%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU125+2 : 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 : n020.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 08:40:56 AM UTC 2026
% Result : Theorem 71.93s 9.63s
% Output : CNFRefutation 71.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 14 unt; 0 def)
% Number of atoms : 96 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 75 ( 26 ~; 39 |; 3 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 8 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(d10_xboole_0,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(d2_xboole_0,axiom,
! [X0,X1,X2] :
( X2 = 'set$uunion2'(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(idempotence_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X0) = X0 ).
fof(t7_xboole_1,lemma,
! [X0,X1] : subset(X0,'set$uunion2'(X0,X1)) ).
fof(t8_xboole_1,conjecture,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset('set$uunion2'(X0,X2),X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset('set$uunion2'(X0,X2),X1) ),
inference(negate_conjecture,[status(cth)],[t8_xboole_1]) ).
cnf(c1,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[d10_xboole_0]) ).
cnf(c8,plain,
( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2)
| 'set$uunion2'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d2_xboole_0]) ).
cnf(c9,plain,
( ~ in(X3,X0)
| in(X3,X2)
| 'set$uunion2'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d2_xboole_0]) ).
cnf(c10,plain,
( ~ in(X3,X1)
| in(X3,X2)
| 'set$uunion2'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d2_xboole_0]) ).
cnf(c16,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c17,plain,
( in(sK20(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c18,plain,
( ~ in(sK20(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c32,plain,
'set$uunion2'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_k2_xboole_0]) ).
cnf(c49,plain,
subset(X0,'set$uunion2'(X0,X1)),
inference(clausification,[status(esa)],[t7_xboole_1]) ).
cnf(c51,plain,
subset(sK66,sK65),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c52,plain,
subset(sK64,sK65),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c53,plain,
~ subset('set$uunion2'(sK64,sK66),sK65),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( in(X0,X1)
| in(X0,X2)
| ~ in(X0,'set$uunion2'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(d1,plain,
( subset('set$uunion2'(X0,X1),X2)
| in(sK20('set$uunion2'(X0,X1),X2),X0)
| in(sK20('set$uunion2'(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( ~ in(X0,X2)
| in(X0,'set$uunion2'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c10]) ).
cnf(d3,plain,
( subset(X0,'set$uunion2'(X1,X2))
| ~ in(sK20(X0,'set$uunion2'(X1,X2)),X2) ),
inference(resolution,[status(thm)],[d2,c18]) ).
cnf(d4,plain,
( subset('set$uunion2'(X0,X1),'set$uunion2'(X2,X1))
| in(sK20('set$uunion2'(X0,X1),'set$uunion2'(X2,X1)),X0)
| subset('set$uunion2'(X0,X1),'set$uunion2'(X2,X1)) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ in(X0,sK66)
| in(X0,sK65) ),
inference(resolution,[status(thm)],[c16,c51]) ).
cnf(d6,plain,
( in(sK20(sK66,X0),sK65)
| subset(sK66,X0) ),
inference(resolution,[status(thm)],[c17,d5]) ).
cnf(d7,plain,
( ~ in(X0,X1)
| in(X0,'set$uunion2'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d8,plain,
( subset(X0,'set$uunion2'(X1,X2))
| ~ in(sK20(X0,'set$uunion2'(X1,X2)),X1) ),
inference(resolution,[status(thm)],[d7,c18]) ).
cnf(d9,plain,
( subset(sK66,'set$uunion2'(sK65,X0))
| subset(sK66,'set$uunion2'(sK65,X0)) ),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( ~ in(X0,sK66)
| in(X0,'set$uunion2'(sK65,X1)) ),
inference(resolution,[status(thm)],[d9,c16]) ).
cnf(d11,plain,
( subset(X0,'set$uunion2'(sK65,X1))
| ~ in(sK20(X0,'set$uunion2'(sK65,X1)),sK66) ),
inference(resolution,[status(thm)],[d10,c18]) ).
cnf(d12,plain,
( subset('set$uunion2'(sK66,X0),'set$uunion2'(sK65,X0))
| subset('set$uunion2'(sK66,X0),'set$uunion2'(sK65,X0)) ),
inference(resolution,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
( ~ subset('set$uunion2'(X0,X1),X0)
| X0 = 'set$uunion2'(X0,X1) ),
inference(resolution,[status(thm)],[c5,c49]) ).
cnf(d14,plain,
( subset('set$uunion2'(X0,X1),'set$uunion2'(X2,X0))
| in(sK20('set$uunion2'(X0,X1),'set$uunion2'(X2,X0)),X1)
| subset('set$uunion2'(X0,X1),'set$uunion2'(X2,X0)) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d15,plain,
( ~ in(X0,sK64)
| in(X0,sK65) ),
inference(resolution,[status(thm)],[c16,c52]) ).
cnf(d16,plain,
( in(sK20(sK64,X0),sK65)
| subset(sK64,X0) ),
inference(resolution,[status(thm)],[c17,d15]) ).
cnf(d17,plain,
( subset(sK64,'set$uunion2'(sK65,X0))
| subset(sK64,'set$uunion2'(sK65,X0)) ),
inference(resolution,[status(thm)],[d8,d16]) ).
cnf(d18,plain,
( ~ in(X0,sK64)
| in(X0,'set$uunion2'(sK65,X1)) ),
inference(resolution,[status(thm)],[d17,c16]) ).
cnf(d19,plain,
( subset(X0,'set$uunion2'(sK65,X1))
| ~ in(sK20(X0,'set$uunion2'(sK65,X1)),sK64) ),
inference(resolution,[status(thm)],[d18,c18]) ).
cnf(d20,plain,
( subset('set$uunion2'(X0,sK64),'set$uunion2'(sK65,X0))
| subset('set$uunion2'(X0,sK64),'set$uunion2'(sK65,X0)) ),
inference(resolution,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
subset('set$uunion2'(sK65,sK64),sK65),
inference(superposition,[status(thm)],[c32,d20]) ).
cnf(d22,plain,
sK65 = 'set$uunion2'(sK65,sK64),
inference(resolution,[status(thm)],[d21,d13]) ).
cnf(d23,plain,
subset('set$uunion2'(sK66,sK64),sK65),
inference(superposition,[status(thm)],[d22,d12]) ).
cnf(d24,plain,
~ subset('set$uunion2'(sK66,sK64),sK65),
inference(demodulation,[status(thm)],[c53,c1]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d24,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU125+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n020.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 08:38:48 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.93/9.63 % SZS status Theorem for theBenchmark.p
% 71.93/9.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------