%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX217-1 : 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 : 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 09:15:41 AM UTC 2026
% Result : Unsatisfiable 140.36s 20.81s
% Output : CNFRefutation 140.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 26
% Syntax : Number of clauses : 140 ( 140 unt; 0 nHn; 66 RR)
% Number of literals : 140 ( 139 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-2 aty)
% Number of variables : 97 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
aux(X0,btrue) = cons(o,shw(half(suc(X0)))) ).
cnf(axiom_001,axiom,
aux(X0,bfalse) = cons(i,shw(half(suc(X0)))) ).
cnf(axiom_002,axiom,
notb(btrue) = bfalse ).
cnf(axiom_003,axiom,
notb(bfalse) = btrue ).
cnf(axiom_004,axiom,
half(zero) = zero ).
cnf(axiom_005,axiom,
half(suc(zero)) = zero ).
cnf(axiom_006,axiom,
half(suc(suc(X0))) = suc(half(X0)) ).
cnf(axiom_007,axiom,
evenNat(zero) = btrue ).
cnf(axiom_008,axiom,
evenNat(suc(X0)) = notb(evenNat(X0)) ).
cnf(axiom_009,axiom,
shw(zero) = nil ).
cnf(axiom_010,axiom,
shw(suc(X0)) = aux(X0,evenNat(suc(X0))) ).
cnf(axiom_011,axiom,
append(nil,X0) = X0 ).
cnf(axiom_012,axiom,
append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ).
cnf(axiom_013,axiom,
addNat(zero,X0) = X0 ).
cnf(axiom_014,axiom,
addNat(suc(X0),X1) = suc(addNat(X0,X1)) ).
cnf(axiom_015,axiom,
double(X0) = addNat(X0,X0) ).
cnf(axiom_016,axiom,
rd(nil) = zero ).
cnf(axiom_017,axiom,
rd(cons(i,X0)) = suc(double(rd(X0))) ).
cnf(axiom_018,axiom,
rd(cons(o,X0)) = double(rd(X0)) ).
cnf(axiom_019,axiom,
x(X0,X1) = rd(append(shw(X0),shw(X1))) ).
cnf(axiom_020,axiom,
'sat$ucomm'(X0,X1) = eq(x(X0,X1),x(X1,X0)) ).
cnf(axiom_025,axiom,
eq(suc(X0),suc(X1)) = eq(X0,X1) ).
cnf(axiom_027,axiom,
eq(suc(X0),zero) = bfalse ).
cnf(axiom_028,axiom,
eq(X0,X0) = btrue ).
cnf(axiom_029,axiom,
eq2(X0,X0) = btrue ).
cnf(goal,negated_conjecture,
eq2('sat$ucomm'(X0,X1),bfalse) != btrue ).
cnf(c0,plain,
cons(o,shw(half(suc(X0)))) = aux(X0,btrue),
inference(clausification,[status(esa)],[axiom]) ).
cnf(c1,plain,
cons(i,shw(half(suc(X0)))) = aux(X0,bfalse),
inference(clausification,[status(esa)],[axiom_001]) ).
cnf(c2,plain,
notb(btrue) = bfalse,
inference(clausification,[status(esa)],[axiom_002]) ).
cnf(c3,plain,
notb(bfalse) = btrue,
inference(clausification,[status(esa)],[axiom_003]) ).
cnf(c4,plain,
half(zero) = zero,
inference(clausification,[status(esa)],[axiom_004]) ).
cnf(c5,plain,
half(suc(zero)) = zero,
inference(clausification,[status(esa)],[axiom_005]) ).
cnf(c6,plain,
suc(half(X0)) = half(suc(suc(X0))),
inference(clausification,[status(esa)],[axiom_006]) ).
cnf(c7,plain,
evenNat(zero) = btrue,
inference(clausification,[status(esa)],[axiom_007]) ).
cnf(c8,plain,
notb(evenNat(X0)) = evenNat(suc(X0)),
inference(clausification,[status(esa)],[axiom_008]) ).
cnf(c9,plain,
shw(zero) = nil,
inference(clausification,[status(esa)],[axiom_009]) ).
