TSTP Solution File: SWW473+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWW473+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 : 600s
% DateTime : Thu Jul 21 01:28:36 EDT 2022
% Result : Theorem 13.53s 13.71s
% Output : Refutation 13.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 31
% Syntax : Number of clauses : 73 ( 37 unt; 11 nHn; 73 RR)
% Number of literals : 121 ( 0 equ; 50 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 16 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
is_bool(bot_bot_bool),
file('SWW473+2.p',unknown),
[] ).
cnf(11,axiom,
is_fun_pname_bool(u__dfg),
file('SWW473+2.p',unknown),
[] ).
cnf(12,axiom,
is_pname(pn),
file('SWW473+2.p',unknown),
[] ).
cnf(16,axiom,
is_bool(wt(u)),
file('SWW473+2.p',unknown),
[] ).
cnf(33,axiom,
~ hBOOL(fFalse),
file('SWW473+2.p',unknown),
[] ).
cnf(71,axiom,
equal(collect_fun_nat_bool(u),u),
file('SWW473+2.p',unknown),
[] ).
cnf(121,axiom,
equal(collect_fun_nat_bool(cOMBK_1994329625t_bool(fFalse)),bot_bo1701429464l_bool),
file('SWW473+2.p',unknown),
[] ).
cnf(165,axiom,
hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),u)),
file('SWW473+2.p',unknown),
[] ).
cnf(203,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u__dfg)),
file('SWW473+2.p',unknown),
[] ).
cnf(218,axiom,
( ~ is_fun_pname_bool(u)
| is_fun_a_bool(image_pname_a(v,u)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(230,axiom,
( ~ is_a(u)
| is_fun949378684l_bool(hAPP_a85458249l_bool(v,u)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(232,axiom,
( ~ is_pname(u)
| is_a(hAPP_pname_a(v,u)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(263,axiom,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,u),bot_bot_fun_a_bool)),
file('SWW473+2.p',unknown),
[] ).
cnf(275,axiom,
( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,u)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(285,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,u),insert_a(u,v))),
file('SWW473+2.p',unknown),
[] ).
cnf(307,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u__dfg))),
file('SWW473+2.p',unknown),
[] ).
cnf(331,axiom,
( hBOOL(hAPP_f54304608l_bool(u,skf225(u)))
| equal(collect_fun_nat_bool(u),bot_bo1701429464l_bool) ),
file('SWW473+2.p',unknown),
[] ).
cnf(356,axiom,
( ~ is_bool(u)
| equal(u,fFalse)
| equal(u,fTrue) ),
file('SWW473+2.p',unknown),
[] ).
cnf(363,axiom,
( ~ is_bool(u)
| equal(hAPP_f54304608l_bool(cOMBK_1994329625t_bool(u),v),u) ),
file('SWW473+2.p',unknown),
[] ).
cnf(370,axiom,
( ~ is_a(u)
| ~ is_fun_a_bool(v)
| is_bool(hAPP_a_bool(v,u)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(372,axiom,
( ~ is_fun_a_bool(u)
| ~ is_fun949378684l_bool(v)
| is_bool(hAPP_fun_a_bool_bool(v,u)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(451,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,u),v))
| hBOOL(hAPP_pname_bool(v,u)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(452,axiom,
( ~ hBOOL(hAPP_pname_bool(u,v))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,v),u)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(453,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,u),v))
| hBOOL(hAPP_a_bool(v,u)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(454,axiom,
( ~ hBOOL(hAPP_a_bool(u,v))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,v),u)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(513,axiom,
( ~ hBOOL(u)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,u),bot_bot_bool))
| hBOOL(bot_bot_bool) ),
file('SWW473+2.p',unknown),
[] ).
cnf(527,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,u),u__dfg))
| hBOOL(wt(the_com(body(u)))) ),
file('SWW473+2.p',unknown),
[] ).
cnf(568,axiom,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u__dfg))),
file('SWW473+2.p',unknown),
[] ).
cnf(579,axiom,
equal(insert_a(hAPP_pname_a(u,v),image_pname_a(u,w)),image_pname_a(u,insert_pname(v,w))),
file('SWW473+2.p',unknown),
[] ).
