%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW470+1 : TPTP v9.2.1. Released v5.3.0.
% 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 : 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 05:32:27 PM UTC 2026
% Result : Theorem 33.29s 20.27s
% Output : CNFRefutation 33.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 32 unt; 0 def)
% Number of atoms : 96 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 28 ~; 28 |; 3 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 41 ( 41 usr; 16 con; 0-4 aty)
% Number of variables : 78 ( 17 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_17_Collect__empty__eq,axiom,
! [X13] :
( collec1266446174iple_a(X13) = bot_bo1687970473a_bool
<=> ! [X27] : ~ hBOOL(hAPP_H1927961489a_bool(X13,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Collect__empty__eq) ).
fof(help_fFalse_1_1_T,axiom,
! [X57] :
( is_bool(X57)
=> ( X57 = fTrue
| X57 = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_Mtc,hypothesis,
! [X1,X2] : is_bool(hAPP_f1753944735l_bool(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_Mtc) ).
fof(fact_74_Collect__def,axiom,
! [X13] : collec1266446174iple_a(X13) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Collect__def) ).
fof(fact_71_finite_OemptyI,axiom,
hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,bot_bo1687970473a_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_finite_OemptyI) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(fact_41_bot__apply,axiom,
! [X28] :
( hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X28))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_bot__apply) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom,
is_bool(bot_bot_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool,axiom,
! [X1,X2] : is_bool(hAPP_state_bool(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U,axiom,
! [X57,X58] :
( is_bool(X57)
=> hAPP_state_bool(cOMBK_bool_state(X57),X58) = X57 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
fof(fact_5_escape,axiom,
! [X3,X14,X15,X13] :
( ! [X17,X18] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X13,X17),X18))
=> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(X3),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),X18)),X14,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X15,X17)))),bot_bo1687970473a_bool))) )
=> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(X3),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(X13,X14,X15)),bot_bo1687970473a_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_escape) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U,axiom,
! [X57,X58] : hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X57),X58) = X57,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).
fof(conj_0,conjecture,
hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(c_0_13,plain,
! [X13] :
( collec1266446174iple_a(X13) = bot_bo1687970473a_bool
<=> ! [X27] : ~ hBOOL(hAPP_H1927961489a_bool(X13,X27)) ),
inference(fof_simplification,[status(thm)],[fact_17_Collect__empty__eq]) ).
fof(c_0_14,plain,
! [X779] :
( ~ is_bool(X779)
| X779 = fTrue
| X779 = fFalse ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T])]) ).
fof(c_0_15,hypothesis,
! [X455,X456] : is_bool(hAPP_f1753944735l_bool(X455,X456)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_Mtc]) ).
fof(c_0_16,plain,
! [X520,X521,X522] :
( ( collec1266446174iple_a(X520) != bot_bo1687970473a_bool
| ~ hBOOL(hAPP_H1927961489a_bool(X520,X521)) )
& ( hBOOL(hAPP_H1927961489a_bool(X522,esk10_1(X522)))
| collec1266446174iple_a(X522) = bot_bo1687970473a_bool ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])]) ).
fof(c_0_17,plain,
! [X672] : collec1266446174iple_a(X672) = X672,
inference(variable_rename,[status(thm)],[fact_74_Collect__def]) ).
cnf(c_0_18,plain,
( X1 = fTrue
| X1 = fFalse
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,hypothesis,
is_bool(hAPP_f1753944735l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( collec1266446174iple_a(X1) != bot_bo1687970473a_bool
| ~ hBOOL(hAPP_H1927961489a_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
collec1266446174iple_a(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,bot_bo1687970473a_bool)),
inference(split_conjunct,[status(thm)],[fact_71_finite_OemptyI]) ).
cnf(c_0_23,hypothesis,
( hAPP_f1753944735l_bool(X1,X2) = fTrue
| hAPP_f1753944735l_bool(X1,X2) = fFalse ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
~ hBOOL(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
fof(c_0_25,plain,
! [X579] :
( ( ~ hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X579))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X579)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_bot__apply])]) ).
cnf(c_0_26,plain,
( X1 != bot_bo1687970473a_bool
| ~ hBOOL(hAPP_H1927961489a_bool(X1,X2)) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,hypothesis,
( hAPP_f1753944735l_bool(finite506133020iple_a,bot_bo1687970473a_bool) = fFalse
| hBOOL(fTrue) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
~ hBOOL(fFalse),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
is_bool(bot_bot_bool),
inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool]) ).
