TSTP Solution File: ANA027-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA027-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14 19:28:52 EDT 2022
% Result : Unsatisfiable 2.23s 2.42s
% Output : Refutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 66
% Syntax : Number of clauses : 136 ( 68 unt; 0 nHn; 136 RR)
% Number of literals : 209 ( 0 equ; 79 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 62 ( 61 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(16,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(u)
| ~ c_lessequals(v,c_minus(w,x,u),u)
| c_lessequals(c_plus(v,x,u),w,u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(u)
| ~ c_lessequals(c_plus(v,w,u),x,u)
| c_lessequals(v,c_minus(x,w,u),u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(26,axiom,
c_lessequals(c_0,c_minus(v(v_x),v_k(v_x),t_b),t_b),
file('ANA027-1.p',unknown),
[] ).
cnf(27,axiom,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
file('ANA027-1.p',unknown),
[] ).
cnf(28,axiom,
~ c_lessequals(c_0,c_minus(v(v_x),v_g(v_x),t_b),t_b),
file('ANA027-1.p',unknown),
[] ).
cnf(29,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA027-1.p',unknown),
[] ).
cnf(1119,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(u)
| equal(c_plus(c_0,v,u),v) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2446,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__ring__1(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2447,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__ring(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2448,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Osemiring__1(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2449,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oaxclass__0__neq__1(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2450,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Omonoid__mult(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2451,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_HOL_Oone(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2452,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2453,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__semiring__0(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2454,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__semiring(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2455,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oab__semigroup__mult(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2456,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Osemiring__0__cancel(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2457,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Osemiring__0(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2458,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oring__1(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2459,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Osemiring(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2460,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Osemigroup__mult(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2461,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_HOL_Otimes(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2462,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Ocomm__monoid__add(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2463,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_HOL_Ozero(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2464,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Ocancel__ab__semigroup__add(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2465,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oab__semigroup__add(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2466,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Ocancel__semigroup__add(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2467,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Osemigroup__add(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2468,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_HOL_Oplus(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2469,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oring(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2470,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oordered__comm__semiring__strict(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2471,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oordered__semiring__strict(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2472,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2473,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Olinorder(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2474,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_LOrder_Olorder(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2475,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_LOrder_Ojoin__semilorder(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2476,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_LOrder_Omeet__semilorder(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2477,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2478,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2479,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2480,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oab__group__add(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2481,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__cancel__semiring(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2482,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__comm__semiring(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2483,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__semiring(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2484,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Opordered__ab__semigroup__add(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2485,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Oorder(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2486,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Oord(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2487,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oaxclass__abs__if(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2488,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oordered__ring__strict(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2489,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Olordered__ring(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2490,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__ring(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2491,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_HOL_Ominus(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2492,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2493,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__meet(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2494,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__join(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2495,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2496,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Opordered__ab__group__add(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2497,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oordered__semidom(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2498,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2499,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oidom(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2500,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2501,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__semiring__1(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2502,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Ocomm__monoid__mult(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(2503,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Osemiring__1__cancel(u) ),
file('ANA027-1.p',unknown),
[] ).
cnf(3080,plain,
class_Ring__and__Field_Ocomm__ring__1(t_b),
inference(res,[status(thm),theory(equality)],[29,2446]),
[iquote('0:Res:29.0,2446.0')] ).
cnf(3081,plain,
class_Ring__and__Field_Ocomm__ring(t_b),
inference(res,[status(thm),theory(equality)],[29,2447]),
[iquote('0:Res:29.0,2447.0')] ).
cnf(3082,plain,
class_Ring__and__Field_Osemiring__1(t_b),
inference(res,[status(thm),theory(equality)],[29,2448]),
[iquote('0:Res:29.0,2448.0')] ).
cnf(3083,plain,
class_Ring__and__Field_Oaxclass__0__neq__1(t_b),
inference(res,[status(thm),theory(equality)],[29,2449]),
[iquote('0:Res:29.0,2449.0')] ).
