%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 09:15:42 AM UTC 2026
% Result : Unsatisfiable 20.41s 8.00s
% Output : CNFRefutation 20.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 61 ( 58 unt; 0 nHn; 12 RR)
% Number of literals : 64 ( 63 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 95 ( 29 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
aux(X0,X1,X2,btrue) = union(X2,X0) ).
cnf(axiom_001,axiom,
aux(X0,X1,X2,bfalse) = cons(X1,union(X2,X0)) ).
cnf(axiom_002,axiom,
barbar(btrue,X0) = btrue ).
cnf(axiom_003,axiom,
barbar(bfalse,X0) = X0 ).
cnf(axiom_005,axiom,
eqNat(s(X0),z) = bfalse ).
cnf(axiom_007,axiom,
eqNat(z,z) = btrue ).
cnf(axiom_008,axiom,
elem(X0,nil) = bfalse ).
cnf(axiom_009,axiom,
elem(X0,cons(X1,X2)) = barbar(eqNat(X0,X1),elem(X0,X2)) ).
cnf(axiom_010,axiom,
union(nil,X0) = X0 ).
cnf(axiom_011,axiom,
union(cons(X0,X1),X2) = aux(X2,X0,X1,elem(X0,X2)) ).
cnf(axiom_012,axiom,
'prop$uunion$ucomm'(X0,X1) = eq(union(X0,X1),union(X1,X0)) ).
cnf(axiom_016,axiom,
eq2(s(X0),z) = bfalse ).
cnf(axiom_018,axiom,
eq(X0,X0) = btrue ).
cnf(axiom_020,axiom,
eq3(X0,X0) = btrue ).
cnf(axiom_021,axiom,
( eq(cons(X0,X2),cons(X1,X3)) = bfalse
| eq2(X0,X1) != bfalse ) ).
cnf(goal,negated_conjecture,
eq3('prop$uunion$ucomm'(X0,X1),bfalse) != btrue ).
cnf(c0,plain,
aux(X0,X1,X2,btrue) = union(X2,X0),
inference(clausification,[status(esa)],[axiom]) ).
cnf(c1,plain,
aux(X0,X1,X2,bfalse) = cons(X1,union(X2,X0)),
inference(clausification,[status(esa)],[axiom_001]) ).
cnf(c2,plain,
barbar(btrue,X0) = btrue,
inference(clausification,[status(esa)],[axiom_002]) ).
cnf(c3,plain,
barbar(bfalse,X0) = X0,
inference(clausification,[status(esa)],[axiom_003]) ).
cnf(c5,plain,
eqNat(s(X0),z) = bfalse,
inference(clausification,[status(esa)],[axiom_005]) ).
cnf(c7,plain,
eqNat(z,z) = btrue,
inference(clausification,[status(esa)],[axiom_007]) ).
cnf(c8,plain,
elem(X0,nil) = bfalse,
inference(clausification,[status(esa)],[axiom_008]) ).
cnf(c9,plain,
elem(X0,cons(X1,X2)) = barbar(eqNat(X0,X1),elem(X0,X2)),
inference(clausification,[status(esa)],[axiom_009]) ).
cnf(c10,plain,
union(nil,X0) = X0,
inference(clausification,[status(esa)],[axiom_010]) ).
cnf(c11,plain,
union(cons(X0,X1),X2) = aux(X2,X0,X1,elem(X0,X2)),
inference(clausification,[status(esa)],[axiom_011]) ).
cnf(c12,plain,
'prop$uunion$ucomm'(X0,X1) = eq(union(X0,X1),union(X1,X0)),
inference(clausification,[status(esa)],[axiom_012]) ).
cnf(c16,plain,
eq2(s(X0),z) = bfalse,
inference(clausification,[status(esa)],[axiom_016]) ).
cnf(c18,plain,
eq(X0,X0) = btrue,
inference(clausification,[status(esa)],[axiom_018]) ).
cnf(c20,plain,
eq3(X0,X0) = btrue,
inference(clausification,[status(esa)],[axiom_020]) ).
cnf(c21,plain,
( eq(cons(X0,X2),cons(X1,X3)) = bfalse
| eq2(X0,X1) != bfalse ),
inference(clausification,[status(esa)],[axiom_021]) ).
cnf(c25,plain,
eq3('prop$uunion$ucomm'(X0,X1),bfalse) != btrue,
inference(clausification,[status(esa)],[goal]) ).
cnf(d0,plain,
( eq(cons(s(X0),X1),cons(z,X2)) = bfalse
| bfalse != bfalse ),
inference(superposition,[status(thm)],[c16,c21]) ).
