%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SWX221+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n019.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 06:59:51 PM UTC 2026
% Result : Theorem 32.46s 5.59s
% Output : CNFRefutation 32.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of clauses : 44 ( 11 unt; 3 nHn; 35 RR)
% Number of literals : 114 ( 45 equ; 92 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 137 ( 29 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_43,negated_conjecture,
( ~ nf(X1)
| ~ tc(nil,X1,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_43) ).
cnf(i_0_38,plain,
( tc(X1,lam(X2),arr(X3,X4))
| ~ tc(cons(X3,X1),X2,X4) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_38) ).
cnf(i_0_34,plain,
( tc(X1,app(X2,X3,X4),X5)
| ~ tc(X1,X3,X4)
| ~ tc(X1,X2,arr(X4,X5)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_34) ).
cnf(i_0_41,plain,
( tc(X1,var(X2),X3)
| X4 != X3
| index(X1,X2) != just(X4) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_41) ).
cnf(i_0_28,plain,
( nf(lam(X1))
| ~ nf(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_28) ).
cnf(i_0_33,plain,
index(cons(X1,X2),suc(X3)) = index(X2,X3),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_33) ).
cnf(i_0_24,plain,
( lam(proj1Lam(X1)) = X1
| nf(app(X1,X2,X3))
| ~ nf(X2)
| ~ nf(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_24) ).
cnf(i_0_30,plain,
nf(var(X1)),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_30) ).
cnf(i_0_21,plain,
app(X1,X2,X3) != lam(X4),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_21) ).
cnf(i_0_32,plain,
index(cons(X1,X2),zero) = just(X1),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_32) ).
cnf(i_0_23,plain,
var(X1) != lam(X2),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tphdm981/input.p',i_0_23) ).
cnf(c_0_55,negated_conjecture,
( ~ nf(X1)
| ~ tc(nil,X1,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))) ),
i_0_43 ).
cnf(c_0_56,plain,
( tc(X1,lam(X2),arr(X3,X4))
| ~ tc(cons(X3,X1),X2,X4) ),
i_0_38 ).
cnf(c_0_57,negated_conjecture,
( ~ tc(cons(arr(a,arr(b,c)),nil),X1,arr(b,arr(a,c)))
| ~ nf(lam(X1)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_58,plain,
( ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),X1,arr(a,c))
| ~ nf(lam(lam(X1))) ),
inference(spm,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_59,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,c)
| ~ nf(lam(lam(lam(X1)))) ),
inference(spm,[status(thm)],[c_0_58,c_0_56]) ).
cnf(c_0_60,plain,
( tc(X1,app(X2,X3,X4),X5)
| ~ tc(X1,X3,X4)
| ~ tc(X1,X2,arr(X4,X5)) ),
i_0_34 ).
cnf(c_0_61,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,arr(X2,c))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3,X2)
| ~ nf(lam(lam(lam(app(X1,X3,X2))))) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_62,plain,
( tc(X1,var(X2),X3)
| X4 != X3
| index(X1,X2) != just(X4) ),
i_0_41 ).
cnf(c_0_63,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,arr(X2,arr(X3,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,X3)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X5,X2)
| ~ nf(lam(lam(lam(app(app(X1,X5,X2),X4,X3))))) ),
inference(spm,[status(thm)],[c_0_61,c_0_60]) ).
cnf(c_0_64,plain,
( tc(X1,var(X2),X3)
| index(X1,X2) != just(X3) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_65,plain,
( index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1) != just(arr(X2,arr(X3,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,X3)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X5,X2)
| ~ nf(lam(lam(lam(app(app(var(X1),X5,X2),X4,X3))))) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_66,plain,
( nf(lam(X1))
| ~ nf(X1) ),
i_0_28 ).
cnf(c_0_67,plain,
( index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1) != just(arr(X2,arr(X3,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,X3)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X5,X2)
| ~ nf(lam(lam(app(app(var(X1),X5,X2),X4,X3)))) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_68,plain,
index(cons(X1,X2),suc(X3)) = index(X2,X3),
i_0_33 ).
cnf(c_0_69,plain,
( index(cons(b,cons(arr(a,arr(b,c)),nil)),X1) != just(arr(X2,arr(X3,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,X3)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X5,X2)
| ~ nf(lam(lam(app(app(var(suc(X1)),X5,X2),X4,X3)))) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_70,plain,
( index(cons(b,cons(arr(a,arr(b,c)),nil)),X1) != just(arr(X2,arr(X3,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,X3)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X5,X2)
| ~ nf(lam(app(app(var(suc(X1)),X5,X2),X4,X3))) ),
inference(spm,[status(thm)],[c_0_69,c_0_66]) ).
cnf(c_0_71,plain,
( lam(proj1Lam(X1)) = X1
| nf(app(X1,X2,X3))
| ~ nf(X2)
| ~ nf(X1) ),
i_0_24 ).
cnf(c_0_72,plain,
nf(var(X1)),
i_0_30 ).
