TSTP Solution File: SET825-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET825-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 2.98s 3.19s
% Output : Refutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 14 ( 7 unt; 3 nHn; 14 RR)
% Number of literals : 24 ( 0 equ; 9 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,
v_Q(v_n),
file('SET825-1.p',unknown),
[] ).
cnf(2,axiom,
~ v_Q(v_m),
file('SET825-1.p',unknown),
[] ).
cnf(3,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('SET825-1.p',unknown),
[] ).
cnf(4,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('SET825-1.p',unknown),
[] ).
cnf(130,axiom,
c_in(c_Pair(u,u,v,v),c_Relation_OId,tc_prod(v,v)),
file('SET825-1.p',unknown),
[] ).
cnf(135,axiom,
( ~ c_in(c_Pair(u,v,w,w),c_Relation_OId,tc_prod(w,w))
| equal(u,v) ),
file('SET825-1.p',unknown),
[] ).
cnf(1374,plain,
( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(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(res,[status(thm),theory(equality)],[130,4]),
[iquote('0:Res:130.0,4.1')] ).
cnf(5010,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)],[3,135]),
[iquote('0:Res:3.2,135.0')] ).
cnf(5026,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)],[5010,130]),
[iquote('0:MRR:5010.0,130.0')] ).
cnf(5028,plain,
( ~ 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(rew,[status(thm),theory(equality)],[5026,1374]),
[iquote('0:Rew:5026.1,1374.0')] ).
cnf(5029,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)],[5028,130]),
[iquote('0:MRR:5028.0,130.0')] ).
cnf(5034,plain,
equal(v_m,v_n),
inference(res,[status(thm),theory(equality)],[5029,135]),
[iquote('0:Res:5029.0,135.0')] ).
cnf(5040,plain,
~ v_Q(v_n),
inference(rew,[status(thm),theory(equality)],[5034,2]),
[iquote('0:Rew:5034.0,2.0')] ).
cnf(5075,plain,
$false,
inference(mrr,[status(thm)],[5040,1]),
[iquote('0:MRR:5040.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET825-1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 03:52:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.98/3.19
% 2.98/3.19 SPASS V 3.9
% 2.98/3.19 SPASS beiseite: Proof found.
% 2.98/3.19 % SZS status Theorem
% 2.98/3.19 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.98/3.19 SPASS derived 3090 clauses, backtracked 24 clauses, performed 1 splits and kept 2945 clauses.
% 2.98/3.19 SPASS allocated 82836 KBytes.
% 2.98/3.19 SPASS spent 0:00:02.73 on the problem.
% 2.98/3.19 0:00:00.09 for the input.
% 2.98/3.19 0:00:00.00 for the FLOTTER CNF translation.
% 2.98/3.19 0:00:00.19 for inferences.
% 2.98/3.19 0:00:00.00 for the backtracking.
% 2.98/3.19 0:00:02.15 for the reduction.
% 2.98/3.19
% 2.98/3.19
% 2.98/3.19 Here is a proof with depth 2, length 14 :
% 2.98/3.19 % SZS output start Refutation
% See solution above
% 2.98/3.19 Formulae used in the proof : cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_Relation_OIdI_0 cls_Relation_Opair__in__Id__conv__iff1_0
% 2.98/3.19
%------------------------------------------------------------------------------