TSTP Solution File: ANA020-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA020-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 19:28:47 EDT 2022
% Result : Unsatisfiable 84.12s 84.38s
% Output : Refutation 84.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 67
% Syntax : Number of clauses : 140 ( 71 unt; 0 nHn; 140 RR)
% Number of literals : 215 ( 0 equ; 83 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 63 ( 62 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_less(v,w,u)
| c_lessequals(v,w,u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(u)
| ~ c_lessequals(c_0,v,u)
| ~ c_lessequals(c_0,w,u)
| c_lessequals(c_0,c_times(w,v,u),u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(6,axiom,
equal(v(c_0),c_0),
file('ANA020-1.p',unknown),
[] ).
cnf(7,axiom,
c_less(c_0,v_c,t_a),
file('ANA020-1.p',unknown),
[] ).
cnf(9,axiom,
equal(c_0,v_x),
file('ANA020-1.p',unknown),
[] ).
cnf(10,axiom,
~ c_lessequals(c_HOL_Oabs(v(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('ANA020-1.p',unknown),
[] ).
cnf(11,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('ANA020-1.p',unknown),
[] ).
cnf(1081,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| equal(c_HOL_Oabs(c_0,u),c_0) ),
file('ANA020-1.p',unknown),
[] ).
cnf(1082,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| c_lessequals(c_0,c_HOL_Oabs(v,u),u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2428,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__ring__1(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2429,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__ring(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2430,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Osemiring__1(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2431,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oaxclass__0__neq__1(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2432,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Omonoid__mult(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2433,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_HOL_Oone(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2434,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2435,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__semiring__0(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2436,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__semiring(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2437,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oab__semigroup__mult(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2438,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Osemiring__0__cancel(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2439,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Osemiring__0(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2440,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oring__1(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2441,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Osemiring(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2442,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Osemigroup__mult(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2443,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_HOL_Otimes(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2444,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Ocomm__monoid__add(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2445,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_HOL_Ozero(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2446,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Ocancel__ab__semigroup__add(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2447,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oab__semigroup__add(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2448,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Ocancel__semigroup__add(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2449,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Osemigroup__add(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2450,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_HOL_Oplus(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2451,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oring(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2452,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oordered__comm__semiring__strict(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2453,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oordered__semiring__strict(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2454,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2455,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Olinorder(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2456,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_LOrder_Olorder(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2457,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_LOrder_Ojoin__semilorder(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2458,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_LOrder_Omeet__semilorder(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2459,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2460,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2461,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2462,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oab__group__add(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2463,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__cancel__semiring(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2464,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__comm__semiring(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2465,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__semiring(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2466,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Opordered__ab__semigroup__add(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2467,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Oorder(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2468,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Oord(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2469,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oaxclass__abs__if(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2470,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oordered__ring__strict(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2471,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Olordered__ring(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2472,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__ring(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2473,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_HOL_Ominus(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2474,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2475,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__meet(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2476,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__join(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2477,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2478,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Opordered__ab__group__add(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2479,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oordered__semidom(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2480,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2481,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Oidom(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2482,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2483,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Ocomm__semiring__1(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2484,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Ocomm__monoid__mult(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2485,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Osemiring__1__cancel(u) ),
file('ANA020-1.p',unknown),
[] ).
cnf(2803,plain,
c_less(v_x,v_c,t_a),
inference(rew,[status(thm),theory(equality)],[9,7]),
[iquote('0:Rew:9.0,7.0')] ).
cnf(2804,plain,
equal(v(v_x),v_x),
inference(rew,[status(thm),theory(equality)],[9,6]),
[iquote('0:Rew:9.0,6.0')] ).
cnf(2900,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| equal(c_HOL_Oabs(v_x,u),v_x) ),
inference(rew,[status(thm),theory(equality)],[9,1081]),
[iquote('0:Rew:9.0,1081.1')] ).
cnf(2931,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| c_lessequals(v_x,c_HOL_Oabs(v,u),u) ),
inference(rew,[status(thm),theory(equality)],[9,1082]),
[iquote('0:Rew:9.0,1082.1')] ).
cnf(3104,plain,
~ c_lessequals(c_HOL_Oabs(v_x,t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(rew,[status(thm),theory(equality)],[2804,10]),
[iquote('0:Rew:2804.0,10.0')] ).
cnf(3245,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(u)
| ~ c_lessequals(v_x,v,u)
| ~ c_lessequals(v_x,w,u)
| c_lessequals(v_x,c_times(v,w,u),u) ),
inference(rew,[status(thm),theory(equality)],[9,3]),
[iquote('0:Rew:9.0,3.3,9.0,3.2,9.0,3.1')] ).
