TSTP Solution File: SET821-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET821-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 : Tue Jul 19 05:28:53 EDT 2022
% Result : Unsatisfiable 0.61s 0.81s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 71
% Syntax : Number of clauses : 83 ( 78 unt; 3 nHn; 83 RR)
% Number of literals : 89 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 69 ( 68 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
c_less(v_a,v_b,tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(2,axiom,
c_less(v_b,v_c,tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(v_b,u,tc_IntDef_Oint)
| c_in(v_a,u,tc_IntDef_Oint)
| c_in(v_c,u,tc_IntDef_Oint) ),
file('SET821-1.p',unknown),
[] ).
cnf(126,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_less(v,v,u) ),
file('SET821-1.p',unknown),
[] ).
cnf(179,axiom,
c_in(u,c_insert(u,v,w),w),
file('SET821-1.p',unknown),
[] ).
cnf(306,axiom,
( ~ c_in(u,c_insert(v,c_emptyset,w),w)
| equal(u,v) ),
file('SET821-1.p',unknown),
[] ).
cnf(330,axiom,
class_HOL_Ominus(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(331,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(332,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(333,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(334,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(335,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(336,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(337,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(338,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(339,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(340,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(341,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(342,axiom,
class_HOL_Oplus(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(343,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(344,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(345,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(346,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(347,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(348,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(349,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(350,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(351,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(352,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(353,axiom,
class_HOL_Otimes(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(354,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(355,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(356,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(357,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(358,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(359,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(360,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(361,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(362,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(363,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(364,axiom,
class_HOL_Ozero(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(365,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(366,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(367,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(368,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(369,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(370,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(371,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(372,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(373,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(374,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(375,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(376,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(377,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(378,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(379,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(380,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(381,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(382,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(383,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(384,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(385,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(386,axiom,
class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(387,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(388,axiom,
class_Divides_Odiv(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(389,axiom,
class_Nat_Opower(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(390,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(391,axiom,
class_Parity_Oeven__odd(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(392,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(393,axiom,
class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(394,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
file('SET821-1.p',unknown),
[] ).
cnf(1368,plain,
( c_in(v_a,c_insert(v_b,u,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_c,c_insert(v_b,u,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(res,[status(thm),theory(equality)],[179,3]),
[iquote('0:Res:179.0,3.0')] ).
cnf(1666,plain,
( c_in(v_a,c_insert(v_b,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)
| equal(v_c,v_b) ),
inference(res,[status(thm),theory(equality)],[1368,306]),
[iquote('0:Res:1368.1,306.0')] ).
cnf(1667,plain,
equal(v_c,v_b),
inference(spt,[spt(split,[position(s1)])],[1666]),
[iquote('1:Spt:1666.1')] ).
cnf(1668,plain,
c_less(v_b,v_b,tc_IntDef_Oint),
inference(rew,[status(thm),theory(equality)],[1667,2]),
[iquote('1:Rew:1667.0,2.0')] ).
cnf(1683,plain,
~ class_Orderings_Oorder(tc_IntDef_Oint),
inference(res,[status(thm),theory(equality)],[1668,126]),
[iquote('1:Res:1668.0,126.1')] ).
cnf(1684,plain,
$false,
inference(ssi,[status(thm)],[1683,391,388,385,389,371,380,347,345,331,357,356,346,358,363,394,359,330,378,377,376,372,368,362,361,373,365,348,333,390,369,366,351,344,341,339,374,360,350,349,343,336,367,387,352,383,379,370,354,340,393,355,337,332,353,338,335,381,375,334,364,382,392,386,342,384]),
[iquote('1:SSi:1683.0,391.0,388.0,385.0,389.0,371.0,380.0,347.0,345.0,331.0,357.0,356.0,346.0,358.0,363.0,394.0,359.0,330.0,378.0,377.0,376.0,372.0,368.0,362.0,361.0,373.0,365.0,348.0,333.0,390.0,369.0,366.0,351.0,344.0,341.0,339.0,374.0,360.0,350.0,349.0,343.0,336.0,367.0,387.0,352.0,383.0,379.0,370.0,354.0,340.0,393.0,355.0,337.0,332.0,353.0,338.0,335.0,381.0,375.0,334.0,364.0,382.0,392.0,386.0,342.0,384.0')] ).
cnf(1685,plain,
~ equal(v_c,v_b),
inference(spt,[spt(split,[position(sa)])],[1684,1667]),
[iquote('1:Spt:1684.0,1666.1,1667.0')] ).
cnf(1686,plain,
c_in(v_a,c_insert(v_b,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint),
inference(spt,[spt(split,[position(s2)])],[1666]),
[iquote('1:Spt:1684.0,1666.0')] ).
cnf(1687,plain,
equal(v_b,v_a),
inference(res,[status(thm),theory(equality)],[1686,306]),
[iquote('1:Res:1686.0,306.0')] ).
cnf(1688,plain,
c_less(v_a,v_a,tc_IntDef_Oint),
inference(rew,[status(thm),theory(equality)],[1687,1]),
[iquote('1:Rew:1687.0,1.0')] ).
