%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX222-1 : 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 : n006.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 09:15:41 AM UTC 2026
% Result : Unsatisfiable 24.48s 8.14s
% Output : CNFRefutation 24.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 12 RR)
% Number of literals : 38 ( 37 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 : 20 ( 20 usr; 6 con; 0-4 aty)
% Number of variables : 50 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_001,axiom,
aux(X0,X1,X2,just(X3)) = eq(X3,X1) ).
cnf(axiom_002,axiom,
notb(btrue) = bfalse ).
cnf(axiom_005,axiom,
index(cons(X0,X1),zero) = just(X0) ).
cnf(axiom_007,axiom,
andb(btrue,X0) = X0 ).
cnf(axiom_012,axiom,
nf(lam(X0)) = nf(X0) ).
cnf(axiom_013,axiom,
nf(var(X0)) = btrue ).
cnf(axiom_015,axiom,
tc(X0,lam(X1),arr(X2,X3)) = tc(cons(X2,X0),X1,X3) ).
cnf(axiom_019,axiom,
tc(X0,var(X1),X2) = aux(X0,X2,X1,index(X0,X1)) ).
cnf(axiom_020,axiom,
'sat$usynth$unf$uk'(X0) = notb(andb(nf(X0),tc(nil,X0,arr(a,arr(b,b))))) ).
cnf(axiom_051,axiom,
eq(X0,X0) = btrue ).
cnf(axiom_054,axiom,
eq4(X0,X0) = btrue ).
cnf(goal,negated_conjecture,
eq4('sat$usynth$unf$uk'(X0),bfalse) != btrue ).
cnf(c1,plain,
eq(X0,X1) = aux(X2,X1,X3,just(X0)),
inference(clausification,[status(esa)],[axiom_001]) ).
cnf(c2,plain,
notb(btrue) = bfalse,
inference(clausification,[status(esa)],[axiom_002]) ).
cnf(c5,plain,
just(X0) = index(cons(X0,X1),zero),
inference(clausification,[status(esa)],[axiom_005]) ).
cnf(c7,plain,
andb(btrue,X0) = X0,
inference(clausification,[status(esa)],[axiom_007]) ).
cnf(c12,plain,
nf(X0) = nf(lam(X0)),
inference(clausification,[status(esa)],[axiom_012]) ).
cnf(c13,plain,
nf(var(X0)) = btrue,
inference(clausification,[status(esa)],[axiom_013]) ).
cnf(c15,plain,
tc(cons(X0,X1),X2,X3) = tc(X1,lam(X2),arr(X0,X3)),
inference(clausification,[status(esa)],[axiom_015]) ).
cnf(c19,plain,
aux(X0,X1,X2,index(X0,X2)) = tc(X0,var(X2),X1),
inference(clausification,[status(esa)],[axiom_019]) ).
cnf(c20,plain,
notb(andb(nf(X0),tc(nil,X0,arr(a,arr(b,b))))) = 'sat$usynth$unf$uk'(X0),
inference(clausification,[status(esa)],[axiom_020]) ).
cnf(c51,plain,
eq(X0,X0) = btrue,
inference(clausification,[status(esa)],[axiom_051]) ).
cnf(c54,plain,
eq4(X0,X0) = btrue,
inference(clausification,[status(esa)],[axiom_054]) ).
cnf(c55,plain,
eq4('sat$usynth$unf$uk'(X0),bfalse) != btrue,
inference(clausification,[status(esa)],[goal]) ).
cnf(d0,plain,
notb(andb(nf(X0),tc(nil,lam(X0),arr(a,arr(b,b))))) = 'sat$usynth$unf$uk'(lam(X0)),
inference(superposition,[status(thm)],[c12,c20]) ).
cnf(d1,plain,
notb(andb(nf(X0),tc(cons(a,nil),X0,arr(b,b)))) = 'sat$usynth$unf$uk'(lam(X0)),
inference(demodulation,[status(thm)],[d0,c15]) ).
cnf(d2,plain,
notb(andb(nf(X0),tc(cons(a,nil),lam(X0),arr(b,b)))) = 'sat$usynth$unf$uk'(lam(lam(X0))),
inference(superposition,[status(thm)],[c12,d1]) ).
cnf(d3,plain,
notb(andb(nf(X0),tc(cons(b,cons(a,nil)),X0,b))) = 'sat$usynth$unf$uk'(lam(lam(X0))),
inference(demodulation,[status(thm)],[d2,c15]) ).
cnf(d4,plain,
aux(cons(X0,X1),X2,zero,just(X0)) = tc(cons(X0,X1),var(zero),X2),
inference(superposition,[status(thm)],[c5,c19]) ).
cnf(d5,plain,
eq(X0,X2) = tc(cons(X0,X1),var(zero),X2),
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
notb(andb(nf(var(zero)),eq(b,b))) = 'sat$usynth$unf$uk'(lam(lam(var(zero)))),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
notb(andb(btrue,eq(b,b))) = 'sat$usynth$unf$uk'(lam(lam(var(zero)))),
inference(demodulation,[status(thm)],[d6,c13]) ).
cnf(d8,plain,
notb(eq(b,b)) = 'sat$usynth$unf$uk'(lam(lam(var(zero)))),
inference(demodulation,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
notb(btrue) = 'sat$usynth$unf$uk'(lam(lam(var(zero)))),
inference(demodulation,[status(thm)],[d8,c51]) ).
cnf(d10,plain,
bfalse = 'sat$usynth$unf$uk'(lam(lam(var(zero)))),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
eq4(bfalse,bfalse) != btrue,
inference(superposition,[status(thm)],[d10,c55]) ).
cnf(d12,plain,
btrue != btrue,
inference(demodulation,[status(thm)],[d11,c54]) ).
cnf(d13,plain,
$false,
inference(equality_resolution,[status(thm)],[d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX222-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 16:58:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.48/8.14 % SZS status Unsatisfiable for theBenchmark.p
% 24.48/8.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------