cnf(3563,plain,
class_Ring__and__Field_Ocomm__ring__1(t_a),
inference(res,[status(thm),theory(equality)],[11,2428]),
[iquote('0:Res:11.0,2428.0')] ).
cnf(3564,plain,
class_Ring__and__Field_Ocomm__ring(t_a),
inference(res,[status(thm),theory(equality)],[11,2429]),
[iquote('0:Res:11.0,2429.0')] ).
cnf(3565,plain,
class_Ring__and__Field_Osemiring__1(t_a),
inference(res,[status(thm),theory(equality)],[11,2430]),
[iquote('0:Res:11.0,2430.0')] ).
cnf(3566,plain,
class_Ring__and__Field_Oaxclass__0__neq__1(t_a),
inference(res,[status(thm),theory(equality)],[11,2431]),
[iquote('0:Res:11.0,2431.0')] ).
cnf(3567,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(res,[status(thm),theory(equality)],[11,2432]),
[iquote('0:Res:11.0,2432.0')] ).
cnf(3568,plain,
class_HOL_Oone(t_a),
inference(res,[status(thm),theory(equality)],[11,2433]),
[iquote('0:Res:11.0,2433.0')] ).
cnf(3569,plain,
class_Ring__and__Field_Ocomm__semiring__0__cancel(t_a),
inference(res,[status(thm),theory(equality)],[11,2434]),
[iquote('0:Res:11.0,2434.0')] ).
cnf(3570,plain,
class_Ring__and__Field_Ocomm__semiring__0(t_a),
inference(res,[status(thm),theory(equality)],[11,2435]),
[iquote('0:Res:11.0,2435.0')] ).
cnf(3571,plain,
class_Ring__and__Field_Ocomm__semiring(t_a),
inference(res,[status(thm),theory(equality)],[11,2436]),
[iquote('0:Res:11.0,2436.0')] ).
cnf(3572,plain,
class_OrderedGroup_Oab__semigroup__mult(t_a),
inference(res,[status(thm),theory(equality)],[11,2437]),
[iquote('0:Res:11.0,2437.0')] ).
cnf(3573,plain,
class_Ring__and__Field_Osemiring__0__cancel(t_a),
inference(res,[status(thm),theory(equality)],[11,2438]),
[iquote('0:Res:11.0,2438.0')] ).
cnf(3574,plain,
class_Ring__and__Field_Osemiring__0(t_a),
inference(res,[status(thm),theory(equality)],[11,2439]),
[iquote('0:Res:11.0,2439.0')] ).
cnf(3575,plain,
class_Ring__and__Field_Oring__1(t_a),
inference(res,[status(thm),theory(equality)],[11,2440]),
[iquote('0:Res:11.0,2440.0')] ).
cnf(3576,plain,
class_Ring__and__Field_Osemiring(t_a),
inference(res,[status(thm),theory(equality)],[11,2441]),
[iquote('0:Res:11.0,2441.0')] ).
cnf(3577,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(res,[status(thm),theory(equality)],[11,2442]),
[iquote('0:Res:11.0,2442.0')] ).
cnf(3578,plain,
class_HOL_Otimes(t_a),
inference(res,[status(thm),theory(equality)],[11,2443]),
[iquote('0:Res:11.0,2443.0')] ).
cnf(3579,plain,
class_OrderedGroup_Ocomm__monoid__add(t_a),
inference(res,[status(thm),theory(equality)],[11,2444]),
[iquote('0:Res:11.0,2444.0')] ).
cnf(3580,plain,
class_HOL_Ozero(t_a),
inference(res,[status(thm),theory(equality)],[11,2445]),
[iquote('0:Res:11.0,2445.0')] ).
cnf(3581,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(t_a),
inference(res,[status(thm),theory(equality)],[11,2446]),
[iquote('0:Res:11.0,2446.0')] ).
cnf(3582,plain,
class_OrderedGroup_Oab__semigroup__add(t_a),
inference(res,[status(thm),theory(equality)],[11,2447]),
[iquote('0:Res:11.0,2447.0')] ).
cnf(3583,plain,
class_OrderedGroup_Ocancel__semigroup__add(t_a),
inference(res,[status(thm),theory(equality)],[11,2448]),
[iquote('0:Res:11.0,2448.0')] ).
cnf(3584,plain,
class_OrderedGroup_Osemigroup__add(t_a),
inference(res,[status(thm),theory(equality)],[11,2449]),
[iquote('0:Res:11.0,2449.0')] ).
