%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX223+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 : n006.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 05:34:46 PM UTC 2026
% Result : Theorem 2.09s 1.96s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 18 unt; 0 def)
% Number of atoms : 132 ( 48 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 160 ( 80 ~; 62 |; 11 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 152 ( 27 sgn 59 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_036,conjecture,
? [X7] :
( nf(X7)
& tc(nil,X7,arr(arr(a,arr(a,b)),arr(a,b))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_036) ).
fof(axiom_033,axiom,
! [X1,X7,X12,X13] :
( tc(X1,lam(X7),arr(X12,X13))
<=> tc(cons(X12,X1),X7,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
fof(axiom_031,axiom,
! [X1,X6,X10,X2,X11] :
( tc(X1,app(X10,X2,X11),X6)
<=> ( tc(X1,X10,arr(X11,X6))
& tc(X1,X2,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
fof(axiom_035,axiom,
! [X1,X6,X3,X14] :
( index(X1,X3) = just(X14)
=> ( tc(X1,var(X3),X6)
<=> X14 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_035) ).
fof(axiom_026,axiom,
! [X7] :
( nf(lam(X7))
<=> nf(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(axiom_024,axiom,
! [X5,X6,X2] :
( X5 != lam(proj1Lam(X5))
=> ( nf(app(X5,X6,X2))
<=> ( nf(X5)
& nf(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(axiom_027,axiom,
! [X4] : nf(var(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(axiom_023,axiom,
! [X1,X2] : lam(X1) != var(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
fof(axiom_021,axiom,
! [X1,X2,X3,X4] : app(X1,X2,X3) != lam(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
fof(axiom_029,axiom,
! [X6,X8] : index(cons(X6,X8),zero) = just(X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
fof(axiom_030,axiom,
! [X6,X8,X9] : index(cons(X6,X8),suc(X9)) = index(X8,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
fof(c_0_11,negated_conjecture,
~ ? [X7] :
( nf(X7)
& tc(nil,X7,arr(arr(a,arr(a,b)),arr(a,b))) ),
inference(assume_negation,[status(cth)],[goal_036]) ).
fof(c_0_12,negated_conjecture,
! [X164] :
( ~ nf(X164)
| ~ tc(nil,X164,arr(arr(a,arr(a,b)),arr(a,b))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_13,plain,
! [X153,X154,X155,X156] :
( ( ~ tc(X153,lam(X154),arr(X155,X156))
| tc(cons(X155,X153),X154,X156) )
& ( ~ tc(cons(X155,X153),X154,X156)
| tc(X153,lam(X154),arr(X155,X156)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_033])]) ).
cnf(c_0_14,negated_conjecture,
( ~ nf(X1)
| ~ tc(nil,X1,arr(arr(a,arr(a,b)),arr(a,b))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
( tc(X2,lam(X3),arr(X1,X4))
| ~ tc(cons(X1,X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
( ~ tc(cons(arr(a,arr(a,b)),nil),X1,arr(a,b))
| ~ nf(lam(X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_17,plain,
! [X145,X146,X147,X148,X149] :
( ( tc(X145,X147,arr(X149,X146))
| ~ tc(X145,app(X147,X148,X149),X146) )
& ( tc(X145,X148,X149)
| ~ tc(X145,app(X147,X148,X149),X146) )
& ( ~ tc(X145,X147,arr(X149,X146))
| ~ tc(X145,X148,X149)
| tc(X145,app(X147,X148,X149),X146) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_031])])]) ).
cnf(c_0_18,negated_conjecture,
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,b)
| ~ nf(lam(lam(X1))) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_19,plain,
( tc(X1,app(X2,X5,X3),X4)
| ~ tc(X1,X2,arr(X3,X4))
| ~ tc(X1,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X160,X161,X162,X163] :
( ( ~ tc(X160,var(X162),X161)
| X163 = X161
| index(X160,X162) != just(X163) )
& ( X163 != X161
| tc(X160,var(X162),X161)
| index(X160,X162) != just(X163) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_035])])]) ).
cnf(c_0_21,negated_conjecture,
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,arr(X2,b))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X3,X2)
| ~ nf(lam(lam(app(X1,X3,X2)))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( tc(X3,var(X4),X2)
| X1 != X2
| index(X3,X4) != just(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,arr(X2,arr(X3,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X4,X3)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X5,X2)
| ~ nf(lam(lam(app(app(X1,X5,X2),X4,X3)))) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_24,plain,
( tc(X1,var(X2),X3)
| index(X1,X2) != just(X3) ),
inference(er,[status(thm)],[c_0_22]) ).
