%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SWX197+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n021.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 06:59:47 PM UTC 2026
% Result : Theorem 217.46s 29.26s
% Output : CNFRefutation 217.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of clauses : 88 ( 67 unt; 0 nHn; 5 RR)
% Number of literals : 109 ( 108 equ; 23 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 4 con; 0-3 aty)
% Number of variables : 257 ( 64 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_64,plain,
cons(eval(X1,X2),run(X1,X3)) = run(X1,cons2(print(X2),X3)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_64) ).
cnf(i_0_63,plain,
run(X1,nil2) = nil,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_63) ).
cnf(i_0_70,plain,
cons2(apply1(X1,X2),map(X1,X3)) = map(X1,cons2(X2,X3)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_70) ).
cnf(i_0_69,plain,
map(X1,nil2) = nil2,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_69) ).
cnf(i_0_35,plain,
head(cons(X1,X2)) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_35) ).
cnf(i_0_38,plain,
head2(cons2(X1,X2)) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_38) ).
cnf(i_0_68,plain,
( run(X1,cons2(if(X2,X3,X4),X5)) = run(X1,append(X3,X5))
| eval(X1,X2) != suc(X6) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_68) ).
cnf(i_0_58,plain,
addNat(eval(X1,X2),eval(X1,X3)) = eval(X1,add(X2,X3)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_58) ).
cnf(i_0_57,plain,
eval(X1,n(X2)) = X2,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_57) ).
cnf(i_0_60,plain,
( eval(X1,eq(X2,X3)) = suc(zero)
| eval(X1,X2) != eval(X1,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_60) ).
cnf(i_0_72,plain,
cons2(X1,append(X2,X3)) = append(cons2(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_72) ).
cnf(i_0_71,plain,
append(nil2,X1) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_71) ).
cnf(i_0_67,plain,
( run(X1,cons2(if(X2,X3,X4),X5)) = run(X1,append(X4,X5))
| eval(X1,X2) != zero ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_67) ).
cnf(i_0_53,plain,
suc(addNat(X1,suc(X2))) = addNat(suc(X1),suc(X2)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_53) ).
cnf(i_0_47,plain,
if(add(n(suc(zero)),X1),X2,X3) = apply1(lam,if(X1,X3,X2)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_47) ).
cnf(i_0_51,plain,
addNat(zero,X1) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_51) ).
cnf(i_0_48,plain,
eval(nil,v(X1)) = zero,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_48) ).
cnf(i_0_66,plain,
run(X1,cons2(if(X2,append(X3,cons2(while(X2,X3),nil2)),nil2),X4)) = run(X1,cons2(while(X2,X3),X4)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_66) ).
cnf(i_0_74,negated_conjecture,
run(nil,cons2(apply1(lam,X1),nil2)) = run(nil,cons2(X1,nil2)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_74) ).
cnf(i_0_37,plain,
cons(X1,X2) != nil,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-80axqo0h/input.p',i_0_37) ).
cnf(c_0_95,plain,
cons(eval(X1,X2),run(X1,X3)) = run(X1,cons2(print(X2),X3)),
i_0_64 ).
cnf(c_0_96,plain,
run(X1,nil2) = nil,
i_0_63 ).
cnf(c_0_97,plain,
cons2(apply1(X1,X2),map(X1,X3)) = map(X1,cons2(X2,X3)),
i_0_70 ).
cnf(c_0_98,plain,
map(X1,nil2) = nil2,
i_0_69 ).
cnf(c_0_99,plain,
head(cons(X1,X2)) = X1,
i_0_35 ).
cnf(c_0_100,plain,
cons(eval(X1,X2),nil) = run(X1,cons2(print(X2),nil2)),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,plain,
head2(cons2(X1,X2)) = X1,
i_0_38 ).
cnf(c_0_102,plain,
cons2(apply1(X1,X2),nil2) = map(X1,cons2(X2,nil2)),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_103,plain,
( run(X1,cons2(if(X2,X3,X4),X5)) = run(X1,append(X3,X5))
| eval(X1,X2) != suc(X6) ),
i_0_68 ).