cnf(c10,plain,
aux(X0,evenNat(suc(X0))) = shw(suc(X0)),
inference(clausification,[status(esa)],[axiom_010]) ).
cnf(c11,plain,
append(nil,X0) = X0,
inference(clausification,[status(esa)],[axiom_011]) ).
cnf(c12,plain,
cons(X0,append(X1,X2)) = append(cons(X0,X1),X2),
inference(clausification,[status(esa)],[axiom_012]) ).
cnf(c13,plain,
addNat(zero,X0) = X0,
inference(clausification,[status(esa)],[axiom_013]) ).
cnf(c14,plain,
suc(addNat(X0,X1)) = addNat(suc(X0),X1),
inference(clausification,[status(esa)],[axiom_014]) ).
cnf(c15,plain,
addNat(X0,X0) = double(X0),
inference(clausification,[status(esa)],[axiom_015]) ).
cnf(c16,plain,
rd(nil) = zero,
inference(clausification,[status(esa)],[axiom_016]) ).
cnf(c17,plain,
suc(double(rd(X0))) = rd(cons(i,X0)),
inference(clausification,[status(esa)],[axiom_017]) ).
cnf(c18,plain,
double(rd(X0)) = rd(cons(o,X0)),
inference(clausification,[status(esa)],[axiom_018]) ).
cnf(c19,plain,
rd(append(shw(X0),shw(X1))) = x(X0,X1),
inference(clausification,[status(esa)],[axiom_019]) ).
cnf(c20,plain,
eq(x(X0,X1),x(X1,X0)) = 'sat$ucomm'(X0,X1),
inference(clausification,[status(esa)],[axiom_020]) ).
cnf(c25,plain,
eq(X0,X1) = eq(suc(X0),suc(X1)),
inference(clausification,[status(esa)],[axiom_025]) ).
cnf(c27,plain,
eq(suc(X0),zero) = bfalse,
inference(clausification,[status(esa)],[axiom_027]) ).
cnf(c28,plain,
eq(X0,X0) = btrue,
inference(clausification,[status(esa)],[axiom_028]) ).
cnf(c29,plain,
eq2(X0,X0) = btrue,
inference(clausification,[status(esa)],[axiom_029]) ).
cnf(c31,plain,
eq2('sat$ucomm'(X0,X1),bfalse) != btrue,
inference(clausification,[status(esa)],[goal]) ).
cnf(d0,plain,
eq(addNat(X0,X1),X2) = eq(addNat(suc(X0),X1),suc(X2)),
inference(superposition,[status(thm)],[c14,c25]) ).
cnf(d1,plain,
eq(addNat(X0,suc(X0)),X1) = eq(double(suc(X0)),suc(X1)),
inference(superposition,[status(thm)],[c15,d0]) ).
cnf(d2,plain,
suc(X0) = addNat(suc(zero),X0),
inference(superposition,[status(thm)],[c13,c14]) ).
cnf(d3,plain,
eq(suc(suc(suc(zero))),X0) = eq(double(suc(suc(zero))),suc(X0)),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
eq(X2,addNat(X0,X1)) = eq(suc(X2),addNat(suc(X0),X1)),
inference(superposition,[status(thm)],[c14,c25]) ).
cnf(d5,plain,
eq(X1,addNat(X0,suc(X0))) = eq(suc(X1),double(suc(X0))),
inference(superposition,[status(thm)],[c15,d4]) ).
cnf(d6,plain,
eq(X0,suc(suc(suc(zero)))) = eq(suc(X0),double(suc(suc(zero)))),
inference(superposition,[status(thm)],[d2,d5]) ).
cnf(d7,plain,
suc(suc(X0)) = addNat(suc(suc(zero)),X0),
inference(superposition,[status(thm)],[d2,c14]) ).
cnf(d8,plain,
suc(suc(suc(suc(zero)))) = double(suc(suc(zero))),
inference(superposition,[status(thm)],[d7,c15]) ).
cnf(d9,plain,
eq(suc(suc(suc(suc(suc(zero))))),X0) = eq(double(suc(suc(suc(zero)))),suc(X0)),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d10,plain,
eq(suc(double(suc(suc(zero)))),X0) = eq(double(suc(suc(suc(zero)))),suc(X0)),
inference(demodulation,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
rd(append(nil,shw(X0))) = x(zero,X0),
inference(superposition,[status(thm)],[c9,c19]) ).
