%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW385+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 : n016.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 11.88s 8.01s
% Output : CNFRefutation 11.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 53 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 19 ~; 13 |; 2 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-3 aty)
% Number of variables : 36 ( 1 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_3,conjecture,
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X3),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X3))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
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/sandbox2/benchmark/theBenchmark.p',fact_singleton__conv2) ).
fof(fact_Collect__def,axiom,
! [X20,X5] : hAPP(c_Set_OCollect(X5),X20) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_MGF,axiom,
! [X7] :
( c_Hoare__Mirabelle_Ostate__not__singleton
=> ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,X7))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_MGF) ).
fof(conj_0,hypothesis,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(conj_1,hypothesis,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(fact_WT_OBody,axiom,
! [X37] :
( hAPP(c_Com_Obody,X37) != c_Option_Ooption_ONone(tc_Com_Ocom)
=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X37))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_OBody) ).
fof(fact_domIff,axiom,
! [X94,X16,X6,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Map_Odom(X5,X16,X94)))
<=> hAPP(X94,X6) != c_Option_Ooption_ONone(X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_domIff) ).
fof(c_0_8,negated_conjecture,
~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X3),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X3))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
inference(assume_negation,[status(cth)],[conj_3]) ).
fof(c_0_9,plain,
! [X28187,X28188] : hAPP(c_Set_OCollect(X28188),hAPP(c_fequal,X28187)) = hAPP(hAPP(c_Set_Oinsert(X28188),X28187),c_Orderings_Obot__class_Obot(tc_fun(X28188,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).
fof(c_0_10,plain,
! [X28159,X28160] : hAPP(c_Set_OCollect(X28160),X28159) = X28159,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_11,plain,
! [X16980] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ hBOOL(hAPP(c_Com_OWT,X16980))
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X16980)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_MGF])]) ).
fof(c_0_12,negated_conjecture,
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),esk532_0),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
& ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,esk532_0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_13,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_9]) ).
cnf(c_0_14,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,hypothesis,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(split_conjunct,[status(thm)],[conj_0]) ).
cnf(c_0_17,hypothesis,
c_Com_OWT__bodies,
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_18,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,esk532_0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,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_13,c_0_14]) ).
cnf(c_0_20,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_21,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,esk532_0)))),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X1)))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
fof(c_0_23,plain,
! [X17099] :
( hAPP(c_Com_Obody,X17099) = c_Option_Ooption_ONone(tc_Com_Ocom)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17099))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OBody])]) ).
fof(c_0_24,plain,
! [X17841,X17842,X17843,X17844] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X17844),X17843),c_Map_Odom(X17844,X17842,X17841)))
| hAPP(X17841,X17843) != c_Option_Ooption_ONone(X17842) )
& ( hAPP(X17841,X17843) = c_Option_Ooption_ONone(X17842)
| hBOOL(hAPP(hAPP(c_member(X17844),X17843),c_Map_Odom(X17844,X17842,X17841))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_domIff])]) ).
cnf(c_0_25,negated_conjecture,
~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,esk532_0))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))
| hAPP(X4,X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),esk532_0),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
hAPP(c_Com_Obody,esk532_0) = c_Option_Ooption_ONone(tc_Com_Ocom),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW385+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n016.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 06:45:51 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 11.88/8.01 % Version : CSE_E---1.7
% 11.88/8.01 % Problem : theBenchmark.p
% 11.88/8.01 % SZS status Theorem for theBenchmark.p
% 11.88/8.01 % SZS output start CNFRefutation
% See solution above
% 11.88/8.02 % Total time : 7.017s
%------------------------------------------------------------------------------