TSTP Solution File: SET822-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET822-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 7 unt; 2 nHn; 12 RR)
% Number of literals : 19 ( 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 : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_in(u,c_emptyset,v),
file('SET822-2.p',unknown),
[] ).
cnf(2,axiom,
c_in(u,c_insert(u,v,w),w),
file('SET822-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,c_insert(v,w,x),x)
| equal(u,v)
| c_in(u,w,x) ),
file('SET822-2.p',unknown),
[] ).
cnf(4,axiom,
v_P(v(v_b)),
file('SET822-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(v(u),v,tc_IntDef_Oint)
| c_in(v_x(u,v),v,tc_IntDef_Oint) ),
file('SET822-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ v_P(v_x(u,v))
| ~ c_in(v(u),v,tc_IntDef_Oint) ),
file('SET822-2.p',unknown),
[] ).
cnf(7,plain,
~ v_P(v_x(u,c_insert(v(u),v,tc_IntDef_Oint))),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.0,6.1')] ).
cnf(10,plain,
( ~ c_in(v(u),c_insert(v,w,tc_IntDef_Oint),tc_IntDef_Oint)
| equal(v_x(u,c_insert(v,w,tc_IntDef_Oint)),v)
| c_in(v_x(u,c_insert(v,w,tc_IntDef_Oint)),w,tc_IntDef_Oint) ),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.1,3.0')] ).
cnf(11,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)],[10,1]),
[iquote('0:Res:10.2,1.0')] ).
cnf(13,plain,
equal(v_x(u,c_insert(v(u),c_emptyset,tc_IntDef_Oint)),v(u)),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.0,11.0')] ).
cnf(19,plain,
~ v_P(v(u)),
inference(spl,[status(thm),theory(equality)],[13,7]),
[iquote('0:SpL:13.0,7.0')] ).
cnf(20,plain,
$false,
inference(unc,[status(thm)],[19,4]),
[iquote('0:UnC:19.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SET822-2 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jul 11 11:03:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.42
% 0.21/0.42 SPASS V 3.9
% 0.21/0.42 SPASS beiseite: Proof found.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.42 SPASS derived 13 clauses, backtracked 0 clauses, performed 0 splits and kept 14 clauses.
% 0.21/0.42 SPASS allocated 63111 KBytes.
% 0.21/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.21/0.42 0:00:00.04 for the input.
% 0.21/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42 0:00:00.00 for inferences.
% 0.21/0.42 0:00:00.00 for the backtracking.
% 0.21/0.42 0:00:00.00 for the reduction.
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 Here is a proof with depth 4, length 12 :
% 0.21/0.42 % SZS output start Refutation
% See solution above
% 0.21/0.42 Formulae used in the proof : cls_Set_OemptyE_0 cls_Set_OinsertCI_1 cls_Set_OinsertE_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.21/0.42
%------------------------------------------------------------------------------