%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU305+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 : n010.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 12.87s 2.14s
% Output : CNFRefutation 12.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 141 ( 39 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 160 ( 66 ~; 65 |; 15 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_lattices,axiom,
! [X0,X1,X2] :
( ( element(X2,'the$ucarrier'(X0))
& element(X1,'the$ucarrier'(X0))
& 'join$usemilatt$ustr'(X0)
& 'join$ucommutative'(X0)
& ~ 'empty$ucarrier'(X0) )
=> 'join$ucommut'(X0,X1,X2) = 'join$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$ucarrier'(X0))
=> ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 ) ) ) ) ).
fof(redefinition_k3_lattices,axiom,
! [X0,X1,X2] :
( ( element(X2,'the$ucarrier'(X0))
& element(X1,'the$ucarrier'(X0))
& 'join$usemilatt$ustr'(X0)
& 'join$ucommutative'(X0)
& ~ 'empty$ucarrier'(X0) )
=> 'join$ucommut'(X0,X1,X2) = join(X0,X1,X2) ) ).
fof(t26_lattices,conjecture,
! [X0] :
( ( 'join$usemilatt$ustr'(X0)
& 'join$ucommutative'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,'the$ucarrier'(X0))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> ( ( below(X0,X2,X1)
& below(X0,X1,X2) )
=> X1 = X2 ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'join$usemilatt$ustr'(X0)
& 'join$ucommutative'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,'the$ucarrier'(X0))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> ( ( below(X0,X2,X1)
& below(X0,X1,X2) )
=> X1 = X2 ) ) ) ),
inference(negate_conjecture,[status(cth)],[t26_lattices]) ).
cnf(c4,plain,
( ~ element(X2,'the$ucarrier'(X1))
| ~ 'join$usemilatt$ustr'(X1)
| 'empty$ucarrier'(X1)
| ~ 'join$ucommutative'(X1)
| 'join$ucommut'(X1,X2,X0) = 'join$ucommut'(X1,X0,X2)
| ~ element(X0,'the$ucarrier'(X1)) ),
inference(clausification,[status(esa)],[commutativity_k3_lattices]) ).
cnf(c6,plain,
( ~ 'join$usemilatt$ustr'(X0)
| 'empty$ucarrier'(X0)
| ~ element(X2,'the$ucarrier'(X0))
| ~ element(X1,'the$ucarrier'(X0))
| join(X0,X1,X2) = X2
| ~ below(X0,X1,X2) ),
inference(clausification,[status(esa)],[d3_lattices]) ).
cnf(c31,plain,
( ~ element(X2,'the$ucarrier'(X0))
| 'join$ucommut'(X0,X1,X2) = join(X0,X1,X2)
| 'empty$ucarrier'(X0)
| ~ element(X1,'the$ucarrier'(X0))
| ~ 'join$usemilatt$ustr'(X0)
| ~ 'join$ucommutative'(X0) ),
inference(clausification,[status(esa)],[redefinition_k3_lattices]) ).
cnf(c44,plain,
~ 'empty$ucarrier'(sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c45,plain,
'join$ucommutative'(sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c46,plain,
'join$usemilatt$ustr'(sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
element(sK77,'the$ucarrier'(sK76)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
element(sK78,'the$ucarrier'(sK76)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c49,plain,
below(sK76,sK77,sK78),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c50,plain,
below(sK76,sK78,sK77),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c51,plain,
sK77 != sK78,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'empty$ucarrier'(sK76)
| ~ element(sK78,'the$ucarrier'(sK76))
| ~ element(sK77,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| join(sK76,sK78,sK77) = sK77 ),
inference(resolution,[status(thm)],[c50,c6]) ).
cnf(d1,plain,
( ~ element(sK78,'the$ucarrier'(sK76))
| ~ element(sK77,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| join(sK76,sK78,sK77) = sK77 ),
inference(resolution,[status(thm)],[c44,d0]) ).
cnf(d2,plain,
( ~ element(sK78,'the$ucarrier'(sK76))
| ~ element(sK77,'the$ucarrier'(sK76))
| join(sK76,sK78,sK77) = sK77 ),
inference(resolution,[status(thm)],[c46,d1]) ).
cnf(d3,plain,
( ~ element(sK78,'the$ucarrier'(sK76))
| join(sK76,sK78,sK77) = sK77 ),
inference(resolution,[status(thm)],[c47,d2]) ).
cnf(d4,plain,
join(sK76,sK78,sK77) = sK77,
inference(resolution,[status(thm)],[c48,d3]) ).
cnf(d5,plain,
( 'empty$ucarrier'(sK76)
| ~ element(sK77,'the$ucarrier'(sK76))
| ~ element(sK78,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| join(sK76,sK77,sK78) = sK78 ),
inference(resolution,[status(thm)],[c6,c49]) ).
cnf(d6,plain,
( ~ element(sK78,'the$ucarrier'(sK76))
| ~ element(sK77,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| join(sK76,sK77,sK78) = sK78 ),
inference(resolution,[status(thm)],[c44,d5]) ).
