf(c11,plain,
~ 'contains$upq'('create$upq',X0),
inference(clausification,[status(esa)],[ax8]) ).
cnf(c14,plain,
( X1 != X2
| 'contains$upq'('insert$upq'(X0,X1),X2) ),
inference(clausification,[status(esa)],[ax9]) ).
cnf(c15,plain,
( 'less$uthan'(X1,X2)
| ~ 'contains$upq'(X0,X2)
| ~ 'issmallestelement$upq'(X0,X1) ),
inference(clausification,[status(esa)],[ax10]) ).
cnf(c16,plain,
( 'contains$upq'(X0,sK24(X0,X1))
| 'issmallestelement$upq'(X0,X1) ),
inference(clausification,[status(esa)],[ax10]) ).
cnf(c17,plain,
( ~ 'less$uthan'(X1,sK24(X0,X1))
| 'issmallestelement$upq'(X0,X1) ),
inference(clausification,[status(esa)],[ax10]) ).
cnf(c18,plain,
'remove$upq'('insert$upq'(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[ax11]) ).
cnf(c19,plain,
( 'remove$upq'('insert$upq'(X0,X2),X1) = 'insert$upq'('remove$upq'(X0,X1),X2)
| X2 = X1
| ~ 'contains$upq'(X0,X1) ),
inference(clausification,[status(esa)],[ax12]) ).
cnf(c60,plain,
'findmin$ucpq$ueff'(triple(X0,'create$uslb',X1)) = triple(X0,'create$uslb',bad),
inference(clausification,[status(esa)],[ax46]) ).
cnf(c64,plain,
'findmin$ucpq$ures'(triple(X0,'create$uslb',X1)) = bottom,
inference(clausification,[status(esa)],[ax50]) ).
cnf(c65,plain,
( 'findmin$ucpq$ures'(triple(X1,X0,X2)) = 'findmin$upqp$ures'(X1)
| X0 = 'create$uslb' ),
inference(clausification,[status(esa)],[ax51]) ).
cnf(c68,plain,
i(triple(X0,'create$uslb',X1)) = 'create$upq',
inference(clausification,[status(esa)],[ax54]) ).
cnf(c70,plain,
( 'contains$upq'(X0,X1)
| ~ 'pi$usharp$uremove'(X0,X1) ),
inference(clausification,[status(esa)],[ax56]) ).
cnf(c71,plain,
( ~ 'contains$upq'(X0,X1)
| 'pi$usharp$uremove'(X0,X1) ),
inference(clausification,[status(esa)],[ax56]) ).
cnf(c72,plain,
( 'pi$usharp$uremove'(i(X0),X1)
| ~ 'pi$uremove'(X0,X1) ),
inference(clausification,[status(esa)],[ax57]) ).
cnf(c73,plain,
( ~ 'pi$usharp$uremove'(i(X0),X1)
| 'pi$uremove'(X0,X1) ),
inference(clausification,[status(esa)],[ax57]) ).
cnf(c76,plain,
( ~ 'issmallestelement$upq'(X0,X1)
| ~ 'contains$upq'(X0,X1)
| 'pi$usharp$ufind$umin'(X0,X1) ),
inference(clausification,[status(esa)],[ax58]) ).
cnf(c88,plain,
phi('findmin$ucpq$ueff'(triple(sK173,sK174,sK175))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c89,plain,
~ 'pi$usharp$ufind$umin'(i(triple(sK173,sK174,sK175)),'findmin$ucpq$ures'(triple(sK173,sK174,sK175))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( sK174 = 'create$uslb'
| ~ 'pi$usharp$ufind$umin'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173)) ),
inference(superposition,[status(thm)],[c65,c89]) ).
cnf(d1,plain,
( X1 = 'create$uslb'
| ~ phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
| 'contains$upq'(i(triple(X0,X1,X2)),'findmin$upqp$ures'(X0)) ),
inference(superposition,[status(thm)],[c65,c0]) ).
cnf(d2,plain,
( 'issmallestelement$upq'(X0,X1)
| 'pi$usharp$uremove'(X0,sK24(X0,X1)) ),
inference(resolution,[status(thm)],[c71,c16]) ).
cnf(d3,plain,
( 'pi$uremove'(X0,sK24(i(X0),X1))
| 'issmallestelement$upq'(i(X0),X1) ),
inference(resolution,[status(thm)],[d2,c73]) ).
