%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX200-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 09:15:37 AM UTC 2026
% Result : Unsatisfiable 13.80s 12.58s
% Output : CNFRefutation 13.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 18 RR)
% Number of literals : 51 ( 50 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-5 aty)
% Number of variables : 73 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_001,axiom,
aux(X0,X1,X2,X3,bfalse) = cons(X2,merge(cons(X0,X1),X3)) ).
cnf(axiom_003,axiom,
aux2(X0,X1,X2,bfalse) = bfalse ).
cnf(axiom_005,axiom,
leqNat(s(X0),z) = bfalse ).
cnf(axiom_007,axiom,
merge(nil,X0) = X0 ).
cnf(axiom_010,axiom,
ord(nil) = btrue ).
cnf(axiom_012,axiom,
ord(cons(X0,cons(X1,X2))) = aux2(X0,X1,X2,leqNat(X0,X1)) ).
cnf(axiom_013,axiom,
impl(btrue,X0) = X0 ).
cnf(axiom_014,axiom,
impl(bfalse,X0) = btrue ).
cnf(axiom_015,axiom,
'prop$umerge$uord$unot3'(X0,X1) = impl(eq2(ord(X0),btrue),impl(eq2(ord(X1),bfalse),eq2(ord(merge(X0,X1)),btrue))) ).
cnf(axiom_016,axiom,
eq2(bfalse,btrue) = bfalse ).
cnf(axiom_017,axiom,
eq2(btrue,bfalse) = bfalse ).
cnf(axiom_022,axiom,
eq2(X0,X0) = btrue ).
cnf(goal,negated_conjecture,
eq2('prop$umerge$uord$unot3'(X0,X1),bfalse) != btrue ).
cnf(c1,plain,
aux(X0,X1,X2,X3,bfalse) = cons(X2,merge(cons(X0,X1),X3)),
inference(clausification,[status(esa)],[axiom_001]) ).
cnf(c3,plain,
aux2(X0,X1,X2,bfalse) = bfalse,
inference(clausification,[status(esa)],[axiom_003]) ).
cnf(c5,plain,
leqNat(s(X0),z) = bfalse,
inference(clausification,[status(esa)],[axiom_005]) ).
cnf(c7,plain,
merge(nil,X0) = X0,
inference(clausification,[status(esa)],[axiom_007]) ).
cnf(c10,plain,
ord(nil) = btrue,
inference(clausification,[status(esa)],[axiom_010]) ).
cnf(c12,plain,
ord(cons(X0,cons(X1,X2))) = aux2(X0,X1,X2,leqNat(X0,X1)),
inference(clausification,[status(esa)],[axiom_012]) ).
cnf(c13,plain,
impl(btrue,X0) = X0,
inference(clausification,[status(esa)],[axiom_013]) ).
cnf(c14,plain,
impl(bfalse,X0) = btrue,
inference(clausification,[status(esa)],[axiom_014]) ).
cnf(c15,plain,
'prop$umerge$uord$unot3'(X0,X1) = impl(eq2(ord(X0),btrue),impl(eq2(ord(X1),bfalse),eq2(ord(merge(X0,X1)),btrue))),
inference(clausification,[status(esa)],[axiom_015]) ).
cnf(c16,plain,
eq2(bfalse,btrue) = bfalse,
inference(clausification,[status(esa)],[axiom_016]) ).
cnf(c17,plain,
eq2(btrue,bfalse) = bfalse,
inference(clausification,[status(esa)],[axiom_017]) ).
cnf(c22,plain,
eq2(X0,X0) = btrue,
inference(clausification,[status(esa)],[axiom_022]) ).
cnf(c23,plain,
eq2('prop$umerge$uord$unot3'(X0,X1),bfalse) != btrue,
inference(clausification,[status(esa)],[goal]) ).
cnf(d0,plain,
ord(cons(s(X0),cons(z,X1))) = aux2(s(X0),z,X1,bfalse),
inference(superposition,[status(thm)],[c5,c12]) ).
cnf(d1,plain,
ord(cons(s(X0),cons(z,X1))) = bfalse,
inference(demodulation,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
ord(cons(s(X3),aux(X0,X1,z,X2,bfalse))) = bfalse,
inference(superposition,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
'prop$umerge$uord$unot3'(nil,X0) = impl(eq2(btrue,btrue),impl(eq2(ord(X0),bfalse),eq2(ord(merge(nil,X0)),btrue))),
inference(superposition,[status(thm)],[c10,c15]) ).
cnf(d4,plain,
'prop$umerge$uord$unot3'(nil,X0) = impl(btrue,impl(eq2(ord(X0),bfalse),eq2(ord(merge(nil,X0)),btrue))),
inference(demodulation,[status(thm)],[d3,c22]) ).
