%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU344+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 : n003.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 08:41:43 AM UTC 2026
% Result : Theorem 19.02s 2.85s
% Output : CNFRefutation 19.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 144 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 145 ( 56 ~; 70 |; 5 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 5 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_lattices,axiom,
! [X0] :
( ( 'join$usemilatt$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,'the$ucarrier'(X0))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 ) ) ) ) ).
fof(dt_k1_lattice3,axiom,
! [X0] :
( 'latt$ustr'('boole$ulattice'(X0))
& 'strict$ulatt$ustr'('boole$ulattice'(X0)) ) ).
fof(dt_l3_lattices,axiom,
! [X0] :
( 'latt$ustr'(X0)
=> ( 'join$usemilatt$ustr'(X0)
& 'meet$usemilatt$ustr'(X0) ) ) ).
fof(fc1_lattice3,axiom,
! [X0] :
( 'strict$ulatt$ustr'('boole$ulattice'(X0))
& ~ 'empty$ucarrier'('boole$ulattice'(X0)) ) ).
fof(idempotence_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X0) = X0 ).
fof(t12_xboole_1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> 'set$uunion2'(X0,X1) = X1 ) ).
fof(t1_lattice3,axiom,
! [X0,X1] :
( element(X1,'the$ucarrier'('boole$ulattice'(X0)))
=> ! [X2] :
( element(X2,'the$ucarrier'('boole$ulattice'(X0)))
=> ( meet('boole$ulattice'(X0),X1,X2) = 'set$uintersection2'(X1,X2)
& join('boole$ulattice'(X0),X1,X2) = 'set$uunion2'(X1,X2) ) ) ) ).
fof(t7_xboole_1,axiom,
! [X0,X1] : subset(X0,'set$uunion2'(X0,X1)) ).
fof(t2_lattice3,conjecture,
! [X0,X1] :
( element(X1,'the$ucarrier'('boole$ulattice'(X0)))
=> ! [X2] :
( element(X2,'the$ucarrier'('boole$ulattice'(X0)))
=> ( below('boole$ulattice'(X0),X1,X2)
<=> subset(X1,X2) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( element(X1,'the$ucarrier'('boole$ulattice'(X0)))
=> ! [X2] :
( element(X2,'the$ucarrier'('boole$ulattice'(X0)))
=> ( below('boole$ulattice'(X0),X1,X2)
<=> subset(X1,X2) ) ) ),
inference(negate_conjecture,[status(cth)],[t2_lattice3]) ).
cnf(c9,plain,
( ~ below(X1,X2,X0)
| ~ element(X2,'the$ucarrier'(X1))
| join(X1,X2,X0) = X0
| 'empty$ucarrier'(X1)
| ~ 'join$usemilatt$ustr'(X1)
| ~ element(X0,'the$ucarrier'(X1)) ),
inference(clausification,[status(esa)],[d3_lattices]) ).
cnf(c10,plain,
( join(X1,X2,X0) != X0
| 'empty$ucarrier'(X1)
| ~ element(X2,'the$ucarrier'(X1))
| below(X1,X2,X0)
| ~ 'join$usemilatt$ustr'(X1)
| ~ element(X0,'the$ucarrier'(X1)) ),
inference(clausification,[status(esa)],[d3_lattices]) ).
cnf(c15,plain,
'latt$ustr'('boole$ulattice'(X0)),
inference(clausification,[status(esa)],[dt_k1_lattice3]) ).
cnf(c22,plain,
( 'join$usemilatt$ustr'(X0)
| ~ 'latt$ustr'(X0) ),
inference(clausification,[status(esa)],[dt_l3_lattices]) ).
cnf(c37,plain,
~ 'empty$ucarrier'('boole$ulattice'(X0)),
inference(clausification,[status(esa)],[fc1_lattice3]) ).
cnf(c52,plain,
'set$uunion2'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_k2_xboole_0]) ).
cnf(c73,plain,
( 'set$uunion2'(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t12_xboole_1]) ).
cnf(c75,plain,
( join('boole$ulattice'(X1),X0,X2) = 'set$uunion2'(X0,X2)
| ~ element(X2,'the$ucarrier'('boole$ulattice'(X1)))
| ~ element(X0,'the$ucarrier'('boole$ulattice'(X1))) ),
inference(clausification,[status(esa)],[t1_lattice3]) ).
cnf(c86,plain,
subset(X0,'set$uunion2'(X0,X1)),
inference(clausification,[status(esa)],[t7_xboole_1]) ).
cnf(c88,plain,
element(sK136,'the$ucarrier'('boole$ulattice'(sK135))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c89,plain,
element(sK137,'the$ucarrier'('boole$ulattice'(sK135))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c91,plain,
( subset(sK136,sK137)
| below('boole$ulattice'(sK135),sK136,sK137) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c92,plain,
( ~ below('boole$ulattice'(sK135),sK136,sK137)
| ~ subset(sK136,sK137) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ element(X0,'the$ucarrier'('boole$ulattice'(sK135)))
| join('boole$ulattice'(sK135),X0,sK137) = 'set$uunion2'(X0,sK137) ),
inference(resolution,[status(thm)],[c75,c89]) ).
cnf(d1,plain,
join('boole$ulattice'(sK135),sK136,sK137) = 'set$uunion2'(sK136,sK137),
inference(resolution,[status(thm)],[d0,c88]) ).
cnf(d2,plain,
( subset(sK136,sK137)
| 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| ~ element(sK136,'the$ucarrier'('boole$ulattice'(sK135)))
| ~ element(sK137,'the$ucarrier'('boole$ulattice'(sK135)))
| join('boole$ulattice'(sK135),sK136,sK137) = sK137 ),
inference(resolution,[status(thm)],[c9,c91]) ).
