TSTP Solution File: SET821-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET821-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 0.13s 0.41s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 17 unt; 7 nHn; 29 RR)
% Number of literals : 45 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_less(v,v,u) ),
file('SET821-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,v,w)
| ~ c_in(u,c_uminus(v,tc_set(w)),w) ),
file('SET821-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_insert(x,v,w),w) ),
file('SET821-2.p',unknown),
[] ).
cnf(5,axiom,
c_in(u,c_insert(u,v,w),w),
file('SET821-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(u,c_insert(v,w,x),x)
| equal(u,v)
| c_in(u,w,x) ),
file('SET821-2.p',unknown),
[] ).
cnf(7,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('SET821-2.p',unknown),
[] ).
cnf(8,axiom,
c_less(v_a,v_b,tc_IntDef_Oint),
file('SET821-2.p',unknown),
[] ).
cnf(9,axiom,
c_less(v_b,v_c,tc_IntDef_Oint),
file('SET821-2.p',unknown),
[] ).
cnf(10,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('SET821-2.p',unknown),
[] ).
cnf(11,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)],[5,10]),
[iquote('0:Res:5.0,10.0')] ).
cnf(17,plain,
( c_in(v_a,c_insert(v_b,u,tc_IntDef_Oint),tc_IntDef_Oint)
| equal(v_c,v_b)
| c_in(v_c,u,tc_IntDef_Oint) ),
inference(res,[status(thm),theory(equality)],[11,6]),
[iquote('0:Res:11.1,6.0')] ).
cnf(18,plain,
equal(v_c,v_b),
inference(spt,[spt(split,[position(s1)])],[17]),
[iquote('1:Spt:17.1')] ).
cnf(19,plain,
c_less(v_b,v_b,tc_IntDef_Oint),
inference(rew,[status(thm),theory(equality)],[18,9]),
[iquote('1:Rew:18.0,9.0')] ).
cnf(26,plain,
~ class_Orderings_Oorder(tc_IntDef_Oint),
inference(res,[status(thm),theory(equality)],[19,1]),
[iquote('1:Res:19.0,1.1')] ).
cnf(27,plain,
$false,
inference(ssi,[status(thm)],[26,7]),
[iquote('1:SSi:26.0,7.0')] ).
cnf(28,plain,
~ equal(v_c,v_b),
inference(spt,[spt(split,[position(sa)])],[27,18]),
[iquote('1:Spt:27.0,17.1,18.0')] ).
cnf(29,plain,
( c_in(v_a,c_insert(v_b,u,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_c,u,tc_IntDef_Oint) ),
inference(spt,[spt(split,[position(s2)])],[17]),
[iquote('1:Spt:27.0,17.0,17.2')] ).
cnf(30,plain,
( c_in(v_c,u,tc_IntDef_Oint)
| equal(v_b,v_a)
| c_in(v_a,u,tc_IntDef_Oint) ),
inference(res,[status(thm),theory(equality)],[29,6]),
[iquote('1:Res:29.0,6.0')] ).
cnf(32,plain,
equal(v_b,v_a),
inference(spt,[spt(split,[position(s2s1)])],[30]),
[iquote('2:Spt:30.1')] ).
cnf(33,plain,
c_less(v_a,v_a,tc_IntDef_Oint),
inference(rew,[status(thm),theory(equality)],[32,8]),
[iquote('2:Rew:32.0,8.0')] ).
cnf(41,plain,
~ class_Orderings_Oorder(tc_IntDef_Oint),
inference(res,[status(thm),theory(equality)],[33,1]),
[iquote('2:Res:33.0,1.1')] ).
cnf(42,plain,
$false,
inference(ssi,[status(thm)],[41,7]),
[iquote('2:SSi:41.0,7.0')] ).
cnf(43,plain,
~ equal(v_b,v_a),
inference(spt,[spt(split,[position(s2sa)])],[42,32]),
[iquote('2:Spt:42.0,30.1,32.0')] ).
cnf(44,plain,
( c_in(v_c,u,tc_IntDef_Oint)
| c_in(v_a,u,tc_IntDef_Oint) ),
inference(spt,[spt(split,[position(s2s2)])],[30]),
[iquote('2:Spt:42.0,30.0,30.2')] ).
cnf(45,plain,
( ~ c_in(v_c,u,tc_IntDef_Oint)
| c_in(v_a,c_uminus(u,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(res,[status(thm),theory(equality)],[44,2]),
[iquote('2:Res:44.0,2.1')] ).
cnf(48,plain,
( ~ c_in(v_c,u,tc_IntDef_Oint)
| ~ c_in(v_a,u,tc_IntDef_Oint) ),
inference(res,[status(thm),theory(equality)],[45,2]),
[iquote('2:Res:45.1,2.1')] ).
cnf(49,plain,
~ c_in(v_a,c_insert(v_c,u,tc_IntDef_Oint),tc_IntDef_Oint),
inference(res,[status(thm),theory(equality)],[5,48]),
[iquote('2:Res:5.0,48.0')] ).
cnf(54,plain,
~ c_in(v_a,u,tc_IntDef_Oint),
inference(res,[status(thm),theory(equality)],[4,49]),
[iquote('2:Res:4.1,49.0')] ).
cnf(56,plain,
$false,
inference(unc,[status(thm)],[54,5]),
[iquote('2:UnC:54.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET821-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n007.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 : Mon Jul 11 02:05:47 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.41
% 0.13/0.41 SPASS V 3.9
% 0.13/0.41 SPASS beiseite: Proof found.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41 SPASS derived 38 clauses, backtracked 16 clauses, performed 2 splits and kept 45 clauses.
% 0.13/0.41 SPASS allocated 75629 KBytes.
% 0.13/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.13/0.41 0:00:00.03 for the input.
% 0.13/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.41 0:00:00.00 for inferences.
% 0.13/0.41 0:00:00.00 for the backtracking.
% 0.13/0.41 0:00:00.00 for the reduction.
% 0.13/0.41
% 0.13/0.41
% 0.13/0.41 Here is a proof with depth 9, length 29 :
% 0.13/0.41 % SZS output start Refutation
% See solution above
% 0.13/0.41 Formulae used in the proof : cls_Orderings_Oorder__less__irrefl__iff1_0 cls_Set_OComplD__dest_0 cls_Set_OinsertCI_0 cls_Set_OinsertCI_1 cls_Set_OinsertE_0 clsarity_IntDef__Oint_31 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.13/0.41
%------------------------------------------------------------------------------