fof(c_0_25,plain,
! [X137] :
( ( ~ nf(lam(X137))
| nf(X137) )
& ( ~ nf(X137)
| nf(lam(X137)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_026])]) ).
fof(c_0_26,plain,
! [X131,X132,X133] :
( ( nf(X131)
| ~ nf(app(X131,X132,X133))
| X131 = lam(proj1Lam(X131)) )
& ( nf(X132)
| ~ nf(app(X131,X132,X133))
| X131 = lam(proj1Lam(X131)) )
& ( ~ nf(X131)
| ~ nf(X132)
| nf(app(X131,X132,X133))
| X131 = lam(proj1Lam(X131)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_024])])]) ).
fof(c_0_27,plain,
! [X138] : nf(var(X138)),
inference(variable_rename,[status(thm)],[axiom_027]) ).
cnf(c_0_28,negated_conjecture,
( index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X4,X3)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X5,X2)
| ~ nf(lam(lam(app(app(var(X1),X5,X2),X4,X3)))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( nf(lam(X1))
| ~ nf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( nf(app(X1,X2,X3))
| X1 = lam(proj1Lam(X1))
| ~ nf(X1)
| ~ nf(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
nf(var(X1)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_32,plain,
! [X129,X130] : lam(X129) != var(X130),
inference(variable_rename,[status(thm)],[axiom_023]) ).
cnf(c_0_33,negated_conjecture,
( index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X4,X3)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X5,X2)
| ~ nf(lam(app(app(var(X1),X5,X2),X4,X3))) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( lam(proj1Lam(X1)) = X1
| nf(app(X1,var(X2),X3))
| ~ nf(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
lam(X1) != var(X2),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_36,plain,
! [X121,X122,X123,X124] : app(X121,X122,X123) != lam(X124),
inference(variable_rename,[status(thm)],[axiom_021]) ).
cnf(c_0_37,negated_conjecture,
( index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b)))
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X4) != just(X3)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X5,X2)
| ~ nf(lam(app(app(var(X1),X5,X2),var(X4),X3))) ),
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_38,plain,
nf(app(var(X1),var(X2),X3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_31]),c_0_35]) ).
cnf(c_0_39,plain,
app(X1,X2,X3) != lam(X4),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b)))
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X4) != just(X3)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X5,X2)
| ~ nf(app(app(var(X1),X5,X2),var(X4),X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_41,plain,
nf(app(app(var(X1),var(X2),X3),var(X4),X5)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_38]),c_0_39]) ).
fof(c_0_42,plain,
! [X140,X141] : index(cons(X140,X141),zero) = just(X140),
inference(variable_rename,[status(thm)],[axiom_029]) ).
cnf(c_0_43,negated_conjecture,
( index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b)))
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X4) != just(X3)
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X5) != just(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_24]),c_0_41])]) ).
cnf(c_0_44,plain,
index(cons(X1,X2),zero) = just(X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b)))
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X4) != just(X2)
| just(a) != just(X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_46,plain,
! [X142,X143,X144] : index(cons(X142,X143),suc(X144)) = index(X143,X144),
inference(variable_rename,[status(thm)],[axiom_030]) ).
cnf(c_0_47,negated_conjecture,
( index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b)))
| just(a) != just(X2)
| just(a) != just(X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_48,plain,
index(cons(X1,X2),suc(X3)) = index(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( index(cons(arr(a,arr(a,b)),nil),X1) != just(arr(X2,arr(X3,b)))
| just(a) != just(X2)
| just(a) != just(X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,negated_conjecture,
( just(arr(a,arr(a,b))) != just(arr(X1,arr(X2,b)))
| just(a) != just(X1)
| just(a) != just(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX223+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
% 0.16/0.34 % Computer : n006.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 07:59:16 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.19/0.35 % start to proof: theBenchmark
% 2.09/1.96 % Version : CSE_E---1.7
% 2.09/1.96 % Problem : theBenchmark.p
% 2.09/1.96 % SZS status Theorem for theBenchmark.p
% 2.09/1.96 % SZS output start CNFRefutation
% See solution above
% 2.09/1.96 % Total time : 1.371s
%------------------------------------------------------------------------------