cnf(d1,plain,
elem(s(X0),cons(z,X1)) = barbar(bfalse,elem(s(X0),X1)),
inference(superposition,[status(thm)],[c5,c9]) ).
cnf(d2,plain,
elem(s(X0),cons(z,X1)) = elem(s(X0),X1),
inference(demodulation,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
elem(X0,cons(X1,nil)) = barbar(eqNat(X0,X1),bfalse),
inference(superposition,[status(thm)],[c8,c9]) ).
cnf(d4,plain,
elem(s(X0),cons(z,nil)) = barbar(bfalse,bfalse),
inference(superposition,[status(thm)],[c5,d3]) ).
cnf(d5,plain,
elem(s(X0),nil) = barbar(bfalse,bfalse),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
bfalse = barbar(bfalse,bfalse),
inference(demodulation,[status(thm)],[d5,c8]) ).
cnf(d7,plain,
bfalse = bfalse,
inference(demodulation,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
eq(cons(s(X0),X1),cons(z,X2)) = bfalse,
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
elem(z,cons(z,X0)) = barbar(btrue,elem(z,X0)),
inference(superposition,[status(thm)],[c7,c9]) ).
cnf(d10,plain,
elem(z,cons(z,X0)) = btrue,
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
union(cons(z,X1),cons(z,X0)) = aux(cons(z,X0),z,X1,btrue),
inference(superposition,[status(thm)],[d10,c11]) ).
cnf(d12,plain,
union(cons(z,X1),cons(z,X0)) = union(X1,cons(z,X0)),
inference(demodulation,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
'prop$uunion$ucomm'(cons(z,X1),cons(z,X0)) = eq(union(cons(z,X1),cons(z,X0)),union(X0,cons(z,X1))),
inference(superposition,[status(thm)],[d12,c12]) ).
cnf(d14,plain,
'prop$uunion$ucomm'(cons(z,X0),cons(z,X1)) = eq(union(X0,cons(z,X1)),union(X1,cons(z,X0))),
inference(demodulation,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
union(cons(s(X0),X2),cons(z,X1)) = aux(cons(z,X1),s(X0),X2,elem(s(X0),X1)),
inference(superposition,[status(thm)],[d2,c11]) ).
cnf(d16,plain,
union(cons(s(X0),X1),cons(z,nil)) = aux(cons(z,nil),s(X0),X1,bfalse),
inference(superposition,[status(thm)],[c8,d15]) ).
cnf(d17,plain,
union(cons(s(X0),X1),cons(z,nil)) = cons(s(X0),union(X1,cons(z,nil))),
inference(demodulation,[status(thm)],[d16,c1]) ).
cnf(d18,plain,
'prop$uunion$ucomm'(cons(z,cons(s(X0),X1)),cons(z,nil)) = eq(cons(s(X0),union(X1,cons(z,nil))),union(nil,cons(z,cons(s(X0),X1)))),
inference(superposition,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
'prop$uunion$ucomm'(cons(z,cons(s(X0),X1)),cons(z,nil)) = eq(cons(s(X0),union(X1,cons(z,nil))),cons(z,cons(s(X0),X1))),
inference(demodulation,[status(thm)],[d18,c10]) ).
cnf(d20,plain,
'prop$uunion$ucomm'(cons(z,cons(s(X0),X1)),cons(z,nil)) = bfalse,
inference(demodulation,[status(thm)],[d19,d8]) ).
cnf(d21,plain,
eq3(bfalse,bfalse) != btrue,
inference(superposition,[status(thm)],[d20,c25]) ).
cnf(d22,plain,
btrue != btrue,
inference(demodulation,[status(thm)],[d21,c20]) ).
cnf(d23,plain,
'prop$uunion$ucomm'(X0,X0) = btrue,
inference(superposition,[status(thm)],[c12,c18]) ).
cnf(d24,plain,
'prop$uunion$ucomm'(nil,X0) = eq(X0,union(X0,nil)),
inference(superposition,[status(thm)],[c10,c12]) ).
cnf(d25,plain,
'prop$uunion$ucomm'(nil,nil) = eq(nil,nil),
inference(superposition,[status(thm)],[c10,d24]) ).
cnf(d26,plain,
btrue = eq(nil,nil),
inference(demodulation,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
btrue = btrue,
inference(demodulation,[status(thm)],[d26,c18]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[d27,d22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n019.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 17:00:40 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.41/8.00 % SZS status Unsatisfiable for theBenchmark.p
% 20.41/8.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------