%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW474+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:14:21 AM UTC 2026
% Result : Theorem 63.91s 9.65s
% Output : CNFRefutation 63.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 40 unt; 0 def)
% Number of atoms : 83 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 28 ~; 22 |; 0 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 11 con; 0-2 aty)
% Number of variables : 48 ( 5 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_0_empty,axiom,
! [G] : hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),bot_bo620288102e_bool)),
file('theBenchmark.p',fact_0_empty) ).
fof(fact_4_cut,axiom,
! [G,G_1,Ts] :
( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G_1),Ts))
=> ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),G_1))
=> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts)) ) ),
file('theBenchmark.p',fact_4_cut) ).
fof(fact_103_MGF,axiom,
! [C_1] :
( hBOOL(hoare_165779456gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(wt(C_1))
=> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,C_1),bot_bo620288102e_bool))) ) ) ),
file('theBenchmark.p',fact_103_MGF) ).
fof(fact_187_insert__compr,axiom,
! [A_2,B] : insert1415133716_state(A_2,B) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),B))),
file('theBenchmark.p',fact_187_insert__compr) ).
fof(fact_255_Collect__def,axiom,
! [P_1] : collec307967673_state(P_1) = P_1,
file('theBenchmark.p',fact_255_Collect__def) ).
fof(fact_280_singleton__conv,axiom,
! [A_2] : collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)) = insert1415133716_state(A_2,bot_bo620288102e_bool),
file('theBenchmark.p',fact_280_singleton__conv) ).
fof(fact_284_singleton__conv2,axiom,
! [A_2] : collec307967673_state(hAPP_H1049623551e_bool(fequal1111551311_state,A_2)) = insert1415133716_state(A_2,bot_bo620288102e_bool),
file('theBenchmark.p',fact_284_singleton__conv2) ).
fof(fact_288_WT__bodiesD,axiom,
! [Pn,B_2] :
( hBOOL(wT_bodies)
=> ( hAPP_p799580910on_com(body,Pn) = some_com(B_2)
=> hBOOL(wt(B_2)) ) ),
file('theBenchmark.p',fact_288_WT__bodiesD) ).
fof(conj_7,conjecture,
hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,y),bot_bo620288102e_bool))),
file('theBenchmark.p',conj_7) ).
fof(conj_7_neg,negated_conjecture,
~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,y),bot_bo620288102e_bool))),
inference(assume_negation,[status(cth)],[conj_7]) ).
cnf(c_602,plain,
hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(A),bot_bo620288102e_bool)),
inference(clausify,[status(thm)],[fact_0_empty]) ).
cnf(c_606,plain,
( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(C),B))
| ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(C),A))
| ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(A),B)) ),
inference(clausify,[status(thm)],[fact_4_cut]) ).
cnf(c_675,plain,
( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,A),bot_bo620288102e_bool)))
| ~ hBOOL(wt(A))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_165779456gleton) ),
inference(clausify,[status(thm)],[fact_103_MGF]) ).
cnf(c_777,plain,
collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),B))) = insert1415133716_state(A,B),
inference(clausify,[status(thm)],[fact_187_insert__compr]) ).
cnf(c_778,plain,
insert1415133716_state(A,B) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),B))),
inference(copy,[status(thm)],[c_777]) ).
cnf(c_889,plain,
collec307967673_state(A) = A,
inference(clausify,[status(thm)],[fact_255_Collect__def]) ).
cnf(c_958,plain,
collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)) = insert1415133716_state(A,bot_bo620288102e_bool),
inference(clausify,[status(thm)],[fact_280_singleton__conv]) ).
cnf(c_3203,plain,
hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A) = insert1415133716_state(A,bot_bo620288102e_bool),
inference(paramod,[status(thm)],[c_889,c_958]) ).
cnf(c_3204,plain,
hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool))),
inference(paramod,[status(thm)],[c_778,c_3203]) ).
cnf(c_3205,plain,
hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A) = cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool)),
inference(paramod,[status(thm)],[c_889,c_3204]) ).
cnf(c_959,plain,
cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool)) = hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A),
inference(copy,[status(thm)],[c_3205]) ).
cnf(c_966,plain,
collec307967673_state(hAPP_H1049623551e_bool(fequal1111551311_state,A)) = insert1415133716_state(A,bot_bo620288102e_bool),
inference(clausify,[status(thm)],[fact_284_singleton__conv2]) ).
cnf(c_3206,plain,
hAPP_H1049623551e_bool(fequal1111551311_state,A) = insert1415133716_state(A,bot_bo620288102e_bool),
inference(paramod,[status(thm)],[c_889,c_966]) ).
cnf(c_3207,plain,
hAPP_H1049623551e_bool(fequal1111551311_state,A) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool))),
inference(paramod,[status(thm)],[c_778,c_3206]) ).
cnf(c_3208,plain,
hAPP_H1049623551e_bool(fequal1111551311_state,A) = collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)),
inference(paramod,[status(thm)],[c_959,c_3207]) ).
cnf(c_3209,plain,
hAPP_H1049623551e_bool(fequal1111551311_state,A) = hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A),
inference(paramod,[status(thm)],[c_889,c_3208]) ).
cnf(c_967,plain,
hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A) = hAPP_H1049623551e_bool(fequal1111551311_state,A),
inference(copy,[status(thm)],[c_3209]) ).