cnf(3084,plain,
class_OrderedGroup_Omonoid__mult(t_b),
inference(res,[status(thm),theory(equality)],[29,2450]),
[iquote('0:Res:29.0,2450.0')] ).
cnf(3085,plain,
class_HOL_Oone(t_b),
inference(res,[status(thm),theory(equality)],[29,2451]),
[iquote('0:Res:29.0,2451.0')] ).
cnf(3086,plain,
class_Ring__and__Field_Ocomm__semiring__0__cancel(t_b),
inference(res,[status(thm),theory(equality)],[29,2452]),
[iquote('0:Res:29.0,2452.0')] ).
cnf(3087,plain,
class_Ring__and__Field_Ocomm__semiring__0(t_b),
inference(res,[status(thm),theory(equality)],[29,2453]),
[iquote('0:Res:29.0,2453.0')] ).
cnf(3088,plain,
class_Ring__and__Field_Ocomm__semiring(t_b),
inference(res,[status(thm),theory(equality)],[29,2454]),
[iquote('0:Res:29.0,2454.0')] ).
cnf(3089,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(res,[status(thm),theory(equality)],[29,2455]),
[iquote('0:Res:29.0,2455.0')] ).
cnf(3090,plain,
class_Ring__and__Field_Osemiring__0__cancel(t_b),
inference(res,[status(thm),theory(equality)],[29,2456]),
[iquote('0:Res:29.0,2456.0')] ).
cnf(3091,plain,
class_Ring__and__Field_Osemiring__0(t_b),
inference(res,[status(thm),theory(equality)],[29,2457]),
[iquote('0:Res:29.0,2457.0')] ).
cnf(3092,plain,
class_Ring__and__Field_Oring__1(t_b),
inference(res,[status(thm),theory(equality)],[29,2458]),
[iquote('0:Res:29.0,2458.0')] ).
cnf(3093,plain,
class_Ring__and__Field_Osemiring(t_b),
inference(res,[status(thm),theory(equality)],[29,2459]),
[iquote('0:Res:29.0,2459.0')] ).
cnf(3094,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(res,[status(thm),theory(equality)],[29,2460]),
[iquote('0:Res:29.0,2460.0')] ).
cnf(3095,plain,
class_HOL_Otimes(t_b),
inference(res,[status(thm),theory(equality)],[29,2461]),
[iquote('0:Res:29.0,2461.0')] ).
cnf(3096,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(res,[status(thm),theory(equality)],[29,2462]),
[iquote('0:Res:29.0,2462.0')] ).
cnf(3097,plain,
class_HOL_Ozero(t_b),
inference(res,[status(thm),theory(equality)],[29,2463]),
[iquote('0:Res:29.0,2463.0')] ).
cnf(3098,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(t_b),
inference(res,[status(thm),theory(equality)],[29,2464]),
[iquote('0:Res:29.0,2464.0')] ).
cnf(3099,plain,
class_OrderedGroup_Oab__semigroup__add(t_b),
inference(res,[status(thm),theory(equality)],[29,2465]),
[iquote('0:Res:29.0,2465.0')] ).
cnf(3100,plain,
class_OrderedGroup_Ocancel__semigroup__add(t_b),
inference(res,[status(thm),theory(equality)],[29,2466]),
[iquote('0:Res:29.0,2466.0')] ).
cnf(3101,plain,
class_OrderedGroup_Osemigroup__add(t_b),
inference(res,[status(thm),theory(equality)],[29,2467]),
[iquote('0:Res:29.0,2467.0')] ).
cnf(3102,plain,
class_HOL_Oplus(t_b),
inference(res,[status(thm),theory(equality)],[29,2468]),
[iquote('0:Res:29.0,2468.0')] ).
cnf(3103,plain,
class_Ring__and__Field_Oring(t_b),
inference(res,[status(thm),theory(equality)],[29,2469]),
[iquote('0:Res:29.0,2469.0')] ).
cnf(3104,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(t_b),
inference(res,[status(thm),theory(equality)],[29,2470]),
[iquote('0:Res:29.0,2470.0')] ).
