TSTP Solution File: SET822-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET822-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 05:28:54 EDT 2022
% Result : Unsatisfiable 0.70s 0.89s
% Output : Refutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 6 unt; 0 nHn; 10 RR)
% Number of literals : 14 ( 0 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v_P(v(v_b)),
file('SET822-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(v(u),v,tc_IntDef_Oint)
| c_in(v_x(u,v),v,tc_IntDef_Oint) ),
file('SET822-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ v_P(v_x(u,v))
| ~ c_in(v(u),v,tc_IntDef_Oint) ),
file('SET822-1.p',unknown),
[] ).
cnf(179,axiom,
c_in(u,c_insert(u,v,w),w),
file('SET822-1.p',unknown),
[] ).
cnf(306,axiom,
( ~ c_in(u,c_insert(v,c_emptyset,w),w)
| equal(u,v) ),
file('SET822-1.p',unknown),
[] ).
cnf(1510,plain,
~ v_P(v_x(u,c_insert(v(u),v,tc_IntDef_Oint))),
inference(res,[status(thm),theory(equality)],[179,3]),
[iquote('0:Res:179.0,3.1')] ).
cnf(1527,plain,
( ~ c_in(v(u),c_insert(v,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)
| equal(v_x(u,c_insert(v,c_emptyset,tc_IntDef_Oint)),v) ),
inference(res,[status(thm),theory(equality)],[2,306]),
[iquote('0:Res:2.1,306.0')] ).
cnf(2176,plain,
equal(v_x(u,c_insert(v(u),c_emptyset,tc_IntDef_Oint)),v(u)),
inference(res,[status(thm),theory(equality)],[179,1527]),
[iquote('0:Res:179.0,1527.0')] ).
cnf(2186,plain,
~ v_P(v(u)),
inference(spl,[status(thm),theory(equality)],[2176,1510]),
[iquote('0:SpL:2176.0,1510.0')] ).
cnf(2188,plain,
$false,
inference(unc,[status(thm)],[2186,1]),
[iquote('0:UnC:2186.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET822-1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n021.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 : Sat Jul 9 16:55:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.70/0.89
% 0.70/0.89 SPASS V 3.9
% 0.70/0.89 SPASS beiseite: Proof found.
% 0.70/0.89 % SZS status Theorem
% 0.70/0.89 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.70/0.89 SPASS derived 706 clauses, backtracked 0 clauses, performed 0 splits and kept 1576 clauses.
% 0.70/0.89 SPASS allocated 78584 KBytes.
% 0.70/0.89 SPASS spent 0:00:00.53 on the problem.
% 0.70/0.89 0:00:00.09 for the input.
% 0.70/0.89 0:00:00.00 for the FLOTTER CNF translation.
% 0.70/0.89 0:00:00.05 for inferences.
% 0.70/0.89 0:00:00.00 for the backtracking.
% 0.70/0.89 0:00:00.18 for the reduction.
% 0.70/0.89
% 0.70/0.89
% 0.70/0.89 Here is a proof with depth 3, length 10 :
% 0.70/0.89 % SZS output start Refutation
% See solution above
% 0.70/0.89 Formulae used in the proof : cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_Set_OinsertCI_1 cls_Set_OsingletonD__dest_0
% 0.70/0.89
%------------------------------------------------------------------------------