cnf(d7,plain,
( ~ element(sK78,'the$ucarrier'(sK76))
| ~ element(sK77,'the$ucarrier'(sK76))
| join(sK76,sK77,sK78) = sK78 ),
inference(resolution,[status(thm)],[c46,d6]) ).
cnf(d8,plain,
( ~ element(sK78,'the$ucarrier'(sK76))
| join(sK76,sK77,sK78) = sK78 ),
inference(resolution,[status(thm)],[c47,d7]) ).
cnf(d9,plain,
join(sK76,sK77,sK78) = sK78,
inference(resolution,[status(thm)],[c48,d8]) ).
cnf(d10,plain,
( 'empty$ucarrier'(sK76)
| ~ 'join$ucommutative'(sK76)
| ~ element(X0,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| 'join$ucommut'(sK76,X0,sK78) = join(sK76,X0,sK78) ),
inference(resolution,[status(thm)],[c31,c48]) ).
cnf(d11,plain,
( ~ 'join$ucommutative'(sK76)
| ~ element(X0,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| 'join$ucommut'(sK76,X0,sK78) = join(sK76,X0,sK78) ),
inference(resolution,[status(thm)],[c44,d10]) ).
cnf(d12,plain,
( ~ element(X0,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| 'join$ucommut'(sK76,X0,sK78) = join(sK76,X0,sK78) ),
inference(resolution,[status(thm)],[c45,d11]) ).
cnf(d13,plain,
( ~ element(X0,'the$ucarrier'(sK76))
| 'join$ucommut'(sK76,X0,sK78) = join(sK76,X0,sK78) ),
inference(resolution,[status(thm)],[c46,d12]) ).
cnf(d14,plain,
'join$ucommut'(sK76,sK77,sK78) = join(sK76,sK77,sK78),
inference(resolution,[status(thm)],[d13,c47]) ).
cnf(d15,plain,
'join$ucommut'(sK76,sK77,sK78) = sK78,
inference(demodulation,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
( 'empty$ucarrier'(sK76)
| ~ 'join$ucommutative'(sK76)
| ~ element(X0,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| 'join$ucommut'(sK76,sK77,X0) = 'join$ucommut'(sK76,X0,sK77) ),
inference(resolution,[status(thm)],[c4,c47]) ).
cnf(d17,plain,
( ~ 'join$ucommutative'(sK76)
| ~ element(X0,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| 'join$ucommut'(sK76,sK77,X0) = 'join$ucommut'(sK76,X0,sK77) ),
inference(resolution,[status(thm)],[c44,d16]) ).
cnf(d18,plain,
( ~ element(X0,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| 'join$ucommut'(sK76,sK77,X0) = 'join$ucommut'(sK76,X0,sK77) ),
inference(resolution,[status(thm)],[c45,d17]) ).
cnf(d19,plain,
( ~ element(X0,'the$ucarrier'(sK76))
| 'join$ucommut'(sK76,sK77,X0) = 'join$ucommut'(sK76,X0,sK77) ),
inference(resolution,[status(thm)],[c46,d18]) ).
cnf(d20,plain,
'join$ucommut'(sK76,sK77,sK78) = 'join$ucommut'(sK76,sK78,sK77),
inference(resolution,[status(thm)],[d19,c48]) ).
cnf(d21,plain,
sK78 = 'join$ucommut'(sK76,sK78,sK77),
inference(demodulation,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
( 'empty$ucarrier'(sK76)
| ~ 'join$ucommutative'(sK76)
| ~ element(X0,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| 'join$ucommut'(sK76,X0,sK77) = join(sK76,X0,sK77) ),
inference(resolution,[status(thm)],[c31,c47]) ).
cnf(d23,plain,
( ~ 'join$ucommutative'(sK76)
| ~ element(X0,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| 'join$ucommut'(sK76,X0,sK77) = join(sK76,X0,sK77) ),
inference(resolution,[status(thm)],[c44,d22]) ).
cnf(d24,plain,
( ~ element(X0,'the$ucarrier'(sK76))
| ~ 'join$usemilatt$ustr'(sK76)
| 'join$ucommut'(sK76,X0,sK77) = join(sK76,X0,sK77) ),
inference(resolution,[status(thm)],[c45,d23]) ).
cnf(d25,plain,
( ~ element(X0,'the$ucarrier'(sK76))
| 'join$ucommut'(sK76,X0,sK77) = join(sK76,X0,sK77) ),
inference(resolution,[status(thm)],[c46,d24]) ).
cnf(d26,plain,
'join$ucommut'(sK76,sK78,sK77) = join(sK76,sK78,sK77),
inference(resolution,[status(thm)],[d25,c48]) ).
cnf(d27,plain,
sK78 = join(sK76,sK78,sK77),
inference(demodulation,[status(thm)],[d26,d21]) ).
cnf(d28,plain,
sK78 = sK77,
inference(demodulation,[status(thm)],[d27,d4]) ).
cnf(d29,plain,
sK77 != sK77,
inference(demodulation,[status(thm)],[c51,d28]) ).
cnf(d30,plain,
$false,
inference(equality_resolution,[status(thm)],[d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU305+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 : n010.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 09:09:45 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.87/2.14 % SZS status Theorem for theBenchmark.p
% 12.87/2.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------