%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX224+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 4.03s 2.76s
% Output : CNFRefutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 74 ( 33 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 89 ( 47 ~; 33 |; 5 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 98 ( 23 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_032,conjecture,
? [X11] : tc(nil,X11,arr(arr(a,arr(a,b)),arr(a,b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_032) ).
fof(axiom_029,axiom,
! [X1,X11,X12,X13] :
( tc(X1,lam(X11),arr(X12,X13))
<=> tc(cons(X12,X1),X11,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
fof(axiom_027,axiom,
! [X1,X6,X9,X2,X10] :
( tc(X1,app(X9,X2,X10),X6)
<=> ( tc(X1,X9,arr(X10,X6))
& tc(X1,X2,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
fof(axiom_031,axiom,
! [X1,X6,X3,X14] :
( index(X1,X3) = just(X14)
=> ( tc(X1,var(X3),X6)
<=> X14 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
fof(axiom_025,axiom,
! [X6,X7] : index(cons(X6,X7),zero) = just(X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
fof(axiom_026,axiom,
! [X6,X7,X8] : index(cons(X6,X7),suc(X8)) = index(X7,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
fof(c_0_6,negated_conjecture,
~ ? [X11] : tc(nil,X11,arr(arr(a,arr(a,b)),arr(a,b))),
inference(assume_negation,[status(cth)],[goal_032]) ).
fof(c_0_7,negated_conjecture,
! [X148] : ~ tc(nil,X148,arr(arr(a,arr(a,b)),arr(a,b))),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
fof(c_0_8,plain,
! [X137,X138,X139,X140] :
( ( ~ tc(X137,lam(X138),arr(X139,X140))
| tc(cons(X139,X137),X138,X140) )
& ( ~ tc(cons(X139,X137),X138,X140)
| tc(X137,lam(X138),arr(X139,X140)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_029])]) ).
cnf(c_0_9,negated_conjecture,
~ tc(nil,X1,arr(arr(a,arr(a,b)),arr(a,b))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( tc(X2,lam(X3),arr(X1,X4))
| ~ tc(cons(X1,X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
~ tc(cons(arr(a,arr(a,b)),nil),X1,arr(a,b)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_12,plain,
! [X129,X130,X131,X132,X133] :
( ( tc(X129,X131,arr(X133,X130))
| ~ tc(X129,app(X131,X132,X133),X130) )
& ( tc(X129,X132,X133)
| ~ tc(X129,app(X131,X132,X133),X130) )
& ( ~ tc(X129,X131,arr(X133,X130))
| ~ tc(X129,X132,X133)
| tc(X129,app(X131,X132,X133),X130) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_027])])]) ).
cnf(c_0_13,negated_conjecture,
~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,b),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_14,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_12]) ).
fof(c_0_15,plain,
! [X144,X145,X146,X147] :
( ( ~ tc(X144,var(X146),X145)
| X147 = X145
| index(X144,X146) != just(X147) )
& ( X147 != X145
| tc(X144,var(X146),X145)
| index(X144,X146) != just(X147) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_031])])]) ).
cnf(c_0_16,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) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( tc(X3,var(X4),X2)
| X1 != X2
| index(X3,X4) != just(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,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) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_19,plain,
( tc(X1,var(X2),X3)
| index(X1,X2) != just(X3) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_20,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) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,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) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
fof(c_0_22,plain,
! [X124,X125] : index(cons(X124,X125),zero) = just(X124),
inference(variable_rename,[status(thm)],[axiom_025]) ).
cnf(c_0_23,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(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_24,plain,
index(cons(X1,X2),zero) = just(X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,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_23,c_0_24]) ).
fof(c_0_26,plain,
! [X126,X127,X128] : index(cons(X126,X127),suc(X128)) = index(X127,X128),
inference(variable_rename,[status(thm)],[axiom_026]) ).
cnf(c_0_27,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_25,c_0_24]) ).
cnf(c_0_28,plain,
index(cons(X1,X2),suc(X3)) = index(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,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_27,c_0_28]) ).
cnf(c_0_30,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_29,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWX224+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 07:59:01 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 4.03/2.76 % Version : CSE_E---1.7
% 4.03/2.76 % Problem : theBenchmark.p
% 4.03/2.76 % SZS status Theorem for theBenchmark.p
% 4.03/2.76 % SZS output start CNFRefutation
% See solution above
% 4.03/2.76 % Total time : 2.361s
%------------------------------------------------------------------------------