%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU170+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 08:41:08 AM UTC 2026
% Result : Theorem 29.15s 4.65s
% Output : CNFRefutation 29.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 21 unt; 0 def)
% Number of atoms : 127 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 106 ( 40 ~; 46 |; 6 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 4 sgn 24 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(d4_xboole_0,axiom,
! [X0,X1,X2] :
( X2 = 'set$udifference'(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ) ).
fof(d5_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> 'subset$ucomplement'(X0,X1) = 'set$udifference'(X0,X1) ) ).
fof(dt_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element('subset$ucomplement'(X0,X1),powerset(X0)) ) ).
fof(involutiveness_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> 'subset$ucomplement'(X0,'subset$ucomplement'(X0,X1)) = X1 ) ).
fof(symmetry_r1_xboole_0,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ) ).
fof(t3_xboole_0,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ) ).
fof(t43_subset_1,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,'subset$ucomplement'(X0,X2)) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,'subset$ucomplement'(X0,X2)) ) ) ),
inference(negate_conjecture,[status(cth)],[t43_subset_1]) ).
cnf(c1,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c2,plain,
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c3,plain,
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c4,plain,
( in(X3,X0)
| ~ in(X3,X2)
| 'set$udifference'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d4_xboole_0]) ).
cnf(c5,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| 'set$udifference'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d4_xboole_0]) ).
cnf(c6,plain,
( ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2)
| 'set$udifference'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d4_xboole_0]) ).
cnf(c12,plain,
( 'set$udifference'(X1,X0) = 'subset$ucomplement'(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[d5_subset_1]) ).
cnf(c13,plain,
( element('subset$ucomplement'(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[dt_k3_subset_1]) ).
cnf(c17,plain,
( 'subset$ucomplement'(X1,'subset$ucomplement'(X1,X0)) = X0
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[involutiveness_k3_subset_1]) ).
cnf(c26,plain,
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_r1_xboole_0]) ).
cnf(c28,plain,
( in(sK37(X0,X1),X0)
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[t3_xboole_0]) ).
cnf(c29,plain,
( in(sK37(X0,X1),X1)
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[t3_xboole_0]) ).
cnf(c30,plain,
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t3_xboole_0]) ).
cnf(c35,plain,
element(sK46,powerset(sK45)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c36,plain,
element(sK47,powerset(sK45)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c38,plain,
( subset(sK46,'subset$ucomplement'(sK45,sK47))
| disjoint(sK46,sK47) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c39,plain,
( ~ disjoint(sK46,sK47)
| ~ subset(sK46,'subset$ucomplement'(sK45,sK47)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset(X0,X1)
| ~ disjoint(X2,X0)
| ~ in(sK5(X0,X1),X2) ),
inference(resolution,[status(thm)],[c30,c2]) ).
cnf(d1,plain,
'set$udifference'(sK45,sK46) = 'subset$ucomplement'(sK45,sK46),
inference(resolution,[status(thm)],[c12,c35]) ).
cnf(d2,plain,
'subset$ucomplement'(sK45,'subset$ucomplement'(sK45,sK46)) = sK46,
inference(resolution,[status(thm)],[c17,c35]) ).
cnf(d3,plain,
'subset$ucomplement'(sK45,'set$udifference'(sK45,sK46)) = sK46,
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
element('subset$ucomplement'(sK45,sK46),powerset(sK45)),
inference(resolution,[status(thm)],[c13,c35]) ).
cnf(d5,plain,
element('set$udifference'(sK45,sK46),powerset(sK45)),
inference(demodulation,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
'set$udifference'(sK45,'set$udifference'(sK45,sK46)) = 'subset$ucomplement'(sK45,'set$udifference'(sK45,sK46)),
inference(resolution,[status(thm)],[d5,c12]) ).
