%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX217-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:34:45 PM UTC 2026
% Result : Unsatisfiable 1.43s 1.76s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 25
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 40 RR)
% Number of literals : 87 ( 86 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 69 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_017,axiom,
rd(cons(i,X1)) = suc(double(rd(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
cnf(axiom_015,axiom,
double(X1) = addNat(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
cnf(axiom_018,axiom,
rd(cons(o,X1)) = double(rd(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
cnf(axiom_008,axiom,
evenNat(suc(X1)) = notb(evenNat(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
cnf(axiom_007,axiom,
evenNat(zero) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_002,axiom,
notb(btrue) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(axiom_016,axiom,
rd(nil) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
cnf(axiom_013,axiom,
addNat(zero,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
cnf(axiom_010,axiom,
shw(suc(X1)) = aux(X1,evenNat(suc(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
cnf(axiom_003,axiom,
notb(bfalse) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
cnf(axiom_001,axiom,
aux(X1,bfalse) = cons(i,shw(half(suc(X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
cnf(axiom_005,axiom,
half(suc(zero)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
cnf(axiom_009,axiom,
shw(zero) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
cnf(axiom,axiom,
aux(X1,btrue) = cons(o,shw(half(suc(X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_006,axiom,
half(suc(suc(X1))) = suc(half(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
cnf(axiom_004,axiom,
half(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
cnf(axiom_020,axiom,
sat_comm(X1,X2) = eq(x(X1,X2),x(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
cnf(axiom_019,axiom,
x(X1,X2) = rd(append(shw(X1),shw(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
cnf(axiom_014,axiom,
addNat(suc(X1),X2) = suc(addNat(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
cnf(goal,negated_conjecture,
eq2(sat_comm(X1,X2),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(axiom_012,axiom,
append(cons(X1,X2),X3) = cons(X1,append(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
cnf(axiom_011,axiom,
append(nil,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
cnf(axiom_025,axiom,
eq(suc(X1),suc(X2)) = eq(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
cnf(axiom_027,axiom,
eq(suc(X1),zero) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
cnf(axiom_029,axiom,
eq2(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
cnf(c_0_25,axiom,
rd(cons(i,X1)) = suc(double(rd(X1))),
axiom_017 ).
cnf(c_0_26,axiom,
double(X1) = addNat(X1,X1),
axiom_015 ).
cnf(c_0_27,axiom,
rd(cons(o,X1)) = double(rd(X1)),
axiom_018 ).
cnf(c_0_28,axiom,
evenNat(suc(X1)) = notb(evenNat(X1)),
axiom_008 ).
cnf(c_0_29,axiom,
evenNat(zero) = btrue,
axiom_007 ).
cnf(c_0_30,axiom,
notb(btrue) = bfalse,
axiom_002 ).
cnf(c_0_31,plain,
rd(cons(i,X1)) = suc(addNat(rd(X1),rd(X1))),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
rd(cons(o,X1)) = addNat(rd(X1),rd(X1)),
inference(rw,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_33,axiom,
rd(nil) = zero,
axiom_016 ).
cnf(c_0_34,axiom,
addNat(zero,X1) = X1,
axiom_013 ).
cnf(c_0_35,axiom,
shw(suc(X1)) = aux(X1,evenNat(suc(X1))),
axiom_010 ).
cnf(c_0_36,plain,
evenNat(suc(zero)) = bfalse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_37,axiom,
notb(bfalse) = btrue,
axiom_003 ).
cnf(c_0_38,plain,
suc(rd(cons(o,X1))) = rd(cons(i,X1)),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
rd(cons(o,nil)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_40,axiom,
aux(X1,bfalse) = cons(i,shw(half(suc(X1)))),
axiom_001 ).
cnf(c_0_41,axiom,
half(suc(zero)) = zero,
axiom_005 ).
cnf(c_0_42,axiom,
shw(zero) = nil,
axiom_009 ).
cnf(c_0_43,plain,
aux(zero,bfalse) = shw(suc(zero)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,axiom,
aux(X1,btrue) = cons(o,shw(half(suc(X1)))),
axiom ).
cnf(c_0_45,axiom,
half(suc(suc(X1))) = suc(half(X1)),
axiom_006 ).
cnf(c_0_46,plain,
evenNat(suc(suc(zero))) = btrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_37]) ).
cnf(c_0_47,plain,
rd(cons(i,nil)) = suc(zero),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,plain,
cons(i,nil) = shw(suc(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]) ).
cnf(c_0_49,plain,
cons(o,shw(suc(half(X1)))) = aux(suc(X1),btrue),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,axiom,
half(zero) = zero,
axiom_004 ).
cnf(c_0_51,plain,
aux(suc(zero),btrue) = shw(suc(suc(zero))),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_52,axiom,
sat_comm(X1,X2) = eq(x(X1,X2),x(X2,X1)),
axiom_020 ).
cnf(c_0_53,axiom,
x(X1,X2) = rd(append(shw(X1),shw(X2))),
axiom_019 ).
cnf(c_0_54,plain,
rd(shw(suc(zero))) = suc(zero),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,axiom,
addNat(suc(X1),X2) = suc(addNat(X1,X2)),
axiom_014 ).
cnf(c_0_56,plain,
cons(o,shw(suc(zero))) = shw(suc(suc(zero))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_57,negated_conjecture,
eq2(sat_comm(X1,X2),bfalse) != btrue,
goal ).