cnf(c_978,plain,
( hBOOL(wt(A))
| some_com(A) != hAPP_p799580910on_com(body,B)
| ~ hBOOL(wT_bodies) ),
inference(clausify,[status(thm)],[fact_288_WT__bodiesD]) ).
fof(conj_0,axiom,
hBOOL(hoare_165779456gleton),
file('theBenchmark.p',conj_0) ).
cnf(c_1056,plain,
hBOOL(hoare_165779456gleton),
inference(clausify,[status(thm)],[conj_0]) ).
fof(conj_1,axiom,
hBOOL(wT_bodies),
file('theBenchmark.p',conj_1) ).
cnf(c_1057,plain,
hBOOL(wT_bodies),
inference(clausify,[status(thm)],[conj_1]) ).
fof(conj_5,axiom,
hAPP_p799580910on_com(body,pn) = some_com(y),
file('theBenchmark.p',conj_5) ).
cnf(c_1061,plain,
hAPP_p799580910on_com(body,pn) = some_com(y),
inference(clausify,[status(thm)],[conj_5]) ).
cnf(c_1062,plain,
some_com(y) = hAPP_p799580910on_com(body,pn),
inference(copy,[status(thm)],[c_1061]) ).
cnf(c_1064,negated_conjecture,
~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,y),bot_bo620288102e_bool))),
inference(clausify,[status(thm)],[conj_7_neg]) ).
cnf(c_3210,negated_conjecture,
~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),hAPP_c1126217667_state(hoare_Mirabelle_MGT,y))),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool))))),
inference(paramod,[status(thm)],[c_778,c_1064]) ).
cnf(c_3211,negated_conjecture,
~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y))),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool))))),
inference(paramod,[status(thm)],[c_967,c_3210]) ).
cnf(c_1065,negated_conjecture,
~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y))),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool)))),
inference(paramod,[status(thm)],[c_889,c_3211]) ).
cnf(c_3212,plain,
( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),hAPP_c1126217667_state(hoare_Mirabelle_MGT,A))),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool)))))
| ~ hBOOL(wt(A))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_165779456gleton) ),
inference(paramod,[status(thm)],[c_778,c_675]) ).
cnf(c_3213,plain,
( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,A))),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool)))))
| ~ hBOOL(wt(A))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_165779456gleton) ),
inference(paramod,[status(thm)],[c_967,c_3212]) ).
cnf(c_3214,plain,
( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,A))),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool))))
| ~ hBOOL(wt(A))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_165779456gleton) ),
inference(paramod,[status(thm)],[c_889,c_3213]) ).
cnf(c_3215,plain,
( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,A))),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool))))
| ~ hBOOL(wt(A))
| ~ hBOOL(wT_bodies) ),
inference(resolve,[status(thm)],[c_1056,c_3214]) ).
cnf(c_1102,plain,
( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,A))),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool))))
| ~ hBOOL(wt(A)) ),
inference(resolve,[status(thm)],[c_1057,c_3215]) ).
cnf(c_3216,plain,
cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(fequal1111551311_state,A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool)) = hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A),
inference(paramod,[status(thm)],[c_967,c_959]) ).
cnf(c_1194,plain,
cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(fequal1111551311_state,A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool)) = hAPP_H1049623551e_bool(fequal1111551311_state,A),
inference(paramod,[status(thm)],[c_967,c_3216]) ).
cnf(c_1221,plain,
( hBOOL(wt(A))
| some_com(A) != hAPP_p799580910on_com(body,B) ),
inference(resolve,[status(thm)],[c_1057,c_978]) ).
cnf(c_1260,plain,
( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,A))))
| ~ hBOOL(wt(A)) ),
inference(paramod,[status(thm)],[c_1194,c_1102]) ).
cnf(c_1261,negated_conjecture,
~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y)))),
inference(paramod,[status(thm)],[c_1194,c_1065]) ).
cnf(c_1301,plain,
hBOOL(wt(y)),
inference(resolve,[status(thm)],[c_1221,c_1062]) ).
cnf(c_2124,plain,
( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(B),A))
| ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),A)) ),
inference(resolve,[status(thm)],[c_606,c_602]) ).
cnf(c_3200,plain,
hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y)))),
inference(resolve,[status(thm)],[c_1260,c_1301]) ).
cnf(c_3201,plain,
hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(A),hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y)))),
inference(resolve,[status(thm)],[c_3200,c_2124]) ).
cnf(c_3202,plain,
$false,
inference(resolve,[status(thm)],[c_3201,c_1261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW474+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 16:04:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 847727 was started by sandbox2 on n018,
% 0.11/0.37 % Sat Sep 26 16:04:37 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.22/0.46
% 0.22/0.46 % From the command line: assign(max_seconds, 300).
% 0.22/0.46
% 0.22/0.46 % SInE: 297 to sos, 130 to usable, of 427 axioms (tolerance 2.00, depth 0 fixpoint).
% 63.91/9.65
% 63.91/9.65 % SZS status Theorem for theBenchmark
% 63.91/9.65
% 63.91/9.65 % Proof 1 at 0.85 (+ 0.11) seconds.
% 63.91/9.65 % Length of proof is 36.
% 63.91/9.65 % Level of proof is 9.
% 63.91/9.65 % Maximum clause weight is 546.000.
% 63.91/9.65 % Given clauses 460.
% 63.91/9.65
% 63.91/9.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------