cnf(d3,plain,
( subset(sK136,sK137)
| 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| ~ element(sK137,'the$ucarrier'('boole$ulattice'(sK135)))
| join('boole$ulattice'(sK135),sK136,sK137) = sK137 ),
inference(resolution,[status(thm)],[c88,d2]) ).
cnf(d4,plain,
( subset(sK136,sK137)
| 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| join('boole$ulattice'(sK135),sK136,sK137) = sK137 ),
inference(resolution,[status(thm)],[c89,d3]) ).
cnf(d5,plain,
( subset(sK136,sK137)
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| join('boole$ulattice'(sK135),sK136,sK137) = sK137 ),
inference(resolution,[status(thm)],[c37,d4]) ).
cnf(d6,plain,
'join$usemilatt$ustr'('boole$ulattice'(X0)),
inference(resolution,[status(thm)],[c22,c15]) ).
cnf(d7,plain,
( subset(sK136,sK137)
| join('boole$ulattice'(sK135),sK136,sK137) = sK137 ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( join('boole$ulattice'(sK135),sK136,sK137) = sK137
| 'set$uunion2'(sK136,sK137) = sK137 ),
inference(resolution,[status(thm)],[c73,d7]) ).
cnf(d9,plain,
( 'set$uunion2'(sK136,sK137) = sK137
| 'set$uunion2'(sK136,sK137) = sK137 ),
inference(demodulation,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
join('boole$ulattice'(sK135),sK136,sK137) = sK137,
inference(demodulation,[status(thm)],[d1,d9]) ).
cnf(d11,plain,
( below('boole$ulattice'(sK135),sK136,sK137)
| 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| ~ element(sK136,'the$ucarrier'('boole$ulattice'(sK135)))
| ~ element(sK137,'the$ucarrier'('boole$ulattice'(sK135)))
| sK137 != sK137 ),
inference(superposition,[status(thm)],[d10,c10]) ).
cnf(d12,plain,
( below('boole$ulattice'(sK135),sK136,sK137)
| 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| ~ element(sK137,'the$ucarrier'('boole$ulattice'(sK135)))
| sK137 != sK137 ),
inference(resolution,[status(thm)],[c88,d11]) ).
cnf(d13,plain,
( below('boole$ulattice'(sK135),sK136,sK137)
| 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| sK137 != sK137 ),
inference(resolution,[status(thm)],[c89,d12]) ).
cnf(d14,plain,
( below('boole$ulattice'(sK135),sK136,sK137)
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| sK137 != sK137 ),
inference(resolution,[status(thm)],[c37,d13]) ).
cnf(d15,plain,
( below('boole$ulattice'(sK135),sK136,sK137)
| sK137 != sK137 ),
inference(resolution,[status(thm)],[d6,d14]) ).
cnf(d16,plain,
subset(sK136,sK137),
inference(superposition,[status(thm)],[d9,c86]) ).
cnf(d17,plain,
~ below('boole$ulattice'(sK135),sK136,sK137),
inference(resolution,[status(thm)],[d16,c92]) ).
cnf(d18,plain,
sK137 != sK137,
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
join('boole$ulattice'(sK135),sK137,sK137) = 'set$uunion2'(sK137,sK137),
inference(resolution,[status(thm)],[d0,c89]) ).
cnf(d20,plain,
join('boole$ulattice'(sK135),sK137,sK137) = sK137,
inference(demodulation,[status(thm)],[d19,c52]) ).
cnf(d21,plain,
( below('boole$ulattice'(sK135),sK137,sK137)
| 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| ~ element(sK137,'the$ucarrier'('boole$ulattice'(sK135)))
| ~ element(sK137,'the$ucarrier'('boole$ulattice'(sK135)))
| sK137 != sK137 ),
inference(superposition,[status(thm)],[d20,c10]) ).
cnf(d22,plain,
( below('boole$ulattice'(sK135),sK137,sK137)
| 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| sK137 != sK137 ),
inference(resolution,[status(thm)],[c89,d21]) ).
cnf(d23,plain,
( below('boole$ulattice'(sK135),sK137,sK137)
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| sK137 != sK137 ),
inference(resolution,[status(thm)],[c37,d22]) ).
cnf(d24,plain,
( below('boole$ulattice'(sK135),sK137,sK137)
| sK137 != sK137 ),
inference(resolution,[status(thm)],[d6,d23]) ).
cnf(d25,plain,
below('boole$ulattice'(sK135),sK137,sK137),
inference(equality_resolution,[status(thm)],[d24]) ).
cnf(d26,plain,
( 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| ~ element(sK137,'the$ucarrier'('boole$ulattice'(sK135)))
| ~ element(sK137,'the$ucarrier'('boole$ulattice'(sK135)))
| join('boole$ulattice'(sK135),sK137,sK137) = sK137 ),
inference(resolution,[status(thm)],[d25,c9]) ).
cnf(d27,plain,
( 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| ~ element(sK137,'the$ucarrier'('boole$ulattice'(sK135)))
| sK137 = sK137 ),
inference(demodulation,[status(thm)],[d26,d20]) ).
cnf(d28,plain,
( 'empty$ucarrier'('boole$ulattice'(sK135))
| ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| sK137 = sK137 ),
inference(resolution,[status(thm)],[c89,d27]) ).
cnf(d29,plain,
( ~ 'join$usemilatt$ustr'('boole$ulattice'(sK135))
| sK137 = sK137 ),
inference(resolution,[status(thm)],[c37,d28]) ).
cnf(d30,plain,
sK137 = sK137,
inference(resolution,[status(thm)],[d6,d29]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[d30,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU344+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
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 09:17:54 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.02/2.85 % SZS status Theorem for theBenchmark.p
% 19.02/2.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------