cnf(3105,plain,
class_Ring__and__Field_Oordered__semiring__strict(t_b),
inference(res,[status(thm),theory(equality)],[29,2471]),
[iquote('0:Res:29.0,2471.0')] ).
cnf(3106,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(t_b),
inference(res,[status(thm),theory(equality)],[29,2472]),
[iquote('0:Res:29.0,2472.0')] ).
cnf(3107,plain,
class_Orderings_Olinorder(t_b),
inference(res,[status(thm),theory(equality)],[29,2473]),
[iquote('0:Res:29.0,2473.0')] ).
cnf(3108,plain,
class_LOrder_Olorder(t_b),
inference(res,[status(thm),theory(equality)],[29,2474]),
[iquote('0:Res:29.0,2474.0')] ).
cnf(3109,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(res,[status(thm),theory(equality)],[29,2475]),
[iquote('0:Res:29.0,2475.0')] ).
cnf(3110,plain,
class_LOrder_Omeet__semilorder(t_b),
inference(res,[status(thm),theory(equality)],[29,2476]),
[iquote('0:Res:29.0,2476.0')] ).
cnf(3111,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(res,[status(thm),theory(equality)],[29,2477]),
[iquote('0:Res:29.0,2477.0')] ).
cnf(3112,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(t_b),
inference(res,[status(thm),theory(equality)],[29,2478]),
[iquote('0:Res:29.0,2478.0')] ).
cnf(3113,plain,
class_Ring__and__Field_Opordered__cancel__comm__semiring(t_b),
inference(res,[status(thm),theory(equality)],[29,2479]),
[iquote('0:Res:29.0,2479.0')] ).
cnf(3114,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(res,[status(thm),theory(equality)],[29,2480]),
[iquote('0:Res:29.0,2480.0')] ).
cnf(3115,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(res,[status(thm),theory(equality)],[29,2481]),
[iquote('0:Res:29.0,2481.0')] ).
cnf(3116,plain,
class_Ring__and__Field_Opordered__comm__semiring(t_b),
inference(res,[status(thm),theory(equality)],[29,2482]),
[iquote('0:Res:29.0,2482.0')] ).
cnf(3117,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(res,[status(thm),theory(equality)],[29,2483]),
[iquote('0:Res:29.0,2483.0')] ).
cnf(3118,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(t_b),
inference(res,[status(thm),theory(equality)],[29,2484]),
[iquote('0:Res:29.0,2484.0')] ).
cnf(3119,plain,
class_Orderings_Oorder(t_b),
inference(res,[status(thm),theory(equality)],[29,2485]),
[iquote('0:Res:29.0,2485.0')] ).
cnf(3120,plain,
class_Orderings_Oord(t_b),
inference(res,[status(thm),theory(equality)],[29,2486]),
[iquote('0:Res:29.0,2486.0')] ).
cnf(3121,plain,
class_Ring__and__Field_Oaxclass__abs__if(t_b),
inference(res,[status(thm),theory(equality)],[29,2487]),
[iquote('0:Res:29.0,2487.0')] ).
cnf(3122,plain,
class_Ring__and__Field_Oordered__ring__strict(t_b),
inference(res,[status(thm),theory(equality)],[29,2488]),
[iquote('0:Res:29.0,2488.0')] ).
cnf(3123,plain,
class_Ring__and__Field_Olordered__ring(t_b),
inference(res,[status(thm),theory(equality)],[29,2489]),
[iquote('0:Res:29.0,2489.0')] ).
cnf(3124,plain,
class_Ring__and__Field_Opordered__ring(t_b),
inference(res,[status(thm),theory(equality)],[29,2490]),
[iquote('0:Res:29.0,2490.0')] ).
cnf(3125,plain,
class_HOL_Ominus(t_b),
inference(res,[status(thm),theory(equality)],[29,2491]),
[iquote('0:Res:29.0,2491.0')] ).
cnf(3126,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[29,2492]),
[iquote('0:Res:29.0,2492.0')] ).