cnf(3585,plain,
class_HOL_Oplus(t_a),
inference(res,[status(thm),theory(equality)],[11,2450]),
[iquote('0:Res:11.0,2450.0')] ).
cnf(3586,plain,
class_Ring__and__Field_Oring(t_a),
inference(res,[status(thm),theory(equality)],[11,2451]),
[iquote('0:Res:11.0,2451.0')] ).
cnf(3587,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(t_a),
inference(res,[status(thm),theory(equality)],[11,2452]),
[iquote('0:Res:11.0,2452.0')] ).
cnf(3588,plain,
class_Ring__and__Field_Oordered__semiring__strict(t_a),
inference(res,[status(thm),theory(equality)],[11,2453]),
[iquote('0:Res:11.0,2453.0')] ).
cnf(3589,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(t_a),
inference(res,[status(thm),theory(equality)],[11,2454]),
[iquote('0:Res:11.0,2454.0')] ).
cnf(3590,plain,
class_Orderings_Olinorder(t_a),
inference(res,[status(thm),theory(equality)],[11,2455]),
[iquote('0:Res:11.0,2455.0')] ).
cnf(3591,plain,
class_LOrder_Olorder(t_a),
inference(res,[status(thm),theory(equality)],[11,2456]),
[iquote('0:Res:11.0,2456.0')] ).
cnf(3592,plain,
class_LOrder_Ojoin__semilorder(t_a),
inference(res,[status(thm),theory(equality)],[11,2457]),
[iquote('0:Res:11.0,2457.0')] ).
cnf(3593,plain,
class_LOrder_Omeet__semilorder(t_a),
inference(res,[status(thm),theory(equality)],[11,2458]),
[iquote('0:Res:11.0,2458.0')] ).
cnf(3594,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_a),
inference(res,[status(thm),theory(equality)],[11,2459]),
[iquote('0:Res:11.0,2459.0')] ).
cnf(3595,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(t_a),
inference(res,[status(thm),theory(equality)],[11,2460]),
[iquote('0:Res:11.0,2460.0')] ).
cnf(3596,plain,
class_Ring__and__Field_Opordered__cancel__comm__semiring(t_a),
inference(res,[status(thm),theory(equality)],[11,2461]),
[iquote('0:Res:11.0,2461.0')] ).
cnf(3597,plain,
class_OrderedGroup_Oab__group__add(t_a),
inference(res,[status(thm),theory(equality)],[11,2462]),
[iquote('0:Res:11.0,2462.0')] ).
cnf(3598,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(res,[status(thm),theory(equality)],[11,2463]),
[iquote('0:Res:11.0,2463.0')] ).
cnf(3599,plain,
class_Ring__and__Field_Opordered__comm__semiring(t_a),
inference(res,[status(thm),theory(equality)],[11,2464]),
[iquote('0:Res:11.0,2464.0')] ).
cnf(3600,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(res,[status(thm),theory(equality)],[11,2465]),
[iquote('0:Res:11.0,2465.0')] ).
cnf(3601,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(t_a),
inference(res,[status(thm),theory(equality)],[11,2466]),
[iquote('0:Res:11.0,2466.0')] ).
cnf(3602,plain,
class_Orderings_Oorder(t_a),
inference(res,[status(thm),theory(equality)],[11,2467]),
[iquote('0:Res:11.0,2467.0')] ).
cnf(3603,plain,
class_Orderings_Oord(t_a),
inference(res,[status(thm),theory(equality)],[11,2468]),
[iquote('0:Res:11.0,2468.0')] ).
cnf(3604,plain,
class_Ring__and__Field_Oaxclass__abs__if(t_a),
inference(res,[status(thm),theory(equality)],[11,2469]),
[iquote('0:Res:11.0,2469.0')] ).
cnf(3605,plain,
class_Ring__and__Field_Oordered__ring__strict(t_a),
inference(res,[status(thm),theory(equality)],[11,2470]),
[iquote('0:Res:11.0,2470.0')] ).
cnf(3606,plain,
class_Ring__and__Field_Olordered__ring(t_a),
inference(res,[status(thm),theory(equality)],[11,2471]),
[iquote('0:Res:11.0,2471.0')] ).
cnf(3607,plain,
class_Ring__and__Field_Opordered__ring(t_a),
inference(res,[status(thm),theory(equality)],[11,2472]),
[iquote('0:Res:11.0,2472.0')] ).
cnf(3608,plain,
class_HOL_Ominus(t_a),
inference(res,[status(thm),theory(equality)],[11,2473]),
[iquote('0:Res:11.0,2473.0')] ).