cnf(c_0_104,plain,
eval(X1,X2) = head(run(X1,cons2(print(X2),nil2))),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_105,plain,
addNat(eval(X1,X2),eval(X1,X3)) = eval(X1,add(X2,X3)),
i_0_58 ).
cnf(c_0_106,plain,
eval(X1,n(X2)) = X2,
i_0_57 ).
cnf(c_0_107,plain,
( eval(X1,eq(X2,X3)) = suc(zero)
| eval(X1,X2) != eval(X1,X3) ),
i_0_60 ).
cnf(c_0_108,plain,
cons2(X1,append(X2,X3)) = append(cons2(X1,X2),X3),
i_0_72 ).
cnf(c_0_109,plain,
append(nil2,X1) = X1,
i_0_71 ).
cnf(c_0_110,plain,
apply1(X1,X2) = head2(map(X1,cons2(X2,nil2))),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_111,plain,
( run(X1,cons2(if(X2,X3,X4),X5)) = run(X1,append(X4,X5))
| eval(X1,X2) != zero ),
i_0_67 ).
cnf(c_0_112,plain,
( run(X1,cons2(if(X2,X3,X4),X5)) = run(X1,append(X3,X5))
| head(run(X1,cons2(print(X2),nil2))) != suc(X6) ),
inference(rw,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_113,plain,
head(run(X1,cons2(print(add(X2,X3)),nil2))) = addNat(head(run(X1,cons2(print(X2),nil2))),head(run(X1,cons2(print(X3),nil2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_104]),c_0_104]),c_0_104]) ).
cnf(c_0_114,plain,
cons(head(run(X1,cons2(print(X2),nil2))),nil) = run(X1,cons2(print(X2),nil2)),
inference(rw,[status(thm)],[c_0_100,c_0_104]) ).
cnf(c_0_115,plain,
head(run(X1,cons2(print(n(X2)),nil2))) = X2,
inference(rw,[status(thm)],[c_0_106,c_0_104]) ).
cnf(c_0_116,plain,
eval(X1,eq(X2,X2)) = suc(zero),
inference(er,[status(thm)],[c_0_107]) ).
cnf(c_0_117,plain,
cons2(X1,X2) = append(cons2(X1,nil2),X2),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_118,plain,
cons2(head2(map(X1,cons2(X2,nil2))),nil2) = map(X1,cons2(X2,nil2)),
inference(rw,[status(thm)],[c_0_102,c_0_110]) ).
cnf(c_0_119,plain,
( run(X1,cons2(if(X2,X3,X4),X5)) = run(X1,append(X4,X5))
| head(run(X1,cons2(print(X2),nil2))) != zero ),
inference(rw,[status(thm)],[c_0_111,c_0_104]) ).
cnf(c_0_120,plain,
( run(X1,cons2(if(add(X2,X3),X4,X5),X6)) = run(X1,append(X4,X6))
| addNat(head(run(X1,cons2(print(X2),nil2))),head(run(X1,cons2(print(X3),nil2)))) != suc(X7) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_121,plain,
run(X1,cons2(print(n(X2)),nil2)) = cons(X2,nil),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_122,plain,
head(run(X1,cons2(print(eq(X2,X2)),nil2))) = suc(zero),
inference(rw,[status(thm)],[c_0_116,c_0_104]) ).
cnf(c_0_123,plain,
cons2(head2(map(X1,cons2(X2,nil2))),X3) = append(map(X1,cons2(X2,nil2)),X3),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_124,plain,
( run(X1,cons2(if(add(X2,X3),X4,X5),X6)) = run(X1,append(X5,X6))
| addNat(head(run(X1,cons2(print(X2),nil2))),head(run(X1,cons2(print(X3),nil2)))) != zero ),
inference(spm,[status(thm)],[c_0_119,c_0_113]) ).
cnf(c_0_125,plain,
( run(X1,cons2(if(add(n(X2),X3),X4,X5),X6)) = run(X1,append(X4,X6))
| addNat(X2,head(run(X1,cons2(print(X3),nil2)))) != suc(X7) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_99]) ).