cnf(3127,plain,
class_OrderedGroup_Olordered__ab__group__meet(t_b),
inference(res,[status(thm),theory(equality)],[29,2493]),
[iquote('0:Res:29.0,2493.0')] ).
cnf(3128,plain,
class_OrderedGroup_Olordered__ab__group__join(t_b),
inference(res,[status(thm),theory(equality)],[29,2494]),
[iquote('0:Res:29.0,2494.0')] ).
cnf(3129,plain,
class_OrderedGroup_Olordered__ab__group(t_b),
inference(res,[status(thm),theory(equality)],[29,2495]),
[iquote('0:Res:29.0,2495.0')] ).
cnf(3130,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(res,[status(thm),theory(equality)],[29,2496]),
[iquote('0:Res:29.0,2496.0')] ).
cnf(3131,plain,
class_Ring__and__Field_Oordered__semidom(t_b),
inference(res,[status(thm),theory(equality)],[29,2497]),
[iquote('0:Res:29.0,2497.0')] ).
cnf(3132,plain,
class_Ring__and__Field_Oaxclass__no__zero__divisors(t_b),
inference(res,[status(thm),theory(equality)],[29,2498]),
[iquote('0:Res:29.0,2498.0')] ).
cnf(3133,plain,
class_Ring__and__Field_Oidom(t_b),
inference(res,[status(thm),theory(equality)],[29,2499]),
[iquote('0:Res:29.0,2499.0')] ).
cnf(3134,plain,
class_Ring__and__Field_Ocomm__semiring__1__cancel(t_b),
inference(res,[status(thm),theory(equality)],[29,2500]),
[iquote('0:Res:29.0,2500.0')] ).
cnf(3135,plain,
class_Ring__and__Field_Ocomm__semiring__1(t_b),
inference(res,[status(thm),theory(equality)],[29,2501]),
[iquote('0:Res:29.0,2501.0')] ).
cnf(3136,plain,
class_OrderedGroup_Ocomm__monoid__mult(t_b),
inference(res,[status(thm),theory(equality)],[29,2502]),
[iquote('0:Res:29.0,2502.0')] ).
cnf(3137,plain,
class_Ring__and__Field_Osemiring__1__cancel(t_b),
inference(res,[status(thm),theory(equality)],[29,2503]),
[iquote('0:Res:29.0,2503.0')] ).
cnf(3202,plain,
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(v_k(v_x),u,t_b)
| c_lessequals(v_g(v_x),u,t_b) ),
inference(res,[status(thm),theory(equality)],[27,23]),
[iquote('0:Res:27.0,23.2')] ).
cnf(3290,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v(v_x),t_b) ),
inference(res,[status(thm),theory(equality)],[26,16]),
[iquote('0:Res:26.0,16.1')] ).
cnf(3330,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v(v_x),t_b) ),
inference(res,[status(thm),theory(equality)],[17,28]),
[iquote('0:Res:17.2,28.0')] ).
cnf(3347,plain,
c_lessequals(c_plus(c_0,v_k(v_x),t_b),v(v_x),t_b),
inference(mrr,[status(thm)],[3290,3130]),
[iquote('0:MRR:3290.0,3130.0')] ).
cnf(3353,plain,
~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v(v_x),t_b),
inference(mrr,[status(thm)],[3330,3130]),
[iquote('0:MRR:3330.0,3130.0')] ).
cnf(3354,plain,
( ~ c_lessequals(v_k(v_x),u,t_b)
| c_lessequals(v_g(v_x),u,t_b) ),
inference(mrr,[status(thm)],[3202,3119]),
[iquote('0:MRR:3202.0,3119.0')] ).
cnf(4281,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| c_lessequals(v_k(v_x),v(v_x),t_b) ),
inference(spr,[status(thm),theory(equality)],[1119,3347]),
[iquote('0:SpR:1119.1,3347.0')] ).
