TSTP Solution File: SET855-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET855-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 03:37:51 EDT 2022
% Result : Unsatisfiable 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 7 unt; 0 nHn; 12 RR)
% Number of literals : 22 ( 14 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_Osubset__antisym_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| V_A = V_B ) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_4,negated_conjecture,
v_n != c_Union(v_Y,tc_set(t_a)) ).
cnf(refute_0_0,plain,
( ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_Union(v_Y,tc_set(t_a)) = v_n ),
inference(subst,[],[cls_Set_Osubset__antisym_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(c_Union(v_Y,tc_set(t_a)))),bind(V_B,$fot(v_n))]]) ).
cnf(refute_0_1,plain,
( ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_Union(v_Y,tc_set(t_a)) = v_n ),
inference(resolve,[$cnf( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) )],[cls_conjecture_3,refute_0_0]) ).
cnf(refute_0_2,plain,
c_Union(v_Y,tc_set(t_a)) = v_n,
inference(resolve,[$cnf( c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )],[cls_conjecture_2,refute_0_1]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( c_Union(v_Y,tc_set(t_a)) != v_n
| v_n = c_Union(v_Y,tc_set(t_a)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(c_Union(v_Y,tc_set(t_a)))),bind(Y,$fot(v_n))]]) ).
cnf(refute_0_7,plain,
c_Union(v_Y,tc_set(t_a)) != v_n,
inference(resolve,[$cnf( $equal(v_n,c_Union(v_Y,tc_set(t_a))) )],[refute_0_6,cls_conjecture_4]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( $equal(c_Union(v_Y,tc_set(t_a)),v_n) )],[refute_0_2,refute_0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET855-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 10:49:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34
%------------------------------------------------------------------------------