%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW390+1 : TPTP v9.2.1. Released v5.2.0.
% 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 : n024.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 05:32:15 PM UTC 2026
% Result : Theorem 16.81s 10.71s
% Output : CNFRefutation 16.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 26 unt; 0 def)
% Number of atoms : 52 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 7 |; 1 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 80 ( 21 sgn 35 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_bot__apply,axiom,
! [X22,X17,X5] :
( class_Orderings_Obot(X5)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17,X5)),X22) = c_Orderings_Obot__class_Obot(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(fact_empty__def,axiom,
! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X23,X5] : hAPP(c_Set_OCollect(X5),X23) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_singleton__conv2,axiom,
! [X6,X5] : hAPP(c_Set_OCollect(X5),hAPP(c_fequal,X6)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv2) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(fact_inf__bot__left,axiom,
! [X42,X43] :
( class_Lattices_Obounded__lattice__bot(X43)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X43),c_Orderings_Obot__class_Obot(X43)),X42) = c_Orderings_Obot__class_Obot(X43) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__left) ).
fof(conj_0,conjecture,
( ? [X28,X145] : v_P(X28,X145)
=> ? [X308,X309] : c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X308),v_c),X309)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_falseE,axiom,
! [X26,X20,X4,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X5),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),X20),X26)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_falseE) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(c_0_10,plain,
! [X17019,X17020,X17021] :
( ~ class_Orderings_Obot(X17021)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17020,X17021)),X17019) = c_Orderings_Obot__class_Obot(X17021) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).
fof(c_0_11,plain,
! [X27644] : c_Orderings_Obot__class_Obot(tc_fun(X27644,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X27644),hAPP(c_COMBK(tc_HOL_Obool,X27644),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_12,plain,
! [X27642,X27643] : hAPP(c_Set_OCollect(X27643),X27642) = X27642,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_13,plain,
! [X27696,X27697] : hAPP(c_Set_OCollect(X27697),hAPP(c_fequal,X27696)) = hAPP(hAPP(c_Set_Oinsert(X27697),X27696),c_Orderings_Obot__class_Obot(tc_fun(X27697,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).
fof(c_0_14,plain,
! [X16967,X16968] :
( hAPP(X16968,esk1_2(X16967,X16968)) != hAPP(X16967,esk1_2(X16967,X16968))
| X16968 = X16967 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
cnf(c_0_15,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
fof(c_0_17,plain,
! [X18219,X18220] :
( ~ class_Lattices_Obounded__lattice__bot(X18220)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18220),c_Orderings_Obot__class_Obot(X18220)),X18219) = c_Orderings_Obot__class_Obot(X18220) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])]) ).
fof(c_0_18,negated_conjecture,
~ ( ? [X28,X145] : v_P(X28,X145)
=> ? [X308,X309] : c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X308),v_c),X309)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_19,plain,
! [X24080,X24081,X24082,X24083] : c_Hoare__Mirabelle_Ohoare__derivs(X24083,X24082,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X24083)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X24083),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X24083),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),X24081),X24080)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X24083),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_falseE]) ).
cnf(c_0_20,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,plain,
hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_Orderings_Obot__class_Obot(tc_HOL_Obool),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_25,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]) ).
fof(c_0_27,negated_conjecture,
! [X34308,X34309] :
( v_P(esk576_0,esk577_0)
& ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X34308),v_c),X34309)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
cnf(c_0_28,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_30,plain,
hAPP(c_fequal,X1) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(rw,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_31,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(X1,esk1_2(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X1)) != c_Orderings_Obot__class_Obot(tc_HOL_Obool) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X1) = c_Orderings_Obot__class_Obot(tc_HOL_Obool),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),v_c),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),X3),X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_35,plain,
hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),v_c),X2))),
inference(rw,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_37,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)))),X3),X4))),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_36,c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWW390+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.06 % 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
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue May 5 01:44:56 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.26 % start to proof: theBenchmark
% 16.81/10.71 % Version : CSE_E---1.7
% 16.81/10.71 % Problem : theBenchmark.p
% 16.81/10.71 % SZS status Theorem for theBenchmark.p
% 16.81/10.71 % SZS output start CNFRefutation
% See solution above
% 16.81/10.74 % Total time : 9.270s
%------------------------------------------------------------------------------