cnf(d12,plain,
rd(shw(X0)) = x(zero,X0),
inference(demodulation,[status(thm)],[d11,c11]) ).
cnf(d13,plain,
cons(i,shw(zero)) = aux(zero,bfalse),
inference(superposition,[status(thm)],[c5,c1]) ).
cnf(d14,plain,
cons(i,nil) = aux(zero,bfalse),
inference(demodulation,[status(thm)],[d13,c9]) ).
cnf(d15,plain,
aux(X0,notb(evenNat(X0))) = shw(suc(X0)),
inference(demodulation,[status(thm)],[c10,c8]) ).
cnf(d16,plain,
aux(zero,notb(btrue)) = shw(suc(zero)),
inference(superposition,[status(thm)],[c7,d15]) ).
cnf(d17,plain,
aux(zero,bfalse) = shw(suc(zero)),
inference(demodulation,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
cons(i,nil) = shw(suc(zero)),
inference(demodulation,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
rd(append(cons(i,nil),shw(X0))) = x(suc(zero),X0),
inference(superposition,[status(thm)],[d18,c19]) ).
cnf(d20,plain,
rd(cons(i,append(nil,shw(X0)))) = x(suc(zero),X0),
inference(demodulation,[status(thm)],[d19,c12]) ).
cnf(d21,plain,
suc(double(rd(append(nil,shw(X0))))) = x(suc(zero),X0),
inference(demodulation,[status(thm)],[d20,c17]) ).
cnf(d22,plain,
suc(double(rd(shw(X0)))) = x(suc(zero),X0),
inference(demodulation,[status(thm)],[d21,c11]) ).
cnf(d23,plain,
suc(double(x(zero,X0))) = x(suc(zero),X0),
inference(demodulation,[status(thm)],[d22,d12]) ).
cnf(d24,plain,
cons(i,shw(suc(half(X0)))) = aux(suc(X0),bfalse),
inference(superposition,[status(thm)],[c6,c1]) ).
cnf(d25,plain,
cons(i,shw(suc(suc(half(X0))))) = aux(suc(suc(suc(X0))),bfalse),
inference(superposition,[status(thm)],[c6,d24]) ).
cnf(d26,plain,
suc(double(rd(shw(suc(suc(half(X0))))))) = rd(aux(suc(suc(suc(X0))),bfalse)),
inference(superposition,[status(thm)],[d25,c17]) ).
cnf(d27,plain,
suc(double(x(zero,suc(suc(half(X0)))))) = rd(aux(suc(suc(suc(X0))),bfalse)),
inference(demodulation,[status(thm)],[d26,d12]) ).
cnf(d28,plain,
x(suc(zero),suc(suc(half(X0)))) = rd(aux(suc(suc(suc(X0))),bfalse)),
inference(demodulation,[status(thm)],[d27,d23]) ).
cnf(d29,plain,
suc(suc(zero)) = double(suc(zero)),
inference(superposition,[status(thm)],[d2,c15]) ).
cnf(d30,plain,
double(zero) = zero,
inference(superposition,[status(thm)],[c15,c13]) ).
cnf(d31,plain,
rd(cons(i,nil)) = x(zero,suc(zero)),
inference(superposition,[status(thm)],[d18,d12]) ).
cnf(d32,plain,
suc(double(rd(nil))) = x(zero,suc(zero)),
inference(demodulation,[status(thm)],[d31,c17]) ).
cnf(d33,plain,
suc(double(zero)) = x(zero,suc(zero)),
inference(demodulation,[status(thm)],[d32,c16]) ).
cnf(d34,plain,
suc(zero) = x(zero,suc(zero)),
inference(demodulation,[status(thm)],[d33,d30]) ).
cnf(d35,plain,
cons(o,shw(suc(half(X0)))) = aux(suc(X0),btrue),
inference(superposition,[status(thm)],[c6,c0]) ).
cnf(d36,plain,
double(rd(shw(suc(half(X0))))) = rd(aux(suc(X0),btrue)),
inference(superposition,[status(thm)],[d35,c18]) ).