cnf(d5,plain,
'prop$umerge$uord$unot3'(nil,X0) = impl(eq2(ord(X0),bfalse),eq2(ord(merge(nil,X0)),btrue)),
inference(demodulation,[status(thm)],[d4,c13]) ).
cnf(d6,plain,
'prop$umerge$uord$unot3'(nil,X0) = impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue)),
inference(demodulation,[status(thm)],[d5,c7]) ).
cnf(d7,plain,
'prop$umerge$uord$unot3'(nil,cons(s(X0),aux(X1,X2,z,X3,bfalse))) = impl(eq2(bfalse,bfalse),eq2(ord(cons(s(X0),aux(X1,X2,z,X3,bfalse))),btrue)),
inference(superposition,[status(thm)],[d2,d6]) ).
cnf(d8,plain,
'prop$umerge$uord$unot3'(nil,cons(s(X0),aux(X1,X2,z,X3,bfalse))) = impl(btrue,eq2(ord(cons(s(X0),aux(X1,X2,z,X3,bfalse))),btrue)),
inference(demodulation,[status(thm)],[d7,c22]) ).
cnf(d9,plain,
'prop$umerge$uord$unot3'(nil,cons(s(X0),aux(X1,X2,z,X3,bfalse))) = eq2(ord(cons(s(X0),aux(X1,X2,z,X3,bfalse))),btrue),
inference(demodulation,[status(thm)],[d8,c13]) ).
cnf(d10,plain,
'prop$umerge$uord$unot3'(nil,cons(s(X0),aux(X1,X2,z,X3,bfalse))) = eq2(bfalse,btrue),
inference(demodulation,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
'prop$umerge$uord$unot3'(nil,cons(s(X0),aux(X1,X2,z,X3,bfalse))) = bfalse,
inference(demodulation,[status(thm)],[d10,c16]) ).
cnf(d12,plain,
eq2(bfalse,bfalse) != btrue,
inference(superposition,[status(thm)],[d11,c23]) ).
cnf(d13,plain,
btrue != btrue,
inference(demodulation,[status(thm)],[d12,c22]) ).
cnf(d14,plain,
'prop$umerge$uord$unot3'(nil,nil) = impl(eq2(btrue,bfalse),eq2(ord(nil),btrue)),
inference(superposition,[status(thm)],[c10,d6]) ).
cnf(d15,plain,
'prop$umerge$uord$unot3'(nil,nil) = impl(bfalse,eq2(ord(nil),btrue)),
inference(demodulation,[status(thm)],[d14,c17]) ).
cnf(d16,plain,
'prop$umerge$uord$unot3'(nil,nil) = btrue,
inference(demodulation,[status(thm)],[d15,c14]) ).
cnf(d17,plain,
'prop$umerge$uord$unot3'(X0,nil) = impl(eq2(ord(X0),btrue),impl(eq2(btrue,bfalse),eq2(ord(merge(X0,nil)),btrue))),
inference(superposition,[status(thm)],[c10,c15]) ).
cnf(d18,plain,
'prop$umerge$uord$unot3'(X0,nil) = impl(eq2(ord(X0),btrue),impl(bfalse,eq2(ord(merge(X0,nil)),btrue))),
inference(demodulation,[status(thm)],[d17,c17]) ).
cnf(d19,plain,
'prop$umerge$uord$unot3'(X0,nil) = impl(eq2(ord(X0),btrue),btrue),
inference(demodulation,[status(thm)],[d18,c14]) ).
cnf(d20,plain,
'prop$umerge$uord$unot3'(nil,nil) = impl(eq2(btrue,btrue),btrue),
inference(superposition,[status(thm)],[c10,d19]) ).
cnf(d21,plain,
btrue = impl(eq2(btrue,btrue),btrue),
inference(demodulation,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
btrue = impl(btrue,btrue),
inference(demodulation,[status(thm)],[d21,c22]) ).
cnf(d23,plain,
btrue = btrue,
inference(demodulation,[status(thm)],[d22,c13]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[d23,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX200-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.59 % Computer : n010.cluster.edu
% 0.10/10.59 % Model : x86_64 x86_64
% 0.10/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.59 % Memory : 8046.5625MB
% 0.10/10.59 % OS : Linux 6.8.0-71-generic
% 0.10/10.59 % CPULimit : 300
% 0.10/10.59 % WCLimit : 300
% 0.10/10.59 % DateTime : Sat Sep 26 16:55:18 UTC 2026
% 0.10/10.59 % CPUTime :
% 0.10/10.59 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.80/12.58 % SZS status Unsatisfiable for theBenchmark.p
% 13.80/12.58 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------