cnf(d4,plain,
( ~ phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
| 'less$uthan'('findmin$ucpq$ures'(triple(X0,X1,X2)),X3)
| ~ 'contains$upq'(i(triple(X0,X1,X2)),X3) ),
inference(resolution,[status(thm)],[c15,c1]) ).
cnf(d5,plain,
( 'contains$upq'(i(X0),X1)
| ~ 'pi$uremove'(X0,X1) ),
inference(resolution,[status(thm)],[c72,c70]) ).
cnf(d6,plain,
( 'less$uthan'('findmin$ucpq$ures'(triple(X0,X1,X2)),X3)
| ~ phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
| ~ 'pi$uremove'(triple(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
'contains$upq'('insert$upq'(X0,X1),X1),
inference(equality_resolution,[status(thm)],[c14]) ).
cnf(d8,plain,
'pi$usharp$uremove'('insert$upq'(X0,X1),X1),
inference(resolution,[status(thm)],[c71,d7]) ).
cnf(d9,plain,
( ~ phi('findmin$ucpq$ueff'(triple(X1,X2,X3)))
| 'remove$upq'('insert$upq'(i(triple(X1,X2,X3)),X0),'findmin$ucpq$ures'(triple(X1,X2,X3))) = 'insert$upq'('remove$upq'(i(triple(X1,X2,X3)),'findmin$ucpq$ures'(triple(X1,X2,X3))),X0)
| X0 = 'findmin$ucpq$ures'(triple(X1,X2,X3)) ),
inference(resolution,[status(thm)],[c19,c0]) ).
cnf(d10,plain,
( 'remove$upq'('insert$upq'(i(triple(sK173,sK174,sK175)),X0),'findmin$ucpq$ures'(triple(sK173,sK174,sK175))) = 'insert$upq'('remove$upq'(i(triple(sK173,sK174,sK175)),'findmin$ucpq$ures'(triple(sK173,sK174,sK175))),X0)
| X0 = 'findmin$ucpq$ures'(triple(sK173,sK174,sK175)) ),
inference(resolution,[status(thm)],[d9,c88]) ).
cnf(d11,plain,
( sK174 = 'create$uslb'
| X0 = 'findmin$ucpq$ures'(triple(sK173,sK174,sK175))
| 'remove$upq'('insert$upq'(i(triple(sK173,sK174,sK175)),X0),'findmin$upqp$ures'(sK173)) = 'insert$upq'('remove$upq'(i(triple(sK173,sK174,sK175)),'findmin$ucpq$ures'(triple(sK173,sK174,sK175))),X0) ),
inference(superposition,[status(thm)],[c65,d10]) ).
cnf(d12,plain,
( sK174 = 'create$uslb'
| X0 = 'findmin$ucpq$ures'(triple(sK173,sK174,sK175))
| 'pi$usharp$uremove'('remove$upq'('insert$upq'(i(triple(sK173,sK174,sK175)),X0),'findmin$upqp$ures'(sK173)),X0) ),
inference(superposition,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( sK174 = 'create$uslb'
| 'findmin$upqp$ures'(sK173) = 'findmin$ucpq$ures'(triple(sK173,sK174,sK175))
| 'pi$usharp$uremove'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173)) ),
inference(superposition,[status(thm)],[c18,d12]) ).
cnf(d14,plain,
( 'contains$upq'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173))
| sK174 = 'create$uslb'
| 'findmin$upqp$ures'(sK173) = 'findmin$ucpq$ures'(triple(sK173,sK174,sK175)) ),
inference(resolution,[status(thm)],[d13,c70]) ).
cnf(d15,plain,
( X1 = 'create$uslb'
| ~ phi('findmin$ucpq$ueff'(triple(X0,X1,X2)))
| 'issmallestelement$upq'(i(triple(X0,X1,X2)),'findmin$upqp$ures'(X0)) ),
inference(superposition,[status(thm)],[c65,c1]) ).
cnf(d16,plain,
( 'pi$usharp$ufind$umin'(i(triple(X1,X0,X2)),'findmin$upqp$ures'(X1))
| ~ 'contains$upq'(i(triple(X1,X0,X2)),'findmin$upqp$ures'(X1))
| ~ phi('findmin$ucpq$ueff'(triple(X1,X0,X2)))
| X0 = 'create$uslb' ),
inference(resolution,[status(thm)],[d15,c76]) ).
