%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU304+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:41:36 AM UTC 2026
% Result : Theorem 13.77s 3.06s
% Output : CNFRefutation 13.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 17 unt; 0 def)
% Number of atoms : 190 ( 33 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 224 ( 93 ~; 93 |; 20 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k4_lattices,axiom,
! [X0,X1,X2] :
( ( element(X2,'the$ucarrier'(X0))
& element(X1,'the$ucarrier'(X0))
& 'meet$usemilatt$ustr'(X0)
& 'meet$ucommutative'(X0)
& ~ 'empty$ucarrier'(X0) )
=> 'meet$ucommut'(X0,X1,X2) = 'meet$ucommut'(X0,X2,X1) ) ).
fof(d3_lattices,axiom,
! [X0] :
( ( 'join$usemilatt$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,'the$ucarrier'(X0))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 ) ) ) ) ).
fof(d8_lattices,axiom,
! [X0] :
( ( 'latt$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ( 'meet$uabsorbing'(X0)
<=> ! [X1] :
( element(X1,'the$ucarrier'(X0))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> join(X0,meet(X0,X1,X2),X2) = X2 ) ) ) ) ).
fof(dt_k2_lattices,axiom,
! [X0,X1,X2] :
( ( element(X2,'the$ucarrier'(X0))
& element(X1,'the$ucarrier'(X0))
& 'meet$usemilatt$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> element(meet(X0,X1,X2),'the$ucarrier'(X0)) ) ).
fof(dt_l3_lattices,axiom,
! [X0] :
( 'latt$ustr'(X0)
=> ( 'join$usemilatt$ustr'(X0)
& 'meet$usemilatt$ustr'(X0) ) ) ).
fof(redefinition_k4_lattices,axiom,
! [X0,X1,X2] :
( ( element(X2,'the$ucarrier'(X0))
& element(X1,'the$ucarrier'(X0))
& 'meet$usemilatt$ustr'(X0)
& 'meet$ucommutative'(X0)
& ~ 'empty$ucarrier'(X0) )
=> 'meet$ucommut'(X0,X1,X2) = meet(X0,X1,X2) ) ).
fof(t23_lattices,conjecture,
! [X0] :
( ( 'latt$ustr'(X0)
& 'meet$uabsorbing'(X0)
& 'meet$ucommutative'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,'the$ucarrier'(X0))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> below(X0,'meet$ucommut'(X0,X1,X2),X1) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'latt$ustr'(X0)
& 'meet$uabsorbing'(X0)
& 'meet$ucommutative'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,'the$ucarrier'(X0))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> below(X0,'meet$ucommut'(X0,X1,X2),X1) ) ) ),
inference(negate_conjecture,[status(cth)],[t23_lattices]) ).
cnf(c4,plain,
( 'meet$ucommut'(X0,X2,X1) = 'meet$ucommut'(X0,X1,X2)
| ~ element(X2,'the$ucarrier'(X0))
| ~ 'meet$ucommutative'(X0)
| 'empty$ucarrier'(X0)
| ~ element(X1,'the$ucarrier'(X0))
| ~ 'meet$usemilatt$ustr'(X0) ),
inference(clausification,[status(esa)],[commutativity_k4_lattices]) ).
cnf(c8,plain,
( 'empty$ucarrier'(X0)
| ~ element(X2,'the$ucarrier'(X0))
| ~ 'join$usemilatt$ustr'(X0)
| ~ element(X1,'the$ucarrier'(X0))
| below(X0,X1,X2)
| join(X0,X1,X2) != X2 ),
inference(clausification,[status(esa)],[d3_lattices]) ).
cnf(c9,plain,
( ~ element(X2,'the$ucarrier'(X0))
| ~ 'meet$uabsorbing'(X0)
| join(X0,meet(X0,X1,X2),X2) = X2
| ~ element(X1,'the$ucarrier'(X0))
| 'empty$ucarrier'(X0)
| ~ 'latt$ustr'(X0) ),
inference(clausification,[status(esa)],[d8_lattices]) ).
