%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET159+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 08:32:12 AM UTC 2026
% Result : Theorem 141.98s 55.61s
% Output : CNFRefutation 141.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 93 ( 49 unt; 0 def)
% Number of atoms : 148 ( 43 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 86 ( 31 ~; 50 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 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 : 236 ( 4 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ) ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(commutativity_of_union,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(reflexivity_of_subset,axiom,
! [X0] : subset(X0,X0) ).
fof(prove_associativity_of_union,conjecture,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(negate_conjecture,[status(cth)],[prove_associativity_of_union]) ).
cnf(c0,plain,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c1,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c2,plain,
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c6,plain,
union(X0,X1) = union(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_union]) ).
cnf(c7,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c8,plain,
( member(sK10(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c9,plain,
( ~ member(sK10(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c10,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_of_subset]) ).
cnf(c17,plain,
union(union(sK16,sK17),sK18) != union(sK16,union(sK17,sK18)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(sK10(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d1,plain,
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
( ~ subset(union(X0,X1),X0)
| union(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( union(X0,X1) = X0
| ~ subset(union(X1,X0),X0) ),
inference(superposition,[status(thm)],[c6,d2]) ).
cnf(d4,plain,
( ~ member(sK10(X0,union(union(X1,X2),X3)),X2)
| subset(X0,union(union(X1,X2),X3)) ),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d5,plain,
( member(sK10(union(X0,X1),X2),X0)
| member(sK10(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d6,plain,
( subset(union(X0,X1),X0)
| subset(union(X0,X1),X0)
| member(sK10(union(X0,X1),X0),X1) ),
inference(resolution,[status(thm)],[d5,c9]) ).
cnf(d7,plain,
( subset(union(union(union(X0,X1),X2),X1),union(union(X0,X1),X2))
| subset(union(union(union(X0,X1),X2),X1),union(union(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
subset(union(X1,union(union(X0,X1),X2)),union(union(X0,X1),X2)),
inference(demodulation,[status(thm)],[d7,c6]) ).
cnf(d9,plain,
union(union(union(X0,X1),X2),X1) = union(union(X0,X1),X2),
inference(resolution,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
union(X1,union(union(X0,X1),X2)) = union(union(X0,X1),X2),
inference(demodulation,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
( ~ member(sK10(X0,union(union(X1,X2),X3)),X1)
| subset(X0,union(union(X1,X2),X3)) ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d12,plain,
( subset(union(union(union(X0,X1),X2),X0),union(union(X0,X1),X2))
| subset(union(union(union(X0,X1),X2),X0),union(union(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d6,d11]) ).
cnf(d13,plain,
subset(union(X0,union(union(X0,X1),X2)),union(union(X0,X1),X2)),
inference(demodulation,[status(thm)],[d12,c6]) ).
cnf(d14,plain,
union(union(union(X0,X1),X2),X0) = union(union(X0,X1),X2),
inference(resolution,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
union(X0,union(union(X0,X1),X2)) = union(union(X0,X1),X2),
inference(demodulation,[status(thm)],[d14,c6]) ).
cnf(d16,plain,
union(X0,union(union(X1,X0),X2)) = union(union(X0,X1),X2),
inference(superposition,[status(thm)],[c6,d15]) ).
cnf(d17,plain,
union(union(X0,X1),X2) = union(union(X1,X0),X2),
inference(superposition,[status(thm)],[d16,d10]) ).
cnf(d18,plain,
union(union(X1,X0),X2) = union(X2,union(X0,X1)),
inference(superposition,[status(thm)],[d17,c6]) ).
cnf(d19,plain,
( ~ member(sK10(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[c9,c2]) ).
cnf(d20,plain,
( ~ member(sK10(X0,union(X1,union(X2,X3))),X3)
| subset(X0,union(X1,union(X2,X3))) ),
inference(resolution,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
( subset(union(X0,X1),union(X0,X2))
| subset(union(X0,X1),union(X0,X2))
| member(sK10(union(X0,X1),union(X0,X2)),X1) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d22,plain,
( subset(union(X0,X1),union(X0,union(X2,X1)))
| subset(union(X0,X1),union(X0,union(X2,X1))) ),
inference(resolution,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
subset(union(X1,X0),union(X0,union(X2,X1))),
inference(superposition,[status(thm)],[c6,d22]) ).
cnf(d24,plain,
( ~ subset(union(X0,union(X1,X2)),union(X2,X0))
| union(X0,union(X1,X2)) = union(X2,X0) ),
inference(resolution,[status(thm)],[d23,c5]) ).
