%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW386+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 : n021.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 12.17s 8.13s
% Output : CNFRefutation 12.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 23 unt; 0 def)
% Number of atoms : 45 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 10 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,
! [X27,X5] : hAPP(c_Set_OCollect(X5),X27) = X27,
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_4,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,v_pn))),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_4) ).
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_option_Osimps_I2_J,axiom,
! [X41,X5] : c_Option_Ooption_ONone(X5) != hAPP(c_Option_Ooption_OSome(X5),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osimps_I2_J) ).
fof(fact_WT_OBody,axiom,
! [X12] :
( hAPP(c_Com_Obody,X12) != c_Option_Ooption_ONone(tc_Com_Ocom)
=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_OBody) ).
fof(conj_3,hypothesis,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(c_0_9,plain,
! [X28302,X28303] : hAPP(c_Set_OCollect(X28303),hAPP(c_fequal,X28302)) = hAPP(hAPP(c_Set_Oinsert(X28303),X28302),c_Orderings_Obot__class_Obot(tc_fun(X28303,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).
fof(c_0_10,plain,
! [X28268,X28269] : hAPP(c_Set_OCollect(X28269),X28268) = X28268,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_11,plain,
! [X16990] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ hBOOL(hAPP(c_Com_OWT,X16990))
| 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,X16990)),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,
~ 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,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_4])]) ).
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,v_pn))),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])]) ).
fof(c_0_21,plain,
! [X17118,X17119] : c_Option_Ooption_ONone(X17119) != hAPP(c_Option_Ooption_OSome(X17119),X17118),
inference(variable_rename,[status(thm)],[fact_option_Osimps_I2_J]) ).
cnf(c_0_22,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,v_pn)))),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,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_24,plain,
! [X17090] :
( hAPP(c_Com_Obody,X17090) = c_Option_Ooption_ONone(tc_Com_Ocom)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17090))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OBody])]) ).
cnf(c_0_25,plain,
c_Option_Ooption_ONone(X1) != hAPP(c_Option_Ooption_OSome(X1),X2),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,hypothesis,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(split_conjunct,[status(thm)],[conj_3]) ).
cnf(c_0_27,negated_conjecture,
~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,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_24]) ).
cnf(c_0_29,hypothesis,
hAPP(c_Com_Obody,v_pn) != 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(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW386+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
% 0.15/0.33 % Computer : n021.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 06:45:10 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 12.17/8.13 % Version : CSE_E---1.7
% 12.17/8.13 % Problem : theBenchmark.p
% 12.17/8.13 % SZS status Theorem for theBenchmark.p
% 12.17/8.13 % SZS output start CNFRefutation
% See solution above
% 12.17/8.14 % Total time : 7.120s
%------------------------------------------------------------------------------