%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA035-2 : 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 19:28:57 EDT 2022
% Result : Unsatisfiable 0.35s 0.52s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 6 unt; 0 nHn; 18 RR)
% Number of literals : 33 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(u)
| equal(c_times(v,w,u),c_times(w,v,u)) ),
file('ANA035-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(u)
| equal(c_times(v,c_times(w,x,u),u),c_times(w,c_times(v,x,u),u)) ),
file('ANA035-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| equal(c_times(c_HOL_Oabs(v,u),c_HOL_Oabs(w,u),u),c_HOL_Oabs(c_times(v,w,u),u)) ),
file('ANA035-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oab__semigroup__mult(u) ),
file('ANA035-2.p',unknown),
[] ).
cnf(5,axiom,
~ equal(c_times(c_times(v_c,c_HOL_Oabs(v(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v(v_x),v_g(v_x),t_b),t_b),t_b)),
file('ANA035-2.p',unknown),
[] ).
cnf(6,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA035-2.p',unknown),
[] ).
cnf(7,plain,
equal(c_times(c_HOL_Oabs(u,t_b),c_HOL_Oabs(v,t_b),t_b),c_HOL_Oabs(c_times(u,v,t_b),t_b)),
inference(res,[status(thm),theory(equality)],[6,3]),
[iquote('0:Res:6.0,3.0')] ).
cnf(8,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.0,4.0')] ).
cnf(156,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(u)
| ~ class_OrderedGroup_Oab__semigroup__mult(u)
| equal(c_times(c_times(v,w,u),x,u),c_times(v,c_times(x,w,u),u)) ),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.1,1.1')] ).
cnf(169,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(u)
| ~ class_OrderedGroup_Oab__semigroup__mult(u)
| equal(c_times(v,c_times(w,x,u),u),c_times(w,c_times(x,v,u),u)) ),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.1,2.1')] ).
cnf(172,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(u)
| equal(c_times(v,c_times(w,x,u),u),c_times(w,c_times(x,v,u),u)) ),
inference(obv,[status(thm),theory(equality)],[169]),
[iquote('0:Obv:169.0')] ).
cnf(176,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(u)
| equal(c_times(c_times(v,w,u),x,u),c_times(v,c_times(x,w,u),u)) ),
inference(obv,[status(thm),theory(equality)],[156]),
[iquote('0:Obv:156.0')] ).
cnf(207,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(u)
| ~ class_OrderedGroup_Oab__semigroup__mult(u)
| equal(c_times(v,c_times(w,x,u),u),c_times(v,c_times(x,w,u),u)) ),
inference(spr,[status(thm),theory(equality)],[172,2]),
[iquote('0:SpR:172.1,2.1')] ).
cnf(253,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(u)
| equal(c_times(v,c_times(w,x,u),u),c_times(v,c_times(x,w,u),u)) ),
inference(obv,[status(thm),theory(equality)],[207]),
[iquote('0:Obv:207.0')] ).
cnf(691,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ equal(c_times(v_c,c_times(c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),c_HOL_Oabs(v(v_x),t_b),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v(v_x),v_g(v_x),t_b),t_b),t_b)) ),
inference(spl,[status(thm),theory(equality)],[176,5]),
[iquote('0:SpL:176.1,5.0')] ).
cnf(692,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ equal(c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v(v_x),v_g(v_x),t_b),t_b),t_b),t_b),c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v(v_x),v_g(v_x),t_b),t_b),t_b),t_b)) ),
inference(rew,[status(thm),theory(equality)],[7,691,253,172,176]),
[iquote('0:Rew:7.0,691.1,253.1,691.1,172.1,691.1,253.1,691.1,253.1,691.1,176.1,691.1')] ).
cnf(693,plain,
~ class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(obv,[status(thm),theory(equality)],[692]),
[iquote('0:Obv:692.1')] ).
cnf(694,plain,
$false,
inference(ssi,[status(thm)],[693,6,8]),
[iquote('0:SSi:693.0,6.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA035-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.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 : Fri Jul 8 05:34:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.35/0.52
% 0.35/0.52 SPASS V 3.9
% 0.35/0.52 SPASS beiseite: Proof found.
% 0.35/0.52 % SZS status Theorem
% 0.35/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/0.52 SPASS derived 330 clauses, backtracked 0 clauses, performed 0 splits and kept 61 clauses.
% 0.35/0.52 SPASS allocated 76194 KBytes.
% 0.35/0.52 SPASS spent 0:00:00.16 on the problem.
% 0.35/0.52 0:00:00.03 for the input.
% 0.35/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.35/0.52 0:00:00.01 for inferences.
% 0.35/0.52 0:00:00.00 for the backtracking.
% 0.35/0.52 0:00:00.09 for the reduction.
% 0.35/0.52
% 0.35/0.52
% 0.35/0.52 Here is a proof with depth 2, length 18 :
% 0.35/0.52 % SZS output start Refutation
% See solution above
% 0.35/0.52 Formulae used in the proof : cls_OrderedGroup_Omult__ac__2_0 cls_OrderedGroup_Omult__ac__3_0 cls_Ring__and__Field_Oabs__mult_0 clsrel_Ring__and__Field_Oordered__idom_17 cls_conjecture_4 tfree_tcs
% 0.35/0.52
%------------------------------------------------------------------------------