%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA037-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 19:28:59 EDT 2022
% Result : Unsatisfiable 0.21s 0.41s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 11 unt; 0 nHn; 21 RR)
% Number of literals : 37 ( 0 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_Orderings_Olinorder(u)
| c_lessequals(v,c_Orderings_Omax(v,w,u),u) ),
file('ANA037-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
file('ANA037-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(c_0,x,u)
| c_lessequals(c_times(v,x,u),c_times(w,x,u),u) ),
file('ANA037-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Olinorder(u) ),
file('ANA037-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__semiring(u) ),
file('ANA037-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Oorder(u) ),
file('ANA037-2.p',unknown),
[] ).
cnf(7,axiom,
c_lessequals(c_0,v(v_xa),t_b),
file('ANA037-2.p',unknown),
[] ).
cnf(8,axiom,
c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),c_times(v_c,v(v_xa),t_b),t_b),
file('ANA037-2.p',unknown),
[] ).
cnf(9,axiom,
~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),c_times(c_Orderings_Omax(v_c,v_ca,t_b),v(v_xa),t_b),t_b),
file('ANA037-2.p',unknown),
[] ).
cnf(10,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA037-2.p',unknown),
[] ).
cnf(11,plain,
class_Orderings_Olinorder(t_b),
inference(res,[status(thm),theory(equality)],[10,4]),
[iquote('0:Res:10.0,4.0')] ).
cnf(12,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(res,[status(thm),theory(equality)],[10,5]),
[iquote('0:Res:10.0,5.0')] ).
cnf(13,plain,
class_Orderings_Oorder(t_b),
inference(res,[status(thm),theory(equality)],[10,6]),
[iquote('0:Res:10.0,6.0')] ).
cnf(21,plain,
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(u,c_times(c_Orderings_Omax(v_c,v_ca,t_b),v(v_xa),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),u,t_b) ),
inference(res,[status(thm),theory(equality)],[2,9]),
[iquote('0:Res:2.3,9.0')] ).
cnf(26,plain,
( ~ c_lessequals(u,c_times(c_Orderings_Omax(v_c,v_ca,t_b),v(v_xa),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_a(v_xa),t_b),u,t_b) ),
inference(mrr,[status(thm)],[21,13]),
[iquote('0:MRR:21.0,13.0')] ).
cnf(27,plain,
~ c_lessequals(c_times(v_c,v(v_xa),t_b),c_times(c_Orderings_Omax(v_c,v_ca,t_b),v(v_xa),t_b),t_b),
inference(res,[status(thm),theory(equality)],[8,26]),
[iquote('0:Res:8.0,26.1')] ).
cnf(60,plain,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(v_c,c_Orderings_Omax(v_c,v_ca,t_b),t_b)
| ~ c_lessequals(c_0,v(v_xa),t_b) ),
inference(res,[status(thm),theory(equality)],[3,27]),
[iquote('0:Res:3.3,27.0')] ).
cnf(61,plain,
( ~ c_lessequals(v_c,c_Orderings_Omax(v_c,v_ca,t_b),t_b)
| ~ c_lessequals(c_0,v(v_xa),t_b) ),
inference(ssi,[status(thm)],[60,10,13,12,11]),
[iquote('0:SSi:60.0,10.0,13.0,12.0,11.0')] ).
cnf(62,plain,
~ c_lessequals(v_c,c_Orderings_Omax(v_c,v_ca,t_b),t_b),
inference(mrr,[status(thm)],[61,7]),
[iquote('0:MRR:61.1,7.0')] ).
cnf(63,plain,
~ class_Orderings_Olinorder(t_b),
inference(res,[status(thm),theory(equality)],[1,62]),
[iquote('0:Res:1.1,62.0')] ).
cnf(64,plain,
$false,
inference(ssi,[status(thm)],[63,10,13,12,11]),
[iquote('0:SSi:63.0,10.0,13.0,12.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA037-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 04:43:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.41
% 0.21/0.41 SPASS V 3.9
% 0.21/0.41 SPASS beiseite: Proof found.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.41 SPASS derived 29 clauses, backtracked 0 clauses, performed 0 splits and kept 30 clauses.
% 0.21/0.41 SPASS allocated 75662 KBytes.
% 0.21/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.21/0.41 0:00:00.04 for the input.
% 0.21/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.41 0:00:00.00 for inferences.
% 0.21/0.41 0:00:00.00 for the backtracking.
% 0.21/0.41 0:00:00.00 for the reduction.
% 0.21/0.41
% 0.21/0.41
% 0.21/0.41 Here is a proof with depth 4, length 21 :
% 0.21/0.41 % SZS output start Refutation
% See solution above
% 0.21/0.41 Formulae used in the proof : cls_Orderings_Ole__maxI1_0 cls_Orderings_Oorder__class_Oorder__trans_0 cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0 clsrel_Ring__and__Field_Oordered__idom_33 clsrel_Ring__and__Field_Oordered__idom_42 clsrel_Ring__and__Field_Oordered__idom_44 cls_conjecture_2 cls_conjecture_4 cls_conjecture_8 tfree_tcs
% 0.21/0.41
%------------------------------------------------------------------------------