%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU107+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 08:40:53 AM UTC 2026
% Result : Theorem 12.73s 2.55s
% Output : CNFRefutation 12.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 72 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 67 ( 25 ~; 28 |; 8 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 33 ( 1 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k2_finsub_1,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> element('prebool$udifference'(X0,X1,X2),X0) ) ).
fof(existence_m1_subset_1,axiom,
! [X0] :
? [X1] : element(X1,X0) ).
fof(redefinition_k2_finsub_1,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> 'prebool$udifference'(X0,X1,X2) = 'set$udifference'(X1,X2) ) ).
fof(reflexivity_r1_tarski,axiom,
! [X0,X1] : subset(X0,X0) ).
fof(t2_subset,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ) ).
fof(t37_xboole_1,axiom,
! [X0,X1] :
( 'set$udifference'(X0,X1) = 'empty$uset'
<=> subset(X0,X1) ) ).
fof(t18_finsub_1,conjecture,
! [X0] :
( ( preboolean(X0)
& ~ empty(X0) )
=> in('empty$uset',X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( preboolean(X0)
& ~ empty(X0) )
=> in('empty$uset',X0) ),
inference(negate_conjecture,[status(cth)],[t18_finsub_1]) ).
cnf(c6,plain,
( ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0)
| empty(X0)
| element('prebool$udifference'(X0,X1,X2),X0) ),
inference(clausification,[status(esa)],[dt_k2_finsub_1]) ).
cnf(c7,plain,
element(sK11(X0),X0),
inference(clausification,[status(esa)],[existence_m1_subset_1]) ).
cnf(c40,plain,
( ~ element(X2,X0)
| ~ preboolean(X0)
| empty(X0)
| ~ element(X1,X0)
| 'prebool$udifference'(X0,X1,X2) = 'set$udifference'(X1,X2) ),
inference(clausification,[status(esa)],[redefinition_k2_finsub_1]) ).
cnf(c41,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(c43,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c45,plain,
( ~ subset(X0,X1)
| 'set$udifference'(X0,X1) = 'empty$uset' ),
inference(clausification,[status(esa)],[t37_xboole_1]) ).
cnf(c55,plain,
~ empty(sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c56,plain,
preboolean(sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c57,plain,
~ in('empty$uset',sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'set$udifference'(X0,X0) = 'empty$uset',
inference(resolution,[status(thm)],[c45,c41]) ).
cnf(d1,plain,
( ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| 'prebool$udifference'(X0,sK11(X0),X1) = 'set$udifference'(sK11(X0),X1) ),
inference(resolution,[status(thm)],[c40,c7]) ).
cnf(d2,plain,
( ~ preboolean(X0)
| empty(X0)
| 'prebool$udifference'(X0,sK11(X0),sK11(X0)) = 'set$udifference'(sK11(X0),sK11(X0)) ),
inference(resolution,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
( ~ preboolean(X0)
| empty(X0)
| 'prebool$udifference'(X0,sK11(X0),sK11(X0)) = 'empty$uset' ),
inference(demodulation,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( empty(sK55)
| 'prebool$udifference'(sK55,sK11(sK55),sK11(sK55)) = 'empty$uset' ),
inference(resolution,[status(thm)],[d3,c56]) ).
cnf(d5,plain,
'prebool$udifference'(sK55,sK11(sK55),sK11(sK55)) = 'empty$uset',
inference(resolution,[status(thm)],[c55,d4]) ).
cnf(d6,plain,
( ~ element(sK11(sK55),sK55)
| ~ element(sK11(sK55),sK55)
| ~ preboolean(sK55)
| empty(sK55)
| element('empty$uset',sK55) ),
inference(superposition,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( element('empty$uset',sK55)
| ~ element(sK11(sK55),sK55)
| ~ preboolean(sK55) ),
inference(resolution,[status(thm)],[c55,d6]) ).
cnf(d8,plain,
( element('empty$uset',sK55)
| ~ element(sK11(sK55),sK55) ),
inference(resolution,[status(thm)],[c56,d7]) ).
cnf(d9,plain,
element('empty$uset',sK55),
inference(resolution,[status(thm)],[c7,d8]) ).
cnf(d10,plain,
( empty(sK55)
| in('empty$uset',sK55) ),
inference(resolution,[status(thm)],[d9,c43]) ).
cnf(d11,plain,
in('empty$uset',sK55),
inference(resolution,[status(thm)],[c55,d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c57,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU107+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:37:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.73/2.55 % SZS status Theorem for theBenchmark.p
% 12.73/2.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------