cnf(d7,plain,
'set$udifference'(sK45,'set$udifference'(sK45,sK46)) = sK46,
inference(demodulation,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
( in(X1,sK45)
| ~ in(X1,X0)
| sK46 != X0 ),
inference(superposition,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
( in(X0,sK45)
| ~ in(X0,sK46) ),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
( subset(sK46,X0)
| in(sK5(sK46,X0),sK45) ),
inference(resolution,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
( ~ in(X0,X1)
| in(X0,X2)
| in(X0,'set$udifference'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(d12,plain,
( subset(sK46,X0)
| in(sK5(sK46,X0),'set$udifference'(sK45,X1))
| in(sK5(sK46,X0),X1) ),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( subset(sK46,X0)
| subset(sK46,X0)
| in(sK5(sK46,X0),'set$udifference'(sK45,X0)) ),
inference(resolution,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
( ~ disjoint('set$udifference'(sK45,X0),sK46)
| subset(sK46,X0)
| subset(sK46,X0) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
'set$udifference'(sK45,sK47) = 'subset$ucomplement'(sK45,sK47),
inference(resolution,[status(thm)],[c12,c36]) ).
cnf(d16,plain,
'subset$ucomplement'(sK45,'subset$ucomplement'(sK45,sK47)) = sK47,
inference(resolution,[status(thm)],[c17,c36]) ).
cnf(d17,plain,
'subset$ucomplement'(sK45,'set$udifference'(sK45,sK47)) = sK47,
inference(demodulation,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
element('subset$ucomplement'(sK45,sK47),powerset(sK45)),
inference(resolution,[status(thm)],[c13,c36]) ).
cnf(d19,plain,
'set$udifference'(sK45,'subset$ucomplement'(sK45,sK47)) = 'subset$ucomplement'(sK45,'subset$ucomplement'(sK45,sK47)),
inference(resolution,[status(thm)],[d18,c12]) ).
cnf(d20,plain,
'set$udifference'(sK45,'set$udifference'(sK45,sK47)) = 'subset$ucomplement'(sK45,'subset$ucomplement'(sK45,sK47)),
inference(demodulation,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
'set$udifference'(sK45,'set$udifference'(sK45,sK47)) = 'subset$ucomplement'(sK45,'set$udifference'(sK45,sK47)),
inference(demodulation,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
'set$udifference'(sK45,'set$udifference'(sK45,sK47)) = sK47,
inference(demodulation,[status(thm)],[d21,d17]) ).
cnf(d23,plain,
( subset(sK46,'set$udifference'(sK45,sK47))
| ~ disjoint(sK47,sK46) ),
inference(superposition,[status(thm)],[d22,d14]) ).
cnf(d24,plain,
( ~ in(X0,X2)
| ~ in(X0,'set$udifference'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c5]) ).
cnf(d25,plain,
( disjoint(X0,X1)
| ~ in(sK37(X0,X1),'set$udifference'(X2,X1)) ),
inference(resolution,[status(thm)],[d24,c29]) ).
cnf(d26,plain,
( disjoint(sK46,sK47)
| subset(sK46,'set$udifference'(sK45,sK47)) ),
inference(demodulation,[status(thm)],[c38,d15]) ).
cnf(d27,plain,
( ~ subset(X0,X2)
| in(sK37(X0,X1),X2)
| disjoint(X0,X1) ),
inference(resolution,[status(thm)],[c28,c1]) ).
cnf(d28,plain,
( disjoint(sK46,sK47)
| disjoint(sK46,X0)
| in(sK37(sK46,X0),'set$udifference'(sK45,sK47)) ),
inference(resolution,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
( disjoint(sK46,sK47)
| disjoint(sK46,sK47)
| disjoint(sK46,sK47) ),
inference(resolution,[status(thm)],[d28,d25]) ).
cnf(d30,plain,
disjoint(sK47,sK46),
inference(resolution,[status(thm)],[d29,c26]) ).
cnf(d31,plain,
subset(sK46,'set$udifference'(sK45,sK47)),
inference(resolution,[status(thm)],[d30,d23]) ).
cnf(d32,plain,
( ~ disjoint(sK46,sK47)
| ~ subset(sK46,'set$udifference'(sK45,sK47)) ),
inference(demodulation,[status(thm)],[c39,d15]) ).
cnf(d33,plain,
~ subset(sK46,'set$udifference'(sK45,sK47)),
inference(resolution,[status(thm)],[d29,d32]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[d33,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU170+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:45:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.15/4.65 % SZS status Theorem for theBenchmark.p
% 29.15/4.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------