cnf(677,axiom,
( ~ is_fun_pname_bool(u)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,v),u))
| equal(insert_pname(v,u),u) ),
file('SWW473+2.p',unknown),
[] ).
cnf(1119,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,u),v))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,w),v))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(u,w)),v)) ),
file('SWW473+2.p',unknown),
[] ).
cnf(1338,plain,
equal(cOMBK_1994329625t_bool(fFalse),bot_bo1701429464l_bool),
inference(rew,[status(thm),theory(equality)],[71,121]),
[iquote('0:Rew:71.0,121.0')] ).
cnf(1367,plain,
( hBOOL(hAPP_f54304608l_bool(u,skf225(u)))
| equal(u,bot_bo1701429464l_bool) ),
inference(rew,[status(thm),theory(equality)],[71,331]),
[iquote('0:Rew:71.0,331.1')] ).
cnf(1509,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u__dfg)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u__dfg))) ),
inference(res,[status(thm),theory(equality)],[1119,568]),
[iquote('0:Res:1119.2,568.0')] ).
cnf(1535,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u__dfg))),
inference(mrr,[status(thm)],[1509,307]),
[iquote('0:MRR:1509.0,307.0')] ).
cnf(1647,plain,
( equal(wt(u),fFalse)
| equal(wt(u),fTrue) ),
inference(ems,[status(thm)],[356,16]),
[iquote('0:EmS:356.0,16.0')] ).
cnf(1648,plain,
( equal(fFalse,bot_bot_bool)
| equal(fTrue,bot_bot_bool) ),
inference(ems,[status(thm)],[356,3]),
[iquote('0:EmS:356.0,3.0')] ).
cnf(1651,plain,
equal(fFalse,bot_bot_bool),
inference(spt,[spt(split,[position(s1)])],[1648]),
[iquote('1:Spt:1648.0')] ).
cnf(1653,plain,
~ hBOOL(bot_bot_bool),
inference(rew,[status(thm),theory(equality)],[1651,33]),
[iquote('1:Rew:1651.0,33.0')] ).
cnf(1655,plain,
equal(cOMBK_1994329625t_bool(bot_bot_bool),bot_bo1701429464l_bool),
inference(rew,[status(thm),theory(equality)],[1651,1338]),
[iquote('1:Rew:1651.0,1338.0')] ).
cnf(1676,plain,
( ~ hBOOL(u)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,u),bot_bot_bool)) ),
inference(mrr,[status(thm)],[513,1653]),
[iquote('1:MRR:513.2,1653.0')] ).
cnf(1841,plain,
( ~ is_bool(u)
| hBOOL(u)
| equal(cOMBK_1994329625t_bool(u),bot_bo1701429464l_bool) ),
inference(spr,[status(thm),theory(equality)],[363,1367]),
[iquote('0:SpR:363.1,1367.0')] ).
cnf(1844,plain,
( ~ is_bool(bot_bot_bool)
| equal(hAPP_f54304608l_bool(bot_bo1701429464l_bool,u),bot_bot_bool) ),
inference(spr,[status(thm),theory(equality)],[1655,363]),
[iquote('1:SpR:1655.0,363.1')] ).
cnf(1846,plain,
equal(hAPP_f54304608l_bool(bot_bo1701429464l_bool,u),bot_bot_bool),
inference(ssi,[status(thm)],[1844,3]),
[iquote('1:SSi:1844.0,3.0')] ).
cnf(1854,plain,
( ~ is_bool(u)
| ~ is_bool(u)
| hBOOL(u)
| equal(hAPP_f54304608l_bool(bot_bo1701429464l_bool,v),u) ),
inference(spr,[status(thm),theory(equality)],[1841,363]),
[iquote('0:SpR:1841.2,363.1')] ).
cnf(1856,plain,
( ~ is_bool(u)
| hBOOL(u)
| equal(hAPP_f54304608l_bool(bot_bo1701429464l_bool,v),u) ),
inference(obv,[status(thm),theory(equality)],[1854]),
[iquote('0:Obv:1854.0')] ).
cnf(1857,plain,
( ~ is_bool(u)
| hBOOL(u)
| equal(bot_bot_bool,u) ),
inference(rew,[status(thm),theory(equality)],[1846,1856]),
[iquote('1:Rew:1846.0,1856.2')] ).