cnf(c15,plain,
( ~ 'meet$usemilatt$ustr'(X0)
| ~ element(X2,'the$ucarrier'(X0))
| ~ element(X1,'the$ucarrier'(X0))
| element(meet(X0,X1,X2),'the$ucarrier'(X0))
| 'empty$ucarrier'(X0) ),
inference(clausification,[status(esa)],[dt_k2_lattices]) ).
cnf(c19,plain,
( 'meet$usemilatt$ustr'(X0)
| ~ 'latt$ustr'(X0) ),
inference(clausification,[status(esa)],[dt_l3_lattices]) ).
cnf(c20,plain,
( 'join$usemilatt$ustr'(X0)
| ~ 'latt$ustr'(X0) ),
inference(clausification,[status(esa)],[dt_l3_lattices]) ).
cnf(c45,plain,
( ~ 'meet$ucommutative'(X0)
| ~ element(X2,'the$ucarrier'(X0))
| 'empty$ucarrier'(X0)
| 'meet$ucommut'(X0,X1,X2) = meet(X0,X1,X2)
| ~ element(X1,'the$ucarrier'(X0))
| ~ 'meet$usemilatt$ustr'(X0) ),
inference(clausification,[status(esa)],[redefinition_k4_lattices]) ).
cnf(c58,plain,
~ 'empty$ucarrier'(sK92),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c59,plain,
'meet$ucommutative'(sK92),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c60,plain,
'meet$uabsorbing'(sK92),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c61,plain,
'latt$ustr'(sK92),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c62,plain,
element(sK93,'the$ucarrier'(sK92)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c63,plain,
element(sK94,'the$ucarrier'(sK92)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c64,plain,
~ below(sK92,'meet$ucommut'(sK92,sK93,sK94),sK93),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'empty$ucarrier'(sK92)
| ~ element(X0,'the$ucarrier'(sK92))
| ~ 'meet$ucommutative'(sK92)
| ~ 'meet$usemilatt$ustr'(sK92)
| 'meet$ucommut'(sK92,sK93,X0) = 'meet$ucommut'(sK92,X0,sK93) ),
inference(resolution,[status(thm)],[c4,c62]) ).
cnf(d1,plain,
( ~ element(X0,'the$ucarrier'(sK92))
| ~ 'meet$ucommutative'(sK92)
| ~ 'meet$usemilatt$ustr'(sK92)
| 'meet$ucommut'(sK92,sK93,X0) = 'meet$ucommut'(sK92,X0,sK93) ),
inference(resolution,[status(thm)],[c58,d0]) ).
cnf(d2,plain,
( ~ element(X0,'the$ucarrier'(sK92))
| ~ 'meet$usemilatt$ustr'(sK92)
| 'meet$ucommut'(sK92,sK93,X0) = 'meet$ucommut'(sK92,X0,sK93) ),
inference(resolution,[status(thm)],[c59,d1]) ).
cnf(d3,plain,
( ~ 'meet$usemilatt$ustr'(sK92)
| 'meet$ucommut'(sK92,sK93,sK94) = 'meet$ucommut'(sK92,sK94,sK93) ),
inference(resolution,[status(thm)],[d2,c63]) ).
cnf(d4,plain,
'meet$usemilatt$ustr'(sK92),
inference(resolution,[status(thm)],[c19,c61]) ).
cnf(d5,plain,
'meet$ucommut'(sK92,sK93,sK94) = 'meet$ucommut'(sK92,sK94,sK93),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( 'empty$ucarrier'(sK92)
| ~ element(X0,'the$ucarrier'(sK92))
| ~ 'meet$ucommutative'(sK92)
| ~ 'meet$usemilatt$ustr'(sK92)
| 'meet$ucommut'(sK92,X0,sK93) = meet(sK92,X0,sK93) ),
inference(resolution,[status(thm)],[c45,c62]) ).
cnf(d7,plain,
( ~ element(X0,'the$ucarrier'(sK92))
| ~ 'meet$ucommutative'(sK92)
| ~ 'meet$usemilatt$ustr'(sK92)
| 'meet$ucommut'(sK92,X0,sK93) = meet(sK92,X0,sK93) ),
inference(resolution,[status(thm)],[c58,d6]) ).
