TSTP Solution File: SWV841-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV841-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% 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 : 600s
% DateTime : Wed Jul 20 21:45:20 EDT 2022
% Result : Unsatisfiable 0.70s 0.86s
% Output : Refutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 32
% Syntax : Number of clauses : 44 ( 26 unt; 0 nHn; 44 RR)
% Number of literals : 63 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(71,axiom,
( ~ class_Lattices_Olattice(u)
| c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u) ),
file('SWV841-1.p',unknown),
[] ).
cnf(107,axiom,
equal(c_Collect(u,v),u),
file('SWV841-1.p',unknown),
[] ).
cnf(423,axiom,
c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v),w),u),tc_fun(v,tc_bool)),
file('SWV841-1.p',unknown),
[] ).
cnf(438,axiom,
( ~ c_lessequals(u,v,tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(v,u,w) ),
file('SWV841-1.p',unknown),
[] ).
cnf(457,axiom,
equal(hAPP(hAPP(c_Set_Oinsert(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Collect(c_fequal(v,u),u)),
file('SWV841-1.p',unknown),
[] ).
cnf(481,axiom,
equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))),w),hAPP(hAPP(c_Set_Oinsert(u),v),w)),
file('SWV841-1.p',unknown),
[] ).
cnf(485,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(u,v,w)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(x,u,w)
| c_Hoare__Mirabelle_Ohoare__derivs(x,v,w) ),
file('SWV841-1.p',unknown),
[] ).
cnf(500,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(u)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(501,axiom,
( ~ class_Lattices_Olattice(u)
| class_Lattices_Oupper__semilattice(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(502,axiom,
( ~ class_Lattices_Olattice(u)
| class_Lattices_Olower__semilattice(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(503,axiom,
( ~ class_Lattices_Odistrib__lattice(u)
| class_Lattices_Odistrib__lattice(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(504,axiom,
( ~ class_Lattices_Obounded__lattice(u)
| class_Lattices_Obounded__lattice(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(506,axiom,
( ~ class_Orderings_Opreorder(u)
| class_Orderings_Opreorder(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(507,axiom,
( ~ class_Lattices_Olattice(u)
| class_Lattices_Olattice(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(508,axiom,
( ~ class_Orderings_Oorder(u)
| class_Orderings_Oorder(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(509,axiom,
( ~ class_Orderings_Obot(u)
| class_Orderings_Obot(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(510,axiom,
( ~ class_HOL_Ominus(u)
| class_HOL_Ominus(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(511,axiom,
( ~ class_HOL_Oord(u)
| class_HOL_Oord(tc_fun(v,u)) ),
file('SWV841-1.p',unknown),
[] ).
cnf(512,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(513,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(514,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(515,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(516,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(517,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(518,axiom,
class_Orderings_Opreorder(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(519,axiom,
class_Lattices_Olattice(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(520,axiom,
class_Orderings_Oorder(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(521,axiom,
class_Orderings_Obot(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(522,axiom,
class_HOL_Ominus(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(523,axiom,
class_HOL_Oord(tc_bool),
file('SWV841-1.p',unknown),
[] ).
cnf(526,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts),t_a),
file('SWV841-1.p',unknown),
[] ).
cnf(527,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('SWV841-1.p',unknown),
[] ).
cnf(532,plain,
equal(hAPP(hAPP(c_Set_Oinsert(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_fequal(v,u)),
inference(rew,[status(thm),theory(equality)],[107,457]),
[iquote('0:Rew:107.0,457.0')] ).
cnf(550,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(rew,[status(thm),theory(equality)],[532,527]),
[iquote('0:Rew:532.0,527.1')] ).
cnf(555,plain,
equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_fequal(v,u)),w),hAPP(hAPP(c_Set_Oinsert(u),v),w)),
inference(rew,[status(thm),theory(equality)],[532,481]),
[iquote('0:Rew:532.0,481.0')] ).
cnf(613,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts),u,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,u,t_a) ),
inference(res,[status(thm),theory(equality)],[526,485]),
[iquote('0:Res:526.0,485.0')] ).
cnf(693,plain,
c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(u)),v),w),w,u),
inference(res,[status(thm),theory(equality)],[423,438]),
[iquote('0:Res:423.0,438.0')] ).