cnf(2055,plain,
~ hBOOL(bot_bot_bool),
inference(res,[status(thm),theory(equality)],[165,1676]),
[iquote('1:Res:165.0,1676.1')] ).
cnf(2538,plain,
( ~ is_bool(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u__dfg)))
| equal(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u__dfg)),bot_bot_bool) ),
inference(res,[status(thm),theory(equality)],[1857,1535]),
[iquote('1:Res:1857.1,1535.0')] ).
cnf(2539,plain,
equal(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u__dfg)),bot_bot_bool),
inference(ssi,[status(thm)],[2538,372,230,232,12,218,11]),
[iquote('1:SSi:2538.0,372.0,230.1,232.0,12.1,218.1,11.2')] ).
cnf(2752,plain,
( ~ hBOOL(hAPP_a_bool(image_pname_a(mgt_call,u__dfg),hAPP_pname_a(mgt_call,pn)))
| hBOOL(bot_bot_bool) ),
inference(spr,[status(thm),theory(equality)],[2539,454]),
[iquote('1:SpR:2539.0,454.1')] ).
cnf(2753,plain,
~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,u)),
inference(res,[status(thm),theory(equality)],[454,263]),
[iquote('0:Res:454.1,263.0')] ).
cnf(2756,plain,
~ hBOOL(hAPP_a_bool(image_pname_a(mgt_call,u__dfg),hAPP_pname_a(mgt_call,pn))),
inference(mrr,[status(thm)],[2752,2055]),
[iquote('1:MRR:2752.1,2055.0')] ).
cnf(2762,plain,
( ~ is_bool(hAPP_a_bool(image_pname_a(mgt_call,u__dfg),hAPP_pname_a(mgt_call,pn)))
| equal(hAPP_a_bool(image_pname_a(mgt_call,u__dfg),hAPP_pname_a(mgt_call,pn)),bot_bot_bool) ),
inference(res,[status(thm),theory(equality)],[1857,2756]),
[iquote('1:Res:1857.1,2756.0')] ).
cnf(2763,plain,
equal(hAPP_a_bool(image_pname_a(mgt_call,u__dfg),hAPP_pname_a(mgt_call,pn)),bot_bot_bool),
inference(ssi,[status(thm)],[2762,370,218,11,232,12]),
[iquote('1:SSi:2762.0,370.0,218.1,11.0,232.1,12.2')] ).
cnf(2850,plain,
hBOOL(hAPP_a_bool(insert_a(u,v),u)),
inference(res,[status(thm),theory(equality)],[285,453]),
[iquote('0:Res:285.0,453.0')] ).
cnf(2856,plain,
hBOOL(hAPP_pname_bool(u__dfg,pn)),
inference(res,[status(thm),theory(equality)],[203,451]),
[iquote('0:Res:203.0,451.0')] ).
cnf(4524,plain,
( ~ hBOOL(hAPP_pname_bool(u__dfg,u))
| hBOOL(wt(the_com(body(u)))) ),
inference(res,[status(thm),theory(equality)],[452,527]),
[iquote('0:Res:452.1,527.0')] ).
cnf(10371,plain,
hBOOL(hAPP_a_bool(image_pname_a(u,insert_pname(v,w)),hAPP_pname_a(u,v))),
inference(spr,[status(thm),theory(equality)],[579,2850]),
[iquote('0:SpR:579.0,2850.0')] ).
cnf(14946,plain,
( ~ is_fun_pname_bool(u__dfg)
| equal(insert_pname(pn,u__dfg),u__dfg) ),
inference(res,[status(thm),theory(equality)],[203,677]),
[iquote('0:Res:203.0,677.1')] ).
cnf(14950,plain,
equal(insert_pname(pn,u__dfg),u__dfg),
inference(ssi,[status(thm)],[14946,11]),
[iquote('0:SSi:14946.0,11.0')] ).
cnf(19612,plain,
hBOOL(hAPP_a_bool(image_pname_a(u,u__dfg),hAPP_pname_a(u,pn))),
inference(spr,[status(thm),theory(equality)],[14950,10371]),
[iquote('0:SpR:14950.0,10371.0')] ).
cnf(19623,plain,
hBOOL(bot_bot_bool),
inference(spr,[status(thm),theory(equality)],[2763,19612]),
[iquote('1:SpR:2763.0,19612.0')] ).