cnf(d25,plain,
( subset(union(X0,X1),union(union(X0,X2),X3))
| subset(union(X0,X1),union(union(X0,X2),X3))
| member(sK10(union(X0,X1),union(union(X0,X2),X3)),X1) ),
inference(resolution,[status(thm)],[d5,d11]) ).
cnf(d26,plain,
( subset(union(X0,X3),union(union(X0,X1),X2))
| member(sK10(union(X0,X3),union(X2,union(X0,X1))),X3) ),
inference(superposition,[status(thm)],[c6,d25]) ).
cnf(d27,plain,
( subset(union(union(X0,X1),X0),union(X0,X1))
| subset(union(union(X0,X1),X0),union(X0,X1)) ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d28,plain,
subset(union(X0,union(X0,X1)),union(X0,X1)),
inference(demodulation,[status(thm)],[d27,c6]) ).
cnf(d29,plain,
union(union(X0,X1),X0) = union(X0,X1),
inference(resolution,[status(thm)],[d28,d3]) ).
cnf(d30,plain,
union(X0,union(X0,X1)) = union(X0,X1),
inference(demodulation,[status(thm)],[d29,c6]) ).
cnf(d31,plain,
union(X0,union(X1,X0)) = union(X0,X1),
inference(superposition,[status(thm)],[c6,d30]) ).
cnf(d32,plain,
( subset(X2,union(X0,X1))
| ~ member(sK10(X2,union(X1,X0)),X0) ),
inference(superposition,[status(thm)],[c6,d0]) ).
cnf(d33,plain,
( subset(union(union(X0,X1),X1),union(X0,X1))
| subset(union(union(X0,X1),X1),union(X0,X1)) ),
inference(resolution,[status(thm)],[d6,d19]) ).
cnf(d34,plain,
subset(union(X1,union(X0,X1)),union(X0,X1)),
inference(demodulation,[status(thm)],[d33,c6]) ).
cnf(d35,plain,
union(union(X0,X1),X1) = union(X0,X1),
inference(resolution,[status(thm)],[d34,d3]) ).
cnf(d36,plain,
union(X1,union(X0,X1)) = union(X0,X1),
inference(demodulation,[status(thm)],[d35,c6]) ).
cnf(d37,plain,
( subset(X2,union(union(X1,X0),X0))
| ~ member(sK10(X2,union(X1,X0)),union(X1,X0)) ),
inference(superposition,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
( subset(X2,union(X1,union(X0,X1)))
| ~ member(sK10(X2,union(X0,X1)),union(X0,X1)) ),
inference(demodulation,[status(thm)],[d37,c6]) ).
cnf(d39,plain,
( subset(X2,union(X0,X1))
| ~ member(sK10(X2,union(X1,X0)),union(X1,X0)) ),
inference(demodulation,[status(thm)],[d38,d31]) ).
cnf(d40,plain,
( ~ member(X0,union(X1,X3))
| member(X0,union(X1,union(X2,X3))) ),
inference(resolution,[status(thm)],[d22,c7]) ).
cnf(d41,plain,
( subset(X0,union(union(X2,X3),X1))
| ~ member(sK10(X0,union(X1,union(X2,X3))),union(X1,X3)) ),
inference(resolution,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
( subset(union(X0,union(X1,X2)),union(union(X0,X2),X1))
| subset(union(X0,union(X1,X2)),union(union(X0,X2),X1)) ),
inference(resolution,[status(thm)],[d41,d26]) ).
cnf(d43,plain,
union(X2,union(X0,X1)) = union(union(X1,X0),X2),
inference(superposition,[status(thm)],[d17,c6]) ).
cnf(d44,plain,
subset(union(X0,union(X2,X1)),union(X2,union(X1,X0))),
inference(superposition,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
union(X2,union(X0,X1)) = union(X2,union(X1,X0)),
inference(superposition,[status(thm)],[d43,c6]) ).
cnf(d46,plain,
( ~ member(sK10(X0,union(X1,union(X2,X3))),X2)
| subset(X0,union(X1,union(X2,X3))) ),
inference(resolution,[status(thm)],[d19,c1]) ).
cnf(d47,plain,
( subset(union(union(X0,union(X1,X2)),X1),union(X0,union(X1,X2)))
| subset(union(union(X0,union(X1,X2)),X1),union(X0,union(X1,X2))) ),
inference(resolution,[status(thm)],[d46,d6]) ).
cnf(d48,plain,
subset(union(X1,union(X0,union(X1,X2))),union(X0,union(X1,X2))),
inference(demodulation,[status(thm)],[d47,c6]) ).
cnf(d49,plain,
union(union(X0,union(X1,X2)),X1) = union(X0,union(X1,X2)),
inference(resolution,[status(thm)],[d48,d3]) ).