cnf(c_0_73,plain,
( index(cons(b,cons(arr(a,arr(b,c)),nil)),X1) != just(arr(X2,arr(X3,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,X3)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X5,X2)
| ~ nf(app(app(var(suc(X1)),X5,X2),X4,X3)) ),
inference(spm,[status(thm)],[c_0_70,c_0_66]) ).
cnf(c_0_74,plain,
( lam(proj1Lam(X1)) = X1
| nf(app(X1,var(X2),X3))
| ~ nf(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,plain,
app(X1,X2,X3) != lam(X4),
i_0_21 ).
cnf(c_0_76,plain,
( index(cons(b,cons(arr(a,arr(b,c)),nil)),X1) != just(arr(X2,arr(X3,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),var(X4),X3)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X5,X2)
| ~ nf(app(var(suc(X1)),X5,X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_77,plain,
( index(cons(b,cons(arr(a,arr(b,c)),nil)),X1) != just(arr(X2,arr(X3,c)))
| index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4) != just(X3)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X5,X2)
| ~ nf(app(var(suc(X1)),X5,X2)) ),
inference(spm,[status(thm)],[c_0_76,c_0_64]) ).
cnf(c_0_78,plain,
( index(cons(b,cons(arr(a,arr(b,c)),nil)),X1) != just(arr(X2,arr(X3,c)))
| index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4) != just(X3)
| index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X5) != just(X2)
| ~ nf(app(var(suc(X1)),var(X5),X2)) ),
inference(spm,[status(thm)],[c_0_77,c_0_64]) ).
cnf(c_0_79,plain,
( index(cons(b,cons(arr(a,arr(b,c)),nil)),X1) != just(arr(X2,arr(X3,c)))
| index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4) != just(X2)
| index(cons(b,cons(arr(a,arr(b,c)),nil)),X5) != just(X3)
| ~ nf(app(var(suc(X1)),var(X4),X2)) ),
inference(spm,[status(thm)],[c_0_78,c_0_68]) ).
cnf(c_0_80,plain,
index(cons(X1,X2),zero) = just(X1),
i_0_32 ).
cnf(c_0_81,plain,
( index(cons(b,cons(arr(a,arr(b,c)),nil)),X1) != just(arr(X2,arr(X3,c)))
| index(cons(b,cons(arr(a,arr(b,c)),nil)),X4) != just(X3)
| just(a) != just(X2)
| ~ nf(app(var(suc(X1)),var(zero),X2)) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_82,plain,
( index(cons(b,cons(arr(a,arr(b,c)),nil)),X1) != just(arr(X2,arr(X3,c)))
| just(b) != just(X3)
| just(a) != just(X2)
| ~ nf(app(var(suc(X1)),var(zero),X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_80]) ).
cnf(c_0_83,plain,
var(X1) != lam(X2),
i_0_23 ).
cnf(c_0_84,plain,
( index(cons(b,cons(arr(a,arr(b,c)),nil)),X1) != just(arr(X2,arr(X3,c)))
| just(b) != just(X3)
| just(a) != just(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_74]),c_0_72])]),c_0_83]) ).
cnf(c_0_85,plain,
( index(cons(arr(a,arr(b,c)),nil),X1) != just(arr(X2,arr(X3,c)))
| just(b) != just(X3)
| just(a) != just(X2) ),
inference(spm,[status(thm)],[c_0_84,c_0_68]) ).
cnf(c_0_86,plain,
( just(arr(a,arr(b,c))) != just(arr(X1,arr(X2,c)))
| just(b) != just(X2)
| just(a) != just(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_80]) ).
cnf(c_0_87,plain,
$false,
inference(er,[status(thm)],[c_0_86]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX221+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 12:29:45 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.21/0.44 # ENIGMATIC: Selected complete mode:
% 32.46/5.59 # ENIGMATIC: Solved by Enigma+tptp-cade20-model03-h2e15+lgb-t150-d60-l8000-e0.15+coop-eprover73:
% 32.46/5.59 # ENIGMA: LightGBM model '/export/starexec/sandbox/solver/bin/data/Enigma/tptp-cade20-model03-h2e15/lgb-t150-d60-l8000-e0.15/model.lgb' loaded. (hash_base: 32768; conj_feats: 37; version: 991; iters: 150)
% 32.46/5.59 # Preprocessing time : 1.182 s
% 32.46/5.59 # Presaturation interreduction done
% 32.46/5.59
% 32.46/5.59 # Proof found!
% 32.46/5.59 # SZS status Theorem
% 32.46/5.59 # SZS output start CNFRefutation
% See solution above
% 32.46/5.59 # Training examples: 0 positive, 0 negative
% 32.46/5.59
% 32.46/5.59 # -------------------------------------------------
% 32.46/5.59 # User time : 2.934 s
% 32.46/5.59 # System time : 0.150 s
% 32.46/5.59 # Total time : 3.084 s
% 32.46/5.59 # ...preprocessing : 1.182 s
% 32.46/5.59 # ...main loop : 1.902 s
% 32.46/5.59 # Maximum resident set size: 185584 pages
% 32.46/5.59
%------------------------------------------------------------------------------