cnf(3609,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[11,2474]),
[iquote('0:Res:11.0,2474.0')] ).
cnf(3610,plain,
class_OrderedGroup_Olordered__ab__group__meet(t_a),
inference(res,[status(thm),theory(equality)],[11,2475]),
[iquote('0:Res:11.0,2475.0')] ).
cnf(3611,plain,
class_OrderedGroup_Olordered__ab__group__join(t_a),
inference(res,[status(thm),theory(equality)],[11,2476]),
[iquote('0:Res:11.0,2476.0')] ).
cnf(3612,plain,
class_OrderedGroup_Olordered__ab__group(t_a),
inference(res,[status(thm),theory(equality)],[11,2477]),
[iquote('0:Res:11.0,2477.0')] ).
cnf(3613,plain,
class_OrderedGroup_Opordered__ab__group__add(t_a),
inference(res,[status(thm),theory(equality)],[11,2478]),
[iquote('0:Res:11.0,2478.0')] ).
cnf(3614,plain,
class_Ring__and__Field_Oordered__semidom(t_a),
inference(res,[status(thm),theory(equality)],[11,2479]),
[iquote('0:Res:11.0,2479.0')] ).
cnf(3615,plain,
class_Ring__and__Field_Oaxclass__no__zero__divisors(t_a),
inference(res,[status(thm),theory(equality)],[11,2480]),
[iquote('0:Res:11.0,2480.0')] ).
cnf(3616,plain,
class_Ring__and__Field_Oidom(t_a),
inference(res,[status(thm),theory(equality)],[11,2481]),
[iquote('0:Res:11.0,2481.0')] ).
cnf(3617,plain,
class_Ring__and__Field_Ocomm__semiring__1__cancel(t_a),
inference(res,[status(thm),theory(equality)],[11,2482]),
[iquote('0:Res:11.0,2482.0')] ).
cnf(3618,plain,
class_Ring__and__Field_Ocomm__semiring__1(t_a),
inference(res,[status(thm),theory(equality)],[11,2483]),
[iquote('0:Res:11.0,2483.0')] ).
cnf(3619,plain,
class_OrderedGroup_Ocomm__monoid__mult(t_a),
inference(res,[status(thm),theory(equality)],[11,2484]),
[iquote('0:Res:11.0,2484.0')] ).
cnf(3620,plain,
class_Ring__and__Field_Osemiring__1__cancel(t_a),
inference(res,[status(thm),theory(equality)],[11,2485]),
[iquote('0:Res:11.0,2485.0')] ).
cnf(4097,plain,
( ~ class_Orderings_Oorder(t_a)
| c_lessequals(v_x,v_c,t_a) ),
inference(res,[status(thm),theory(equality)],[2803,2]),
[iquote('0:Res:2803.0,2.1')] ).
cnf(7199,plain,
c_lessequals(v_x,v_c,t_a),
inference(mrr,[status(thm)],[4097,3602]),
[iquote('0:MRR:4097.0,3602.0')] ).
cnf(27199,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ c_lessequals(v_x,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ),
inference(spl,[status(thm),theory(equality)],[2900,3104]),
[iquote('0:SpL:2900.1,3104.0')] ).
cnf(27201,plain,
~ c_lessequals(v_x,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(ssi,[status(thm)],[27199,11,3604,3615,3566,3593,3592,3591,3589,3567,3611,3610,3599,3608,3595,3572,3600,3619,3596,3571,3565,3607,3601,3598,3575,3564,3620,3618,3569,3570,3588,3568,3594,3586,3616,3606,3587,3573,3581,3574,3576,3577,3609,3583,3602,3617,3580,3578,3582,3612,3579,3603,3584,3597,3585,3613,3563,3614,3590,3605]),
[iquote('0:SSi:27199.0,11.0,3604.0,3615.0,3566.0,3593.0,3592.0,3591.0,3589.0,3567.0,3611.0,3610.0,3599.0,3608.0,3595.0,3572.0,3600.0,3619.0,3596.0,3571.0,3565.0,3607.0,3601.0,3598.0,3575.0,3564.0,3620.0,3618.0,3569.0,3570.0,3588.0,3568.0,3594.0,3586.0,3616.0,3606.0,3587.0,3573.0,3581.0,3574.0,3576.0,3577.0,3609.0,3583.0,3602.0,3617.0,3580.0,3578.0,3582.0,3612.0,3579.0,3603.0,3584.0,3597.0,3585.0,3613.0,3563.0,3614.0,3590.0,3605.0')] ).
cnf(122940,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ c_lessequals(v_x,v_c,t_a)
| ~ c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(res,[status(thm),theory(equality)],[3245,27201]),
[iquote('0:Res:3245.3,27201.0')] ).