cnf(712,plain,
( ~ class_Lattices_Olattice(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),w),v,u) ),
inference(res,[status(thm),theory(equality)],[71,438]),
[iquote('0:Res:71.1,438.0')] ).
cnf(717,plain,
c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),w),v,u),
inference(ssi,[status(thm)],[712,511,523,522,521,518,517,515,516,512,520,513,514,519,510,509,506,503,504,500,508,501,502,507]),
[iquote('0:SSi:712.0,511.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1,510.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1,509.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1,506.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1,503.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1,504.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1,500.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1,508.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1,501.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1,502.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1,507.0,523.0,522.0,521.0,518.0,517.0,515.0,516.0,512.0,520.0,513.0,514.0,519.1')] ).
cnf(1024,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,t_a),
inference(res,[status(thm),theory(equality)],[693,613]),
[iquote('0:Res:693.0,613.0')] ).
cnf(1025,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(mrr,[status(thm)],[550,1024]),
[iquote('0:MRR:550.0,1024.0')] ).
cnf(2865,plain,
c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(u)),v),w),c_fequal(v,tc_Hoare__Mirabelle_Otriple(u)),u),
inference(spr,[status(thm),theory(equality)],[555,717]),
[iquote('0:SpR:555.0,717.0')] ).
cnf(2912,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(res,[status(thm),theory(equality)],[2865,613]),
[iquote('0:Res:2865.0,613.0')] ).
cnf(2913,plain,
$false,
inference(mrr,[status(thm)],[2912,1025]),
[iquote('0:MRR:2912.0,1025.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV841-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n021.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 : Wed Jun 15 11:10:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.70/0.86
% 0.70/0.86 SPASS V 3.9
% 0.70/0.86 SPASS beiseite: Proof found.
% 0.70/0.86 % SZS status Theorem
% 0.70/0.86 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.70/0.86 SPASS derived 2034 clauses, backtracked 0 clauses, performed 0 splits and kept 904 clauses.
% 0.70/0.86 SPASS allocated 79036 KBytes.
% 0.70/0.86 SPASS spent 0:00:00.49 on the problem.
% 0.70/0.86 0:00:00.05 for the input.
% 0.70/0.86 0:00:00.00 for the FLOTTER CNF translation.
% 0.70/0.86 0:00:00.04 for inferences.
% 0.70/0.86 0:00:00.00 for the backtracking.
% 0.70/0.86 0:00:00.33 for the reduction.
% 0.70/0.86
% 0.70/0.86
% 0.70/0.86 Here is a proof with depth 3, length 44 :
% 0.70/0.86 % SZS output start Refutation
% See solution above
% 0.70/0.86 Formulae used in the proof : cls_inf__sup__ord_I3_J_0 cls_Collect__def_0 cls_subset__insertI_0 cls_asm_0 cls_singleton__conv2_0 cls_insert__is__Un_0 cls_cut_0 clsarity_fun__Complete__Lattice_Ocomplete__lattice clsarity_fun__Lattices_Oupper__semilattice clsarity_fun__Lattices_Olower__semilattice clsarity_fun__Lattices_Odistrib__lattice clsarity_fun__Lattices_Obounded__lattice clsarity_fun__Orderings_Opreorder clsarity_fun__Lattices_Olattice clsarity_fun__Orderings_Oorder clsarity_fun__Orderings_Obot clsarity_fun__HOL_Ominus clsarity_fun__HOL_Oord clsarity_bool__Complete__Lattice_Ocomplete__lattice clsarity_bool__Lattices_Oupper__semilattice clsarity_bool__Lattices_Olower__semilattice clsarity_bool__Lattices_Odistrib__lattice clsarity_bool__Lattices_Obounded__lattice clsarity_bool__Finite__Set_Ofinite_Ofinite clsarity_bool__Orderings_Opreorder clsarity_bool__Lattices_Olattice clsarity_bool__Orderings_Oorder clsarity_bool__Orderings_Obot clsarity_bool__HOL_Ominus clsarity_bool__HOL_Oord cls_conjecture_0 cls_conjecture_1
% 0.70/0.86
%------------------------------------------------------------------------------