cnf(d17,plain,
( sK174 = 'create$uslb'
| 'findmin$upqp$ures'(sK173) = 'findmin$ucpq$ures'(triple(sK173,sK174,sK175))
| 'pi$usharp$ufind$umin'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173))
| ~ phi('findmin$ucpq$ueff'(triple(sK173,sK174,sK175)))
| sK174 = 'create$uslb' ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( 'pi$usharp$ufind$umin'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173))
| sK174 = 'create$uslb'
| 'findmin$upqp$ures'(sK173) = 'findmin$ucpq$ures'(triple(sK173,sK174,sK175)) ),
inference(resolution,[status(thm)],[c88,d17]) ).
cnf(d19,plain,
( sK174 = 'create$uslb'
| sK174 = 'create$uslb'
| 'findmin$upqp$ures'(sK173) = 'findmin$ucpq$ures'(triple(sK173,sK174,sK175)) ),
inference(resolution,[status(thm)],[d18,d0]) ).
cnf(d20,plain,
( sK174 = 'create$uslb'
| ~ 'pi$uremove'(triple(sK173,sK174,sK175),X0)
| ~ phi('findmin$ucpq$ueff'(triple(sK173,sK174,sK175)))
| 'less$uthan'('findmin$upqp$ures'(sK173),X0) ),
inference(superposition,[status(thm)],[d19,d6]) ).
cnf(d21,plain,
( ~ 'pi$uremove'(triple(sK173,sK174,sK175),X0)
| 'less$uthan'('findmin$upqp$ures'(sK173),X0)
| sK174 = 'create$uslb' ),
inference(resolution,[status(thm)],[c88,d20]) ).
cnf(d22,plain,
( 'issmallestelement$upq'(i(triple(sK173,sK174,sK175)),X0)
| 'less$uthan'('findmin$upqp$ures'(sK173),sK24(i(triple(sK173,sK174,sK175)),X0))
| sK174 = 'create$uslb' ),
inference(resolution,[status(thm)],[d21,d3]) ).
cnf(d23,plain,
( 'issmallestelement$upq'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173))
| 'issmallestelement$upq'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173))
| sK174 = 'create$uslb' ),
inference(resolution,[status(thm)],[d22,c17]) ).
cnf(d24,plain,
( 'pi$usharp$ufind$umin'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173))
| ~ 'contains$upq'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173))
| sK174 = 'create$uslb' ),
inference(resolution,[status(thm)],[d23,c76]) ).
cnf(d25,plain,
( ~ phi('findmin$ucpq$ueff'(triple(sK173,sK174,sK175)))
| sK174 = 'create$uslb'
| 'pi$usharp$ufind$umin'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173))
| sK174 = 'create$uslb' ),
inference(resolution,[status(thm)],[d24,d1]) ).
cnf(d26,plain,
( 'pi$usharp$ufind$umin'(i(triple(sK173,sK174,sK175)),'findmin$upqp$ures'(sK173))
| sK174 = 'create$uslb' ),
inference(resolution,[status(thm)],[c88,d25]) ).
cnf(d27,plain,
( sK174 = 'create$uslb'
| sK174 = 'create$uslb' ),
inference(resolution,[status(thm)],[d26,d0]) ).
cnf(d28,plain,
phi('findmin$ucpq$ueff'(triple(sK173,'create$uslb',sK175))),
inference(demodulation,[status(thm)],[c88,d27]) ).
cnf(d29,plain,
phi(triple(sK173,'create$uslb',bad)),
inference(demodulation,[status(thm)],[d28,c60]) ).
cnf(d30,plain,
( ~ phi('findmin$ucpq$ueff'(triple(X0,'create$uslb',X1)))
| 'contains$upq'(i(triple(X0,'create$uslb',X1)),bottom) ),
inference(superposition,[status(thm)],[c64,c0]) ).
cnf(d31,plain,
( 'contains$upq'(i(triple(X0,'create$uslb',X1)),bottom)
| ~ phi(triple(X0,'create$uslb',bad)) ),
inference(demodulation,[status(thm)],[d30,c60]) ).
cnf(d32,plain,
( 'contains$upq'('create$upq',bottom)
| ~ phi(triple(X0,'create$uslb',bad)) ),
inference(demodulation,[status(thm)],[d31,c68]) ).
cnf(d33,plain,
~ phi(triple(X0,'create$uslb',bad)),
inference(resolution,[status(thm)],[c11,d32]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[d33,d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV371+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
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 13:38:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.34/4.30 % SZS status Theorem for theBenchmark.p
% 30.34/4.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------