cnf(c_0_58,plain,
sat_comm(X1,X2) = eq(rd(append(shw(X1),shw(X2))),rd(append(shw(X2),shw(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53]),c_0_53]) ).
cnf(c_0_59,axiom,
append(cons(X1,X2),X3) = cons(X1,append(X2,X3)),
axiom_012 ).
cnf(c_0_60,axiom,
append(nil,X1) = X1,
axiom_011 ).
cnf(c_0_61,plain,
cons(i,shw(suc(half(X1)))) = aux(suc(X1),bfalse),
inference(spm,[status(thm)],[c_0_40,c_0_45]) ).
cnf(c_0_62,plain,
suc(rd(aux(X1,btrue))) = rd(aux(X1,bfalse)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_44]),c_0_40]) ).
cnf(c_0_63,plain,
rd(shw(suc(suc(zero)))) = suc(suc(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_54]),c_0_55]),c_0_34]),c_0_56]) ).
cnf(c_0_64,plain,
evenNat(suc(suc(suc(zero)))) = bfalse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_46]),c_0_30]) ).
cnf(c_0_65,plain,
suc(addNat(rd(cons(o,X1)),X2)) = addNat(rd(cons(i,X1)),X2),
inference(spm,[status(thm)],[c_0_55,c_0_38]) ).
cnf(c_0_66,negated_conjecture,
eq2(eq(rd(append(shw(X1),shw(X2))),rd(append(shw(X2),shw(X1)))),bfalse) != btrue,
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,plain,
append(shw(suc(zero)),X1) = cons(i,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_48]),c_0_60]) ).
cnf(c_0_68,plain,
cons(i,shw(half(rd(cons(i,X1))))) = aux(rd(cons(o,X1)),bfalse),
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_69,plain,
cons(i,shw(suc(zero))) = aux(suc(zero),bfalse),
inference(spm,[status(thm)],[c_0_61,c_0_50]) ).
cnf(c_0_70,plain,
rd(aux(suc(zero),bfalse)) = suc(suc(suc(zero))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_51]),c_0_63]) ).
cnf(c_0_71,plain,
aux(suc(suc(zero)),bfalse) = shw(suc(suc(suc(zero)))),
inference(spm,[status(thm)],[c_0_35,c_0_64]) ).
cnf(c_0_72,plain,
suc(addNat(rd(aux(X1,btrue)),X2)) = addNat(rd(aux(X1,bfalse)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_44]),c_0_40]) ).
cnf(c_0_73,plain,
aux(suc(suc(zero)),btrue) = shw(suc(suc(zero))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_56]) ).
cnf(c_0_74,negated_conjecture,
eq2(eq(rd(append(shw(X1),shw(suc(zero)))),rd(cons(i,shw(X1)))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,plain,
append(shw(suc(suc(zero))),X1) = cons(o,cons(i,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_56]),c_0_67]) ).
cnf(c_0_76,plain,
aux(suc(zero),bfalse) = shw(suc(suc(suc(zero)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_45]),c_0_41]),c_0_69]),c_0_56]),c_0_63]),c_0_71]) ).
cnf(c_0_77,plain,
addNat(rd(aux(X1,bfalse)),rd(aux(X1,btrue))) = rd(cons(i,aux(X1,btrue))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_32]),c_0_38]) ).
cnf(c_0_78,plain,
rd(shw(suc(suc(suc(zero))))) = suc(suc(suc(zero))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_73]),c_0_63]),c_0_71]) ).
cnf(c_0_79,negated_conjecture,
eq2(eq(rd(cons(o,shw(suc(suc(suc(zero)))))),rd(cons(i,shw(suc(suc(zero)))))),bfalse) != btrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_69]),c_0_76]) ).
cnf(c_0_80,plain,
rd(cons(i,shw(suc(suc(zero))))) = suc(suc(suc(suc(suc(zero))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_51]),c_0_76]),c_0_78]),c_0_63]),c_0_55]),c_0_55]),c_0_55]),c_0_34]) ).
cnf(c_0_81,negated_conjecture,
eq2(eq(rd(cons(o,shw(suc(suc(suc(zero)))))),suc(suc(suc(suc(suc(zero)))))),bfalse) != btrue,
inference(rw,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_82,plain,
rd(cons(o,shw(suc(suc(suc(zero)))))) = suc(suc(suc(suc(suc(suc(zero)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_78]),c_0_55]),c_0_55]),c_0_55]),c_0_34]) ).
cnf(c_0_83,axiom,
eq(suc(X1),suc(X2)) = eq(X1,X2),
axiom_025 ).
cnf(c_0_84,axiom,
eq(suc(X1),zero) = bfalse,
axiom_027 ).
cnf(c_0_85,axiom,
eq2(X1,X1) = btrue,
axiom_029 ).
cnf(c_0_86,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_83]),c_0_83]),c_0_83]),c_0_83]),c_0_84]),c_0_85])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX217-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n010.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 07:58:36 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.43/1.76 % Version : CSE_E---1.7
% 1.43/1.76 % Problem : theBenchmark.p
% 1.43/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.43/1.76 % SZS output start CNFRefutation
% See solution above
% 1.43/1.77 % Total time : 1.368s
%------------------------------------------------------------------------------