cnf(4285,plain,
c_lessequals(v_k(v_x),v(v_x),t_b),
inference(ssi,[status(thm)],[4281,29,3121,3132,3083,3110,3109,3108,3106,3084,3128,3127,3116,3125,3112,3089,3117,3136,3115,3113,3088,3082,3124,3118,3092,3081,3137,3135,3086,3087,3105,3085,3111,3103,3133,3123,3104,3126,3090,3098,3091,3100,3093,3094,3134,3119,3129,3097,3095,3099,3114,3096,3120,3101,3102,3122,3131,3130,3080,3107]),
[iquote('0:SSi:4281.0,29.0,3121.0,3132.0,3083.0,3110.0,3109.0,3108.0,3106.0,3084.0,3128.0,3127.0,3116.0,3125.0,3112.0,3089.0,3117.0,3136.0,3115.0,3113.0,3088.0,3082.0,3124.0,3118.0,3092.0,3081.0,3137.0,3135.0,3086.0,3087.0,3105.0,3085.0,3111.0,3103.0,3133.0,3123.0,3104.0,3126.0,3090.0,3098.0,3091.0,3100.0,3093.0,3094.0,3134.0,3119.0,3129.0,3097.0,3095.0,3099.0,3114.0,3096.0,3120.0,3101.0,3102.0,3122.0,3131.0,3130.0,3080.0,3107.0')] ).
cnf(4468,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ c_lessequals(v_g(v_x),v(v_x),t_b) ),
inference(spl,[status(thm),theory(equality)],[1119,3353]),
[iquote('0:SpL:1119.1,3353.0')] ).
cnf(4469,plain,
~ c_lessequals(v_g(v_x),v(v_x),t_b),
inference(ssi,[status(thm)],[4468,29,3121,3132,3083,3110,3109,3108,3106,3084,3128,3127,3116,3125,3112,3089,3117,3136,3115,3113,3088,3082,3124,3118,3092,3081,3137,3135,3086,3087,3105,3085,3111,3103,3133,3123,3104,3126,3090,3098,3091,3100,3093,3094,3134,3119,3129,3097,3095,3099,3114,3096,3120,3101,3102,3122,3131,3130,3080,3107]),
[iquote('0:SSi:4468.0,29.0,3121.0,3132.0,3083.0,3110.0,3109.0,3108.0,3106.0,3084.0,3128.0,3127.0,3116.0,3125.0,3112.0,3089.0,3117.0,3136.0,3115.0,3113.0,3088.0,3082.0,3124.0,3118.0,3092.0,3081.0,3137.0,3135.0,3086.0,3087.0,3105.0,3085.0,3111.0,3103.0,3133.0,3123.0,3104.0,3126.0,3090.0,3098.0,3091.0,3100.0,3093.0,3094.0,3134.0,3119.0,3129.0,3097.0,3095.0,3099.0,3114.0,3096.0,3120.0,3101.0,3102.0,3122.0,3131.0,3130.0,3080.0,3107.0')] ).
cnf(6445,plain,
~ c_lessequals(v_k(v_x),v(v_x),t_b),
inference(res,[status(thm),theory(equality)],[3354,4469]),
[iquote('0:Res:3354.1,4469.0')] ).
cnf(6446,plain,
$false,
inference(mrr,[status(thm)],[6445,4285]),
[iquote('0:MRR:6445.0,4285.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA027-1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 04:40:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.23/2.42
% 2.23/2.42 SPASS V 3.9
% 2.23/2.42 SPASS beiseite: Proof found.
% 2.23/2.42 % SZS status Theorem
% 2.23/2.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.23/2.42 SPASS derived 2871 clauses, backtracked 0 clauses, performed 1 splits and kept 3327 clauses.
% 2.23/2.42 SPASS allocated 82142 KBytes.
% 2.23/2.42 SPASS spent 0:00:02.07 on the problem.
% 2.23/2.42 0:00:00.27 for the input.
% 2.23/2.42 0:00:00.00 for the FLOTTER CNF translation.
% 2.23/2.42 0:00:00.09 for inferences.
% 2.23/2.42 0:00:00.00 for the backtracking.
% 2.23/2.42 0:00:01.09 for the reduction.