cnf(d50,plain,
union(X1,union(X0,union(X1,X2))) = union(X0,union(X1,X2)),
inference(demodulation,[status(thm)],[d49,c6]) ).
cnf(d51,plain,
union(X1,union(union(X1,X2),X0)) = union(X0,union(X1,X2)),
inference(superposition,[status(thm)],[c6,d50]) ).
cnf(d52,plain,
union(X2,union(X0,X1)) = union(X0,union(X2,union(X0,X1))),
inference(superposition,[status(thm)],[d51,d45]) ).
cnf(d53,plain,
subset(union(union(X0,X2),union(X0,X1)),union(X1,union(X0,X2))),
inference(superposition,[status(thm)],[d52,d44]) ).
cnf(d54,plain,
union(union(X0,X1),union(X0,X2)) = union(X2,union(X0,X1)),
inference(resolution,[status(thm)],[d53,d24]) ).
cnf(d55,plain,
( subset(union(X0,X1),union(X2,X0))
| subset(union(X0,X1),union(X2,X0))
| member(sK10(union(X0,X1),union(X2,X0)),X1) ),
inference(resolution,[status(thm)],[d5,d19]) ).
cnf(d56,plain,
( subset(union(X0,X1),union(union(X2,X1),X0))
| subset(union(X0,X1),union(union(X2,X1),X0)) ),
inference(resolution,[status(thm)],[d55,d4]) ).
cnf(d57,plain,
( ~ subset(union(union(X0,X1),X2),union(X2,X1))
| union(union(X0,X1),X2) = union(X2,X1) ),
inference(resolution,[status(thm)],[d56,c5]) ).
cnf(d58,plain,
subset(union(union(X2,X1),X0),union(union(X0,X2),X1)),
inference(superposition,[status(thm)],[d18,d42]) ).
cnf(d59,plain,
subset(union(union(X1,X2),X0),union(union(X1,X0),X2)),
inference(superposition,[status(thm)],[d17,d58]) ).
cnf(d60,plain,
union(X0,union(X0,X1)) = union(X0,union(X1,X0)),
inference(superposition,[status(thm)],[d31,d30]) ).
cnf(d61,plain,
union(X0,X1) = union(X0,union(X1,X0)),
inference(demodulation,[status(thm)],[d60,d30]) ).
cnf(d62,plain,
union(X1,X0) = union(X1,union(X1,X0)),
inference(superposition,[status(thm)],[c6,d61]) ).
cnf(d63,plain,
subset(union(union(X0,X2),union(X0,X1)),union(union(X0,X1),X2)),
inference(superposition,[status(thm)],[d62,d59]) ).
cnf(d64,plain,
union(union(X0,X1),union(X0,X2)) = union(union(X0,X2),X1),
inference(resolution,[status(thm)],[d63,d57]) ).
cnf(d65,plain,
union(X2,union(X0,X1)) = union(union(X0,X2),X1),
inference(demodulation,[status(thm)],[d64,d54]) ).
cnf(d66,plain,
union(X1,union(X0,X2)) = union(X2,union(X1,X0)),
inference(superposition,[status(thm)],[d65,d18]) ).
cnf(d67,plain,
union(sK18,union(sK16,sK17)) != union(sK16,union(sK17,sK18)),
inference(demodulation,[status(thm)],[c17,c6]) ).
cnf(d68,plain,
union(sK17,union(sK18,sK16)) != union(sK16,union(sK17,sK18)),
inference(demodulation,[status(thm)],[d67,d66]) ).
cnf(d69,plain,
union(sK16,union(sK17,sK18)) != union(sK16,union(sK17,sK18)),
inference(demodulation,[status(thm)],[d68,d66]) ).
cnf(d70,plain,
( subset(union(X0,X0),X0)
| subset(union(X0,X0),X0) ),
inference(resolution,[status(thm)],[d6,c9]) ).
cnf(d71,plain,
union(X0,X0) = X0,
inference(resolution,[status(thm)],[d70,d2]) ).
cnf(d72,plain,
( union(X0,X0) = X0
| ~ subset(X0,X0) ),
inference(superposition,[status(thm)],[d71,d2]) ).
cnf(d73,plain,
( ~ subset(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d72,d71]) ).
cnf(d74,plain,
X0 = X0,
inference(resolution,[status(thm)],[c10,d73]) ).
cnf(d75,plain,
$false,
inference(resolution,[status(thm)],[d74,d69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET159+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 07:14:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 141.98/55.61 % SZS status Theorem for theBenchmark.p
% 141.98/55.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------