cnf(d37,plain,
double(x(zero,suc(half(X0)))) = rd(aux(suc(X0),btrue)),
inference(demodulation,[status(thm)],[d36,d12]) ).
cnf(d38,plain,
double(x(zero,suc(zero))) = rd(aux(suc(zero),btrue)),
inference(superposition,[status(thm)],[c4,d37]) ).
cnf(d39,plain,
double(suc(zero)) = rd(aux(suc(zero),btrue)),
inference(demodulation,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
suc(suc(zero)) = rd(aux(suc(zero),btrue)),
inference(demodulation,[status(thm)],[d39,d29]) ).
cnf(d41,plain,
double(rd(shw(half(suc(X0))))) = rd(aux(X0,btrue)),
inference(superposition,[status(thm)],[c0,c18]) ).
cnf(d42,plain,
suc(double(rd(shw(half(suc(X0)))))) = rd(aux(X0,bfalse)),
inference(superposition,[status(thm)],[c1,c17]) ).
cnf(d43,plain,
suc(rd(aux(X0,btrue))) = rd(aux(X0,bfalse)),
inference(demodulation,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
aux(suc(X0),notb(notb(evenNat(X0)))) = shw(suc(suc(X0))),
inference(superposition,[status(thm)],[c8,d15]) ).
cnf(d45,plain,
aux(suc(zero),notb(notb(btrue))) = shw(suc(suc(zero))),
inference(superposition,[status(thm)],[c7,d44]) ).
cnf(d46,plain,
aux(suc(zero),notb(bfalse)) = shw(suc(suc(zero))),
inference(demodulation,[status(thm)],[d45,c2]) ).
cnf(d47,plain,
aux(suc(zero),btrue) = shw(suc(suc(zero))),
inference(demodulation,[status(thm)],[d46,c3]) ).
cnf(d48,plain,
cons(o,shw(suc(suc(half(X0))))) = aux(suc(suc(suc(X0))),btrue),
inference(superposition,[status(thm)],[c6,d35]) ).
cnf(d49,plain,
cons(o,shw(suc(suc(zero)))) = aux(suc(suc(suc(zero))),btrue),
inference(superposition,[status(thm)],[c4,d48]) ).
cnf(d50,plain,
cons(o,aux(suc(zero),btrue)) = aux(suc(suc(suc(zero))),btrue),
inference(demodulation,[status(thm)],[d49,d47]) ).
cnf(d51,plain,
suc(rd(cons(o,aux(suc(zero),btrue)))) = rd(aux(suc(suc(suc(zero))),bfalse)),
inference(superposition,[status(thm)],[d50,d43]) ).
cnf(d52,plain,
suc(double(rd(aux(suc(zero),btrue)))) = rd(aux(suc(suc(suc(zero))),bfalse)),
inference(demodulation,[status(thm)],[d51,c18]) ).
cnf(d53,plain,
suc(double(suc(suc(zero)))) = rd(aux(suc(suc(suc(zero))),bfalse)),
inference(demodulation,[status(thm)],[d52,d40]) ).
cnf(d54,plain,
suc(double(suc(suc(zero)))) = x(suc(zero),suc(suc(half(zero)))),
inference(demodulation,[status(thm)],[d53,d28]) ).
cnf(d55,plain,
suc(double(suc(suc(zero)))) = x(suc(zero),suc(suc(zero))),
inference(demodulation,[status(thm)],[d54,c4]) ).
cnf(d56,plain,
cons(o,append(shw(suc(half(X0))),X1)) = append(aux(suc(X0),btrue),X1),
inference(superposition,[status(thm)],[d35,c12]) ).
cnf(d57,plain,
cons(o,append(shw(suc(zero)),X0)) = append(aux(suc(zero),btrue),X0),
inference(superposition,[status(thm)],[c4,d56]) ).
cnf(d58,plain,
cons(o,append(cons(i,nil),X0)) = append(aux(suc(zero),btrue),X0),
inference(demodulation,[status(thm)],[d57,d18]) ).
cnf(d59,plain,
cons(o,cons(i,append(nil,X0))) = append(aux(suc(zero),btrue),X0),
inference(demodulation,[status(thm)],[d58,c12]) ).