cnf(122954,plain,
( ~ c_lessequals(v_x,v_c,t_a)
| ~ c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(ssi,[status(thm)],[122940,11,3604,3615,3566,3593,3592,3591,3589,3567,3611,3610,3599,3608,3595,3572,3600,3619,3596,3571,3565,3607,3601,3598,3575,3564,3620,3618,3569,3570,3588,3568,3594,3586,3616,3606,3587,3573,3581,3574,3576,3577,3609,3583,3602,3617,3580,3578,3582,3612,3579,3603,3584,3597,3585,3613,3563,3614,3590,3605]),
[iquote('0:SSi:122940.0,11.0,3604.0,3615.0,3566.0,3593.0,3592.0,3591.0,3589.0,3567.0,3611.0,3610.0,3599.0,3608.0,3595.0,3572.0,3600.0,3619.0,3596.0,3571.0,3565.0,3607.0,3601.0,3598.0,3575.0,3564.0,3620.0,3618.0,3569.0,3570.0,3588.0,3568.0,3594.0,3586.0,3616.0,3606.0,3587.0,3573.0,3581.0,3574.0,3576.0,3577.0,3609.0,3583.0,3602.0,3617.0,3580.0,3578.0,3582.0,3612.0,3579.0,3603.0,3584.0,3597.0,3585.0,3613.0,3563.0,3614.0,3590.0,3605.0')] ).
cnf(122955,plain,
~ c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a),
inference(mrr,[status(thm)],[122954,7199]),
[iquote('0:MRR:122954.0,7199.0')] ).
cnf(122971,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[2931,122955]),
[iquote('0:Res:2931.1,122955.0')] ).
cnf(122973,plain,
$false,
inference(ssi,[status(thm)],[122971,11,3604,3615,3566,3593,3592,3591,3589,3567,3611,3610,3599,3608,3595,3572,3600,3619,3596,3571,3565,3607,3601,3598,3575,3564,3620,3618,3569,3570,3588,3568,3594,3586,3616,3606,3587,3573,3581,3574,3576,3577,3609,3583,3602,3617,3580,3578,3582,3612,3579,3603,3584,3597,3585,3613,3563,3614,3590,3605]),
[iquote('0:SSi:122971.0,11.0,3604.0,3615.0,3566.0,3593.0,3592.0,3591.0,3589.0,3567.0,3611.0,3610.0,3599.0,3608.0,3595.0,3572.0,3600.0,3619.0,3596.0,3571.0,3565.0,3607.0,3601.0,3598.0,3575.0,3564.0,3620.0,3618.0,3569.0,3570.0,3588.0,3568.0,3594.0,3586.0,3616.0,3606.0,3587.0,3573.0,3581.0,3574.0,3576.0,3577.0,3609.0,3583.0,3602.0,3617.0,3580.0,3578.0,3582.0,3612.0,3579.0,3603.0,3584.0,3597.0,3585.0,3613.0,3563.0,3614.0,3590.0,3605.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ANA020-1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Fri Jul 8 03:23:44 EDT 2022
% 0.11/0.32 % CPUTime :
% 84.12/84.38
% 84.12/84.38 SPASS V 3.9
% 84.12/84.38 SPASS beiseite: Proof found.
% 84.12/84.38 % SZS status Theorem
% 84.12/84.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 84.12/84.38 SPASS derived 94843 clauses, backtracked 40 clauses, performed 2 splits and kept 20301 clauses.
% 84.12/84.38 SPASS allocated 159565 KBytes.
% 84.12/84.38 SPASS spent 0:1:23.92 on the problem.
% 84.12/84.38 0:00:00.23 for the input.
% 84.12/84.38 0:00:00.00 for the FLOTTER CNF translation.
% 84.12/84.38 0:00:02.40 for inferences.
% 84.12/84.38 0:00:00.09 for the backtracking.
% 84.12/84.38 0:1:17.92 for the reduction.
% 84.12/84.38
% 84.12/84.38
% 84.12/84.38 Here is a proof with depth 3, length 140 :
% 84.12/84.38 % SZS output start Refutation
% See solution above
% 84.12/84.39 Formulae used in the proof : cls_Orderings_Oorder__less__imp__le_0 cls_Ring__and__Field_Omult__nonneg__nonneg_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_3 cls_conjecture_4 tfree_tcs cls_OrderedGroup_Oabs__eq__0_1 cls_OrderedGroup_Oabs__ge__zero_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
% 87.32/87.52
%------------------------------------------------------------------------------