cnf(c_0_126,plain,
run(X1,cons2(print(eq(X2,X2)),nil2)) = cons(suc(zero),nil),
inference(spm,[status(thm)],[c_0_114,c_0_122]) ).
cnf(c_0_127,plain,
head2(append(map(X1,cons2(X2,nil2)),X3)) = head2(map(X1,cons2(X2,nil2))),
inference(spm,[status(thm)],[c_0_101,c_0_123]) ).
cnf(c_0_128,plain,
append(map(X1,cons2(X2,nil2)),map(X1,X3)) = map(X1,cons2(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_110]),c_0_123]) ).
cnf(c_0_129,plain,
( run(X1,cons2(if(add(X2,n(X3)),X4,X5),X6)) = run(X1,append(X5,X6))
| addNat(head(run(X1,cons2(print(X2),nil2))),X3) != zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_121]),c_0_99]) ).
cnf(c_0_130,plain,
( run(X1,cons2(if(add(n(X2),eq(X3,X3)),X4,X5),X6)) = run(X1,append(X4,X6))
| addNat(X2,suc(zero)) != suc(X7) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_99]) ).
cnf(c_0_131,plain,
suc(addNat(X1,suc(X2))) = addNat(suc(X1),suc(X2)),
i_0_53 ).
cnf(c_0_132,plain,
if(add(n(suc(zero)),X1),X2,X3) = apply1(lam,if(X1,X3,X2)),
i_0_47 ).
cnf(c_0_133,plain,
head2(map(X1,cons2(X2,X3))) = head2(map(X1,cons2(X2,nil2))),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_134,plain,
( run(X1,cons2(if(add(n(X2),n(X3)),X4,X5),X6)) = run(X1,append(X5,X6))
| addNat(X2,X3) != zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_121]),c_0_99]) ).
cnf(c_0_135,plain,
addNat(zero,X1) = X1,
i_0_51 ).
cnf(c_0_136,plain,
( run(X1,cons2(if(add(n(suc(X2)),eq(X3,X3)),X4,X5),X6)) = run(X1,append(X4,X6))
| suc(addNat(X2,suc(zero))) != suc(X7) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_137,plain,
if(add(n(suc(zero)),X1),X2,X3) = head2(map(lam,cons2(if(X1,X3,X2),nil2))),
inference(rw,[status(thm)],[c_0_132,c_0_110]) ).
cnf(c_0_138,plain,
cons2(head2(map(X1,cons2(X2,X3))),X4) = append(map(X1,cons2(X2,nil2)),X4),
inference(spm,[status(thm)],[c_0_123,c_0_133]) ).
cnf(c_0_139,plain,
eval(nil,v(X1)) = zero,
i_0_48 ).
cnf(c_0_140,plain,
( run(X1,cons2(if(add(n(zero),n(X2)),X3,X4),X5)) = run(X1,append(X4,X5))
| X2 != zero ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_141,plain,
( run(X1,append(map(lam,cons2(if(eq(X2,X2),X3,X4),nil2)),X5)) = run(X1,append(X4,X5))
| suc(suc(zero)) != suc(X6) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_135]),c_0_137]),c_0_138]) ).
cnf(c_0_142,plain,
( eval(nil,eq(v(X1),X2)) = suc(zero)
| eval(nil,X2) != zero ),
inference(spm,[status(thm)],[c_0_107,c_0_139]) ).
cnf(c_0_143,plain,
run(X1,cons2(if(X2,append(X3,cons2(while(X2,X3),nil2)),nil2),X4)) = run(X1,cons2(while(X2,X3),X4)),
i_0_66 ).
cnf(c_0_144,plain,
run(X1,cons2(if(add(n(zero),n(zero)),X2,X3),X4)) = run(X1,append(X3,X4)),
inference(er,[status(thm)],[c_0_140]) ).
cnf(c_0_145,negated_conjecture,
run(nil,cons2(apply1(lam,X1),nil2)) = run(nil,cons2(X1,nil2)),
i_0_74 ).