cnf(d60,plain,
cons(o,cons(i,X0)) = append(aux(suc(zero),btrue),X0),
inference(demodulation,[status(thm)],[d59,c11]) ).
cnf(d61,plain,
rd(append(shw(X0),cons(i,nil))) = x(X0,suc(zero)),
inference(superposition,[status(thm)],[d18,c19]) ).
cnf(d62,plain,
rd(append(aux(suc(zero),btrue),cons(i,nil))) = x(suc(suc(zero)),suc(zero)),
inference(superposition,[status(thm)],[d47,d61]) ).
cnf(d63,plain,
rd(cons(o,cons(i,cons(i,nil)))) = x(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d62,d60]) ).
cnf(d64,plain,
double(rd(cons(i,cons(i,nil)))) = x(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d63,c18]) ).
cnf(d65,plain,
double(suc(double(rd(cons(i,nil))))) = x(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d64,c17]) ).
cnf(d66,plain,
double(suc(double(suc(double(rd(nil)))))) = x(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d65,c17]) ).
cnf(d67,plain,
double(suc(double(suc(double(zero))))) = x(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d66,c16]) ).
cnf(d68,plain,
double(suc(double(suc(zero)))) = x(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d67,d30]) ).
cnf(d69,plain,
double(suc(suc(suc(zero)))) = x(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d68,d29]) ).
cnf(d70,plain,
eq(double(suc(suc(suc(zero)))),x(suc(zero),suc(suc(zero)))) = 'sat$ucomm'(suc(suc(zero)),suc(zero)),
inference(superposition,[status(thm)],[d69,c20]) ).
cnf(d71,plain,
eq(double(suc(suc(suc(zero)))),suc(double(suc(suc(zero))))) = 'sat$ucomm'(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d70,d55]) ).
cnf(d72,plain,
eq(suc(double(suc(suc(zero)))),double(suc(suc(zero)))) = 'sat$ucomm'(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d71,d10]) ).
cnf(d73,plain,
eq(double(suc(suc(zero))),suc(suc(suc(zero)))) = 'sat$ucomm'(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d72,d6]) ).
cnf(d74,plain,
eq(suc(suc(suc(zero))),suc(suc(zero))) = 'sat$ucomm'(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d73,d3]) ).
cnf(d75,plain,
eq(suc(suc(zero)),suc(zero)) = 'sat$ucomm'(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d74,c25]) ).
cnf(d76,plain,
eq(suc(zero),zero) = 'sat$ucomm'(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d75,c25]) ).
cnf(d77,plain,
bfalse = 'sat$ucomm'(suc(suc(zero)),suc(zero)),
inference(demodulation,[status(thm)],[d76,c27]) ).
cnf(d78,plain,
eq2(bfalse,bfalse) != btrue,
inference(superposition,[status(thm)],[d77,c31]) ).
cnf(d79,plain,
btrue != btrue,
inference(demodulation,[status(thm)],[d78,c29]) ).
cnf(d80,plain,
btrue = 'sat$ucomm'(X0,X0),
inference(superposition,[status(thm)],[c28,c20]) ).
cnf(d81,plain,
rd(nil) = x(zero,zero),
inference(superposition,[status(thm)],[c9,d12]) ).
cnf(d82,plain,
zero = x(zero,zero),
inference(demodulation,[status(thm)],[d81,c16]) ).
cnf(d83,plain,
eq(zero,x(zero,zero)) = 'sat$ucomm'(zero,zero),
inference(superposition,[status(thm)],[d82,c20]) ).
cnf(d84,plain,
eq(zero,zero) = 'sat$ucomm'(zero,zero),
inference(demodulation,[status(thm)],[d83,d82]) ).
cnf(d85,plain,
btrue = 'sat$ucomm'(zero,zero),
inference(demodulation,[status(thm)],[d84,c28]) ).
cnf(d86,plain,
btrue = btrue,
inference(demodulation,[status(thm)],[d85,d80]) ).
cnf(d87,plain,
$false,
inference(resolution,[status(thm)],[d86,d79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX217-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n020.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 16:58:49 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 140.36/20.81 % SZS status Unsatisfiable for theBenchmark.p
% 140.36/20.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------