TSTP Solution File: SET825-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET825-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 05:28:56 EDT 2022
% Result : Unsatisfiable 0.23s 0.44s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 11 unt; 4 nHn; 18 RR)
% Number of literals : 29 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
c_in(c_Pair(u,u,v,v),c_Relation_OId,tc_prod(v,v)),
file('SET825-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(c_Pair(u,v,w,w),c_Relation_OId,tc_prod(w,w))
| equal(u,v) ),
file('SET825-2.p',unknown),
[] ).
cnf(3,axiom,
v_Q(v_n),
file('SET825-2.p',unknown),
[] ).
cnf(4,axiom,
~ v_Q(v_m),
file('SET825-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(u),v_xa(u),tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat)) ),
file('SET825-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(u)),c_Suc(v_xa(u)),tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat)) ),
file('SET825-2.p',unknown),
[] ).
cnf(8,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| equal(v_xa(c_Relation_OId),v_x(c_Relation_OId)) ),
inference(res,[status(thm),theory(equality)],[5,2]),
[iquote('0:Res:5.2,2.0')] ).
cnf(9,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| equal(v_xa(c_Relation_OId),v_x(c_Relation_OId)) ),
inference(mrr,[status(thm)],[8,1]),
[iquote('0:MRR:8.0,1.0')] ).
cnf(10,plain,
( equal(v_xa(c_Relation_OId),v_x(c_Relation_OId))
| equal(v_m,v_n) ),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.0,2.0')] ).
cnf(12,plain,
equal(v_m,v_n),
inference(spt,[spt(split,[position(s1)])],[10]),
[iquote('1:Spt:10.1')] ).
cnf(13,plain,
~ v_Q(v_n),
inference(rew,[status(thm),theory(equality)],[12,4]),
[iquote('1:Rew:12.0,4.0')] ).
cnf(16,plain,
$false,
inference(mrr,[status(thm)],[13,3]),
[iquote('1:MRR:13.0,3.0')] ).
cnf(17,plain,
~ equal(v_m,v_n),
inference(spt,[spt(split,[position(sa)])],[16,12]),
[iquote('1:Spt:16.0,10.1,12.0')] ).
cnf(18,plain,
equal(v_xa(c_Relation_OId),v_x(c_Relation_OId)),
inference(spt,[spt(split,[position(s2)])],[10]),
[iquote('1:Spt:16.0,10.0')] ).
cnf(22,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(spl,[status(thm),theory(equality)],[18,6]),
[iquote('1:SpL:18.0,6.1')] ).
cnf(23,plain,
c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
inference(mrr,[status(thm)],[22,1]),
[iquote('1:MRR:22.0,22.1,1.0,1.0')] ).
cnf(24,plain,
equal(v_m,v_n),
inference(res,[status(thm),theory(equality)],[23,2]),
[iquote('1:Res:23.0,2.0')] ).
cnf(25,plain,
$false,
inference(mrr,[status(thm)],[24,17]),
[iquote('1:MRR:24.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET825-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.15 % Command : run_spass %d %s
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sun Jul 10 06:26:11 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.23/0.44
% 0.23/0.44 SPASS V 3.9
% 0.23/0.44 SPASS beiseite: Proof found.
% 0.23/0.44 % SZS status Theorem
% 0.23/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.44 SPASS derived 13 clauses, backtracked 5 clauses, performed 1 splits and kept 19 clauses.
% 0.23/0.44 SPASS allocated 63111 KBytes.
% 0.23/0.44 SPASS spent 0:00:00.06 on the problem.
% 0.23/0.44 0:00:00.03 for the input.
% 0.23/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.44 0:00:00.00 for inferences.
% 0.23/0.44 0:00:00.00 for the backtracking.
% 0.23/0.44 0:00:00.00 for the reduction.
% 0.23/0.44
% 0.23/0.44
% 0.23/0.44 Here is a proof with depth 5, length 18 :
% 0.23/0.44 % SZS output start Refutation
% See solution above
% 0.23/0.44 Formulae used in the proof : cls_Relation_OIdI_0 cls_Relation_Opair__in__Id__conv__iff1_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.23/0.44
%------------------------------------------------------------------------------