cnf(c_0_146,plain,
run(X1,append(map(lam,cons2(if(eq(X2,X2),X3,X4),nil2)),X5)) = run(X1,append(X4,X5)),
inference(er,[status(thm)],[c_0_141]) ).
cnf(c_0_147,plain,
append(map(X1,cons2(X2,nil2)),nil2) = map(X1,cons2(X2,nil2)),
inference(rw,[status(thm)],[c_0_118,c_0_123]) ).
cnf(c_0_148,plain,
( run(X1,cons2(if(eq(X2,X2),X3,X4),X5)) = run(X1,append(X3,X5))
| suc(zero) != suc(X6) ),
inference(spm,[status(thm)],[c_0_112,c_0_122]) ).
cnf(c_0_149,plain,
( head(run(nil,cons2(print(eq(v(X1),X2)),nil2))) = suc(zero)
| head(run(nil,cons2(print(X2),nil2))) != zero ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_104]),c_0_104]) ).
cnf(c_0_150,plain,
run(X1,cons2(while(add(n(zero),n(zero)),X2),X3)) = run(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_109]) ).
cnf(c_0_151,negated_conjecture,
run(nil,map(lam,cons2(X1,nil2))) = run(nil,cons2(X1,nil2)),
inference(rw,[status(thm)],[c_0_145,c_0_102]) ).
cnf(c_0_152,plain,
run(X1,map(lam,cons2(if(eq(X2,X2),X3,X4),nil2))) = run(X1,append(X4,nil2)),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_153,plain,
run(X1,cons2(if(eq(X2,X2),X3,X4),X5)) = run(X1,append(X3,X5)),
inference(er,[status(thm)],[c_0_148]) ).
cnf(c_0_154,plain,
( head(run(nil,cons2(print(eq(v(X1),n(X2))),nil2))) = suc(zero)
| X2 != zero ),
inference(spm,[status(thm)],[c_0_149,c_0_115]) ).
cnf(c_0_155,plain,
run(X1,append(cons2(while(add(n(zero),n(zero)),X2),nil2),X3)) = run(X1,X3),
inference(spm,[status(thm)],[c_0_150,c_0_117]) ).
cnf(c_0_156,negated_conjecture,
run(nil,append(X1,nil2)) = run(nil,append(X2,nil2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]) ).
cnf(c_0_157,plain,
head(run(nil,cons2(print(eq(v(X1),n(zero))),nil2))) = suc(zero),
inference(er,[status(thm)],[c_0_154]) ).
cnf(c_0_158,plain,
run(nil,append(X1,nil2)) = nil,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_96]) ).
cnf(c_0_159,plain,
run(nil,cons2(print(eq(v(X1),n(zero))),nil2)) = cons(suc(zero),nil),
inference(spm,[status(thm)],[c_0_114,c_0_157]) ).
cnf(c_0_160,plain,
run(nil,cons2(X1,nil2)) = nil,
inference(spm,[status(thm)],[c_0_158,c_0_117]) ).
cnf(c_0_161,plain,
cons(X1,X2) != nil,
i_0_37 ).
cnf(c_0_162,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160]),c_0_161]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX197+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.16/0.33 % Computer : n021.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 11:03:42 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.30/0.46 # ENIGMATIC: Selected complete mode:
% 217.46/29.26 # ENIGMATIC: Solved by paramils045:
% 217.46/29.26 # Preprocessing time : 0.015 s
% 217.46/29.26
% 217.46/29.26 # Proof found!
% 217.46/29.26 # SZS status Theorem
% 217.46/29.26 # SZS output start CNFRefutation
% See solution above
% 217.46/29.26 # Training examples: 0 positive, 0 negative
% 217.46/29.26
% 217.46/29.26 # -------------------------------------------------
% 217.46/29.26 # User time : 0.074 s
% 217.46/29.26 # System time : 0.003 s
% 217.46/29.26 # Total time : 0.077 s
% 217.46/29.26 # ...preprocessing : 0.015 s
% 217.46/29.26 # ...main loop : 0.062 s
% 217.46/29.26 # Maximum resident set size: 7144 pages
% 217.46/29.26
%------------------------------------------------------------------------------