%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX222+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 : n008.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 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 53 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 26 ~; 18 |; 5 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 2 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_036,conjecture,
? [X7] :
( nf(X7)
& tc(nil,X7,arr(a,arr(b,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_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_029,axiom,
! [X6,X8] : index(cons(X6,X8),zero) = just(X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
fof(axiom_026,axiom,
! [X7] :
( nf(lam(X7))
<=> nf(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(axiom_027,axiom,
! [X4] : nf(var(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(c_0_6,negated_conjecture,
~ ? [X7] :
( nf(X7)
& tc(nil,X7,arr(a,arr(b,b))) ),
inference(assume_negation,[status(cth)],[goal_036]) ).
fof(c_0_7,negated_conjecture,
! [X164] :
( ~ nf(X164)
| ~ tc(nil,X164,arr(a,arr(b,b))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
fof(c_0_8,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_9,negated_conjecture,
( ~ nf(X1)
| ~ tc(nil,X1,arr(a,arr(b,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]) ).
fof(c_0_11,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_12,negated_conjecture,
( ~ tc(cons(a,nil),X1,arr(b,b))
| ~ nf(lam(X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( tc(X3,var(X4),X2)
| X1 != X2
| index(X3,X4) != just(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
( ~ tc(cons(b,cons(a,nil)),X1,b)
| ~ nf(lam(lam(X1))) ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_15,plain,
( tc(X1,var(X2),X3)
| index(X1,X2) != just(X3) ),
inference(er,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X140,X141] : index(cons(X140,X141),zero) = just(X140),
inference(variable_rename,[status(thm)],[axiom_029]) ).
cnf(c_0_17,negated_conjecture,
( index(cons(b,cons(a,nil)),X1) != just(b)
| ~ nf(lam(lam(var(X1)))) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
index(cons(X1,X2),zero) = just(X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X137] :
( ( ~ nf(lam(X137))
| nf(X137) )
& ( ~ nf(X137)
| nf(lam(X137)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_026])]) ).
cnf(c_0_20,negated_conjecture,
~ nf(lam(lam(var(zero)))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( nf(lam(X1))
| ~ nf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X138] : nf(var(X138)),
inference(variable_rename,[status(thm)],[axiom_027]) ).
cnf(c_0_23,negated_conjecture,
~ nf(lam(var(zero))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
nf(var(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX222+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
% 0.16/0.32 % Computer : n008.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 07:58:58 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------