cnf(c_0_30,plain,
( hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
~ hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X1)),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_32,hypothesis,
hBOOL(fTrue),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_27]),c_0_28]) ).
cnf(c_0_33,plain,
( fTrue = bot_bot_bool
| fFalse = bot_bot_bool ),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_34,plain,
~ hBOOL(bot_bot_bool),
inference(sr,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,hypothesis,
fFalse = bot_bot_bool,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
fof(c_0_36,plain,
! [X449,X450] : is_bool(hAPP_state_bool(X449,X450)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool]) ).
fof(c_0_37,plain,
! [X790,X791] :
( ~ is_bool(X790)
| hAPP_state_bool(cOMBK_bool_state(X790),X791) = X790 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U])]) ).
cnf(c_0_38,plain,
( X1 = fTrue
| X1 = bot_bot_bool
| ~ is_bool(X1) ),
inference(rw,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_39,plain,
is_bool(hAPP_state_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,hypothesis,
( hAPP_f1753944735l_bool(X1,X2) = bot_bot_bool
| hAPP_f1753944735l_bool(X1,X2) = fTrue ),
inference(rw,[status(thm)],[c_0_23,c_0_35]) ).
fof(c_0_41,plain,
! [X475,X476,X477,X478] :
( ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X478,esk1_4(X475,X476,X477,X478)),esk2_4(X475,X476,X477,X478)))
| hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(X475),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(X478,X476,X477)),bot_bo1687970473a_bool))) )
& ( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(X475),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),esk2_4(X475,X476,X477,X478))),X476,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X477,esk1_4(X475,X476,X477,X478))))),bot_bo1687970473a_bool)))
| hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(X475),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(X478,X476,X477)),bot_bo1687970473a_bool))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_escape])])])]) ).
fof(c_0_42,plain,
! [X792,X793] : hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X792),X793) = X792,
inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U]) ).
cnf(c_0_43,plain,
( hAPP_state_bool(cOMBK_bool_state(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
( hAPP_state_bool(X1,X2) = bot_bot_bool
| hAPP_state_bool(X1,X2) = fTrue ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,hypothesis,
( hAPP_f1753944735l_bool(X1,X2) = bot_bot_bool
| fTrue != bot_bot_bool ),
inference(ef,[status(thm)],[c_0_40]) ).
fof(c_0_46,negated_conjecture,
~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_47,plain,
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,esk1_4(X2,X3,X4,X1)),esk2_4(X2,X3,X4,X1)))
| hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(X2),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(X1,X3,X4)),bot_bo1687970473a_bool))) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X1),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
( hAPP_state_bool(cOMBK_bool_state(X1),X2) = bot_bot_bool
| fTrue = X1
| ~ is_bool(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,hypothesis,
fTrue != bot_bot_bool,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_45]),c_0_34]) ).
cnf(c_0_51,negated_conjecture,
~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool))),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(X1),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(X2),X3,X4)),bot_bo1687970473a_bool)))
| hBOOL(hAPP_state_bool(X2,esk2_4(X1,X3,X4,cOMBK_1458035955bool_a(X2)))) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
hAPP_state_bool(cOMBK_bool_state(bot_bot_bool),X1) = bot_bot_bool,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_29]),c_0_50]) ).
cnf(c_0_54,negated_conjecture,
~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool))),
inference(rw,[status(thm)],[c_0_51,c_0_35]) ).
cnf(c_0_55,plain,
hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(X1),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),X2,X3)),bot_bo1687970473a_bool))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_34]) ).
cnf(c_0_56,hypothesis,
hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool)) = bot_bot_bool,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_32])]) ).
cnf(c_0_57,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWW470+1 : TPTP v9.2.1. Released v5.3.0.
% 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
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 5 01:51:56 EDT 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 33.29/20.27 % Version : CSE_E---1.7
% 33.29/20.27 % Problem : theBenchmark.p
% 33.29/20.27 % SZS status Theorem for theBenchmark.p
% 33.29/20.27 % SZS output start CNFRefutation
% See solution above
% 33.49/20.41 % Total time : 14.376s
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