cnf(d8,plain,
( ~ element(X0,'the$ucarrier'(sK92))
| ~ 'meet$usemilatt$ustr'(sK92)
| 'meet$ucommut'(sK92,X0,sK93) = meet(sK92,X0,sK93) ),
inference(resolution,[status(thm)],[c59,d7]) ).
cnf(d9,plain,
( ~ element(X0,'the$ucarrier'(sK92))
| 'meet$ucommut'(sK92,X0,sK93) = meet(sK92,X0,sK93) ),
inference(resolution,[status(thm)],[d4,d8]) ).
cnf(d10,plain,
'meet$ucommut'(sK92,sK94,sK93) = meet(sK92,sK94,sK93),
inference(resolution,[status(thm)],[d9,c63]) ).
cnf(d11,plain,
'meet$ucommut'(sK92,sK93,sK94) = meet(sK92,sK94,sK93),
inference(demodulation,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
( ~ 'latt$ustr'(sK92)
| ~ 'meet$uabsorbing'(sK92)
| 'empty$ucarrier'(sK92)
| ~ element(X0,'the$ucarrier'(sK92))
| join(sK92,meet(sK92,X0,sK93),sK93) = sK93 ),
inference(resolution,[status(thm)],[c9,c62]) ).
cnf(d13,plain,
( ~ 'latt$ustr'(sK92)
| ~ 'meet$uabsorbing'(sK92)
| ~ element(X0,'the$ucarrier'(sK92))
| join(sK92,meet(sK92,X0,sK93),sK93) = sK93 ),
inference(resolution,[status(thm)],[c58,d12]) ).
cnf(d14,plain,
( ~ 'latt$ustr'(sK92)
| ~ element(X0,'the$ucarrier'(sK92))
| join(sK92,meet(sK92,X0,sK93),sK93) = sK93 ),
inference(resolution,[status(thm)],[c60,d13]) ).
cnf(d15,plain,
( ~ element(X0,'the$ucarrier'(sK92))
| join(sK92,meet(sK92,X0,sK93),sK93) = sK93 ),
inference(resolution,[status(thm)],[c61,d14]) ).
cnf(d16,plain,
join(sK92,meet(sK92,sK94,sK93),sK93) = sK93,
inference(resolution,[status(thm)],[d15,c63]) ).
cnf(d17,plain,
( below(sK92,meet(sK92,sK94,sK93),sK93)
| ~ 'join$usemilatt$ustr'(sK92)
| 'empty$ucarrier'(sK92)
| ~ element(meet(sK92,sK94,sK93),'the$ucarrier'(sK92))
| ~ element(sK93,'the$ucarrier'(sK92))
| sK93 != sK93 ),
inference(superposition,[status(thm)],[d16,c8]) ).
cnf(d18,plain,
( below(sK92,meet(sK92,sK94,sK93),sK93)
| ~ 'join$usemilatt$ustr'(sK92)
| ~ element(sK93,'the$ucarrier'(sK92))
| ~ element(meet(sK92,sK94,sK93),'the$ucarrier'(sK92))
| sK93 != sK93 ),
inference(resolution,[status(thm)],[c58,d17]) ).
cnf(d19,plain,
( below(sK92,meet(sK92,sK94,sK93),sK93)
| ~ 'join$usemilatt$ustr'(sK92)
| ~ element(meet(sK92,sK94,sK93),'the$ucarrier'(sK92))
| sK93 != sK93 ),
inference(resolution,[status(thm)],[c62,d18]) ).
cnf(d20,plain,
'join$usemilatt$ustr'(sK92),
inference(resolution,[status(thm)],[c20,c61]) ).
cnf(d21,plain,
( below(sK92,meet(sK92,sK94,sK93),sK93)
| ~ element(meet(sK92,sK94,sK93),'the$ucarrier'(sK92))
| sK93 != sK93 ),
inference(resolution,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
( below(sK92,meet(sK92,sK94,sK93),sK93)
| ~ element(meet(sK92,sK94,sK93),'the$ucarrier'(sK92)) ),
inference(equality_resolution,[status(thm)],[d21]) ).
