%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW298+1 : TPTP v9.2.1. Released v5.2.0.
% 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 : n014.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 05:31:20 PM UTC 2026
% Result : Theorem 11.89s 8.04s
% Output : CNFRefutation 11.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 3 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 5 |; 1 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_triple__valid__Suc,axiom,
! [X4,X5,X6] :
( c_Hoare__Mirabelle_Otriple__valid(X6,hAPP(c_Nat_OSuc,X5),X4)
=> c_Hoare__Mirabelle_Otriple__valid(X6,X5,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple__valid__Suc) ).
fof(conj_0,hypothesis,
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(c_0_3,plain,
! [X16725,X16726,X16727] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X16727,hAPP(c_Nat_OSuc,X16726),X16725)
| c_Hoare__Mirabelle_Otriple__valid(X16727,X16726,X16725) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple__valid__Suc])]) ).
fof(c_0_4,hypothesis,
! [X33861] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X33861),v_ts))
| c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X33861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3) ),
inference(assume_negation,[status(cth)],[conj_1]) ).
cnf(c_0_6,plain,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk556_0),v_ts))
& ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,esk556_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts)) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,negated_conjecture,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk556_0),v_ts)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,esk556_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW298+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n014.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 06:35:22 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 11.89/8.04 % Version : CSE_E---1.7
% 11.89/8.04 % Problem : theBenchmark.p
% 11.89/8.04 % SZS status Theorem for theBenchmark.p
% 11.89/8.04 % SZS output start CNFRefutation
% See solution above
% 11.89/8.06 % Total time : 7.020s
%------------------------------------------------------------------------------