cnf(1706,plain,
~ class_Orderings_Oorder(tc_IntDef_Oint),
inference(res,[status(thm),theory(equality)],[1688,126]),
[iquote('1:Res:1688.0,126.1')] ).
cnf(1707,plain,
$false,
inference(ssi,[status(thm)],[1706,391,388,385,389,371,380,347,345,331,357,356,346,358,363,394,359,330,378,377,376,372,368,362,361,373,365,348,333,390,369,366,351,344,341,339,374,360,350,349,343,336,367,387,352,383,379,370,354,340,393,355,337,332,353,338,335,381,375,334,364,382,392,386,342,384]),
[iquote('1:SSi:1706.0,391.0,388.0,385.0,389.0,371.0,380.0,347.0,345.0,331.0,357.0,356.0,346.0,358.0,363.0,394.0,359.0,330.0,378.0,377.0,376.0,372.0,368.0,362.0,361.0,373.0,365.0,348.0,333.0,390.0,369.0,366.0,351.0,344.0,341.0,339.0,374.0,360.0,350.0,349.0,343.0,336.0,367.0,387.0,352.0,383.0,379.0,370.0,354.0,340.0,393.0,355.0,337.0,332.0,353.0,338.0,335.0,381.0,375.0,334.0,364.0,382.0,392.0,386.0,342.0,384.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET821-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 14:22:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.61/0.81
% 0.61/0.81 SPASS V 3.9
% 0.61/0.81 SPASS beiseite: Proof found.
% 0.61/0.81 % SZS status Theorem
% 0.61/0.81 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.81 SPASS derived 297 clauses, backtracked 16 clauses, performed 1 splits and kept 1425 clauses.
% 0.61/0.81 SPASS allocated 78061 KBytes.
% 0.61/0.81 SPASS spent 0:00:00.47 on the problem.
% 0.61/0.81 0:00:00.08 for the input.
% 0.61/0.81 0:00:00.00 for the FLOTTER CNF translation.
% 0.61/0.81 0:00:00.04 for inferences.
% 0.61/0.81 0:00:00.00 for the backtracking.
% 0.61/0.81 0:00:00.10 for the reduction.
% 0.61/0.81
% 0.61/0.81
% 0.61/0.81 Here is a proof with depth 4, length 83 :
% 0.61/0.81 % SZS output start Refutation
% See solution above
% 0.61/0.81 Formulae used in the proof : cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_Orderings_Oorder__less__irrefl__iff1_0 cls_Set_OinsertCI_1 cls_Set_OsingletonD__dest_0 clsarity_IntDef__Oint_0 clsarity_IntDef__Oint_1 clsarity_IntDef__Oint_10 clsarity_IntDef__Oint_11 clsarity_IntDef__Oint_12 clsarity_IntDef__Oint_13 clsarity_IntDef__Oint_14 clsarity_IntDef__Oint_15 clsarity_IntDef__Oint_16 clsarity_IntDef__Oint_17 clsarity_IntDef__Oint_18 clsarity_IntDef__Oint_19 clsarity_IntDef__Oint_2 clsarity_IntDef__Oint_20 clsarity_IntDef__Oint_21 clsarity_IntDef__Oint_22 clsarity_IntDef__Oint_23 clsarity_IntDef__Oint_24 clsarity_IntDef__Oint_25 clsarity_IntDef__Oint_26 clsarity_IntDef__Oint_27 clsarity_IntDef__Oint_28 clsarity_IntDef__Oint_29 clsarity_IntDef__Oint_3 clsarity_IntDef__Oint_30 clsarity_IntDef__Oint_31 clsarity_IntDef__Oint_32 clsarity_IntDef__Oint_33 clsarity_IntDef__Oint_34 clsarity_IntDef__Oint_35 clsarity_IntDef__Oint_36 clsarity_IntDef__Oint_37 clsarity_IntDef__Oint_38 clsarity_IntDef__Oint_39 clsarity_IntDef__Oint_4 clsarity_IntDef__Oint_40 clsarity_IntDef__Oint_41 clsarity_IntDef__Oint_42 clsarity_IntDef__Oint_43 clsarity_IntDef__Oint_44 clsarity_IntDef__Oint_45 clsarity_IntDef__Oint_46 clsarity_IntDef__Oint_47 clsarity_IntDef__Oint_48 clsarity_IntDef__Oint_49 clsarity_IntDef__Oint_5 clsarity_IntDef__Oint_50 clsarity_IntDef__Oint_51 clsarity_IntDef__Oint_52 clsarity_IntDef__Oint_53 clsarity_IntDef__Oint_54 clsarity_IntDef__Oint_55 clsarity_IntDef__Oint_56 clsarity_IntDef__Oint_57 clsarity_IntDef__Oint_58 clsarity_IntDef__Oint_59 clsarity_IntDef__Oint_6 clsarity_IntDef__Oint_60 clsarity_IntDef__Oint_61 clsarity_IntDef__Oint_62 clsarity_IntDef__Oint_63 clsarity_IntDef__Oint_64 clsarity_IntDef__Oint_7 clsarity_IntDef__Oint_8 clsarity_IntDef__Oint_9
% 0.61/0.83
%------------------------------------------------------------------------------