cnf(d23,plain,
( below(sK92,meet(sK92,sK94,sK93),sK93)
| ~ element('meet$ucommut'(sK92,sK93,sK94),'the$ucarrier'(sK92)) ),
inference(demodulation,[status(thm)],[d22,d11]) ).
cnf(d24,plain,
( below(sK92,'meet$ucommut'(sK92,sK93,sK94),sK93)
| ~ element('meet$ucommut'(sK92,sK93,sK94),'the$ucarrier'(sK92)) ),
inference(demodulation,[status(thm)],[d23,d11]) ).
cnf(d25,plain,
~ element('meet$ucommut'(sK92,sK93,sK94),'the$ucarrier'(sK92)),
inference(resolution,[status(thm)],[c64,d24]) ).
cnf(d26,plain,
( 'empty$ucarrier'(sK92)
| ~ element(X0,'the$ucarrier'(sK92))
| ~ 'meet$ucommutative'(sK92)
| ~ 'meet$usemilatt$ustr'(sK92)
| 'meet$ucommut'(sK92,X0,sK94) = meet(sK92,X0,sK94) ),
inference(resolution,[status(thm)],[c45,c63]) ).
cnf(d27,plain,
( ~ element(X0,'the$ucarrier'(sK92))
| ~ 'meet$ucommutative'(sK92)
| ~ 'meet$usemilatt$ustr'(sK92)
| 'meet$ucommut'(sK92,X0,sK94) = meet(sK92,X0,sK94) ),
inference(resolution,[status(thm)],[c58,d26]) ).
cnf(d28,plain,
( ~ element(X0,'the$ucarrier'(sK92))
| ~ 'meet$usemilatt$ustr'(sK92)
| 'meet$ucommut'(sK92,X0,sK94) = meet(sK92,X0,sK94) ),
inference(resolution,[status(thm)],[c59,d27]) ).
cnf(d29,plain,
( ~ element(X0,'the$ucarrier'(sK92))
| 'meet$ucommut'(sK92,X0,sK94) = meet(sK92,X0,sK94) ),
inference(resolution,[status(thm)],[d4,d28]) ).
cnf(d30,plain,
'meet$ucommut'(sK92,sK93,sK94) = meet(sK92,sK93,sK94),
inference(resolution,[status(thm)],[d29,c62]) ).
cnf(d31,plain,
( 'empty$ucarrier'(sK92)
| ~ element(sK94,'the$ucarrier'(sK92))
| ~ element(sK93,'the$ucarrier'(sK92))
| ~ 'meet$usemilatt$ustr'(sK92)
| element('meet$ucommut'(sK92,sK93,sK94),'the$ucarrier'(sK92)) ),
inference(superposition,[status(thm)],[d30,c15]) ).
cnf(d32,plain,
( ~ element(sK94,'the$ucarrier'(sK92))
| ~ element(sK93,'the$ucarrier'(sK92))
| element('meet$ucommut'(sK92,sK93,sK94),'the$ucarrier'(sK92))
| ~ 'meet$usemilatt$ustr'(sK92) ),
inference(resolution,[status(thm)],[c58,d31]) ).
cnf(d33,plain,
( ~ element(sK94,'the$ucarrier'(sK92))
| element('meet$ucommut'(sK92,sK93,sK94),'the$ucarrier'(sK92))
| ~ 'meet$usemilatt$ustr'(sK92) ),
inference(resolution,[status(thm)],[c62,d32]) ).
cnf(d34,plain,
( element('meet$ucommut'(sK92,sK93,sK94),'the$ucarrier'(sK92))
| ~ 'meet$usemilatt$ustr'(sK92) ),
inference(resolution,[status(thm)],[c63,d33]) ).
cnf(d35,plain,
element('meet$ucommut'(sK92,sK93,sK94),'the$ucarrier'(sK92)),
inference(resolution,[status(thm)],[d4,d34]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[d35,d25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU304+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 09:08:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.77/3.06 % SZS status Theorem for theBenchmark.p
% 13.77/3.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------