cnf(19625,plain,
$false,
inference(mrr,[status(thm)],[19623,2055]),
[iquote('1:MRR:19623.0,2055.0')] ).
cnf(19628,plain,
~ equal(fFalse,bot_bot_bool),
inference(spt,[spt(split,[position(sa)])],[19625,1651]),
[iquote('1:Spt:19625.0,1648.0,1651.0')] ).
cnf(19629,plain,
equal(fTrue,bot_bot_bool),
inference(spt,[spt(split,[position(s2)])],[1648]),
[iquote('1:Spt:19625.0,1648.1')] ).
cnf(19631,plain,
~ hBOOL(bot_bot_bool),
inference(mrr,[status(thm)],[275,2753]),
[iquote('0:MRR:275.1,2753.0')] ).
cnf(19633,plain,
( equal(wt(u),fFalse)
| equal(wt(u),bot_bot_bool) ),
inference(rew,[status(thm),theory(equality)],[19629,1647]),
[iquote('1:Rew:19629.0,1647.1')] ).
cnf(20298,plain,
( ~ hBOOL(hAPP_pname_bool(u__dfg,u))
| equal(wt(the_com(body(u))),bot_bot_bool)
| hBOOL(fFalse) ),
inference(spr,[status(thm),theory(equality)],[19633,4524]),
[iquote('1:SpR:19633.0,4524.1')] ).
cnf(20314,plain,
( ~ hBOOL(hAPP_pname_bool(u__dfg,u))
| equal(wt(the_com(body(u))),bot_bot_bool) ),
inference(mrr,[status(thm)],[20298,33]),
[iquote('1:MRR:20298.2,33.0')] ).
cnf(20315,plain,
( ~ hBOOL(hAPP_pname_bool(u__dfg,u))
| hBOOL(bot_bot_bool) ),
inference(rew,[status(thm),theory(equality)],[20314,4524]),
[iquote('1:Rew:20314.1,4524.1')] ).
cnf(20316,plain,
~ hBOOL(hAPP_pname_bool(u__dfg,u)),
inference(mrr,[status(thm)],[20315,19631]),
[iquote('1:MRR:20315.1,19631.0')] ).
cnf(20317,plain,
$false,
inference(unc,[status(thm)],[20316,2856]),
[iquote('1:UnC:20316.0,2856.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW473+2 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 6 02:43:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 13.53/13.71
% 13.53/13.71 SPASS V 3.9
% 13.53/13.71 SPASS beiseite: Proof found.
% 13.53/13.71 % SZS status Theorem
% 13.53/13.71 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.53/13.71 SPASS derived 15826 clauses, backtracked 974 clauses, performed 3 splits and kept 7383 clauses.
% 13.53/13.71 SPASS allocated 116801 KBytes.
% 13.53/13.71 SPASS spent 0:0:13.34 on the problem.
% 13.53/13.71 0:00:00.06 for the input.
% 13.53/13.71 0:00:00.75 for the FLOTTER CNF translation.
% 13.53/13.71 0:00:00.56 for inferences.
% 13.53/13.71 0:00:00.36 for the backtracking.
% 13.53/13.71 0:0:11.08 for the reduction.
% 13.53/13.71
% 13.53/13.71
% 13.53/13.71 Here is a proof with depth 6, length 73 :
% 13.53/13.71 % SZS output start Refutation
% See solution above
% 13.53/13.71 Formulae used in the proof : gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool gsy_v_U gsy_v_pn gsy_v_wt help_fFalse_1_1_U fact_292_Collect__def fact_420_empty__def fact_442_bot__least conj_4 gsy_c_Set_Oimage_000tc__Com__Opname_000t__a gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J gsy_c_hAPP_000tc__Com__Opname_000t__a fact_406_empty__iff fact_430_bot__apply fact_232_insertI1 conj_1 fact_408_empty__Collect__eq help_fFalse_1_1_T help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool gsy_c_hAPP_000t__a_000tc__HOL__Obool gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool fact_288_mem__def fact_289_mem__def fact_437_bot__unique fact_567_assms_I4_J conj_6 fact_337_image__insert fact_264_insert__absorb fact_324_insert__subset
% 13.92/14.16
%------------------------------------------------------------------------------