% 2.23/2.42
% 2.23/2.42
% 2.23/2.42 Here is a proof with depth 3, length 136 :
% 2.23/2.42 % SZS output start Refutation
% See solution above
% 2.23/2.48 Formulae used in the proof : cls_OrderedGroup_Ocompare__rls__9_0 cls_OrderedGroup_Ocompare__rls__9_1 cls_Orderings_Oorder__class_Oorder__trans_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 tfree_tcs cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0 clsrel_Ring__and__Field_Oordered__idom_0 clsrel_Ring__and__Field_Oordered__idom_1 clsrel_Ring__and__Field_Oordered__idom_10 clsrel_Ring__and__Field_Oordered__idom_11 clsrel_Ring__and__Field_Oordered__idom_12 clsrel_Ring__and__Field_Oordered__idom_13 clsrel_Ring__and__Field_Oordered__idom_14 clsrel_Ring__and__Field_Oordered__idom_15 clsrel_Ring__and__Field_Oordered__idom_16 clsrel_Ring__and__Field_Oordered__idom_17 clsrel_Ring__and__Field_Oordered__idom_18 clsrel_Ring__and__Field_Oordered__idom_19 clsrel_Ring__and__Field_Oordered__idom_2 clsrel_Ring__and__Field_Oordered__idom_20 clsrel_Ring__and__Field_Oordered__idom_21 clsrel_Ring__and__Field_Oordered__idom_22 clsrel_Ring__and__Field_Oordered__idom_23 clsrel_Ring__and__Field_Oordered__idom_24 clsrel_Ring__and__Field_Oordered__idom_25 clsrel_Ring__and__Field_Oordered__idom_26 clsrel_Ring__and__Field_Oordered__idom_27 clsrel_Ring__and__Field_Oordered__idom_28 clsrel_Ring__and__Field_Oordered__idom_29 clsrel_Ring__and__Field_Oordered__idom_3 clsrel_Ring__and__Field_Oordered__idom_30 clsrel_Ring__and__Field_Oordered__idom_31 clsrel_Ring__and__Field_Oordered__idom_32 clsrel_Ring__and__Field_Oordered__idom_33 clsrel_Ring__and__Field_Oordered__idom_34 clsrel_Ring__and__Field_Oordered__idom_35 clsrel_Ring__and__Field_Oordered__idom_36 clsrel_Ring__and__Field_Oordered__idom_37 clsrel_Ring__and__Field_Oordered__idom_38 clsrel_Ring__and__Field_Oordered__idom_39 clsrel_Ring__and__Field_Oordered__idom_4 clsrel_Ring__and__Field_Oordered__idom_40 clsrel_Ring__and__Field_Oordered__idom_41 clsrel_Ring__and__Field_Oordered__idom_42 clsrel_Ring__and__Field_Oordered__idom_43 clsrel_Ring__and__Field_Oordered__idom_44 clsrel_Ring__and__Field_Oordered__idom_45 clsrel_Ring__and__Field_Oordered__idom_46 clsrel_Ring__and__Field_Oordered__idom_47 clsrel_Ring__and__Field_Oordered__idom_48 clsrel_Ring__and__Field_Oordered__idom_49 clsrel_Ring__and__Field_Oordered__idom_5 clsrel_Ring__and__Field_Oordered__idom_50 clsrel_Ring__and__Field_Oordered__idom_51 clsrel_Ring__and__Field_Oordered__idom_52 clsrel_Ring__and__Field_Oordered__idom_53 clsrel_Ring__and__Field_Oordered__idom_54 clsrel_Ring__and__Field_Oordered__idom_55 clsrel_Ring__and__Field_Oordered__idom_56 clsrel_Ring__and__Field_Oordered__idom_57 clsrel_Ring__and__Field_Oordered__idom_6 clsrel_Ring__and__Field_Oordered__idom_7 clsrel_Ring__and__Field_Oordered__idom_8 clsrel_Ring__and__Field_Oordered__idom_9
% 2.23/2.48
%------------------------------------------------------------------------------