TSTP Solution File: SET834-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET834-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 03:37:36 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 36 ( 11 unt; 10 nHn; 22 RR)
% Number of literals : 67 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 68 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OUnCI_0,axiom,
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ).
cnf(cls_Set_OUnCI_1,axiom,
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ).
cnf(cls_Set_OUnE_0,axiom,
( ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a) ) ).
cnf(cls_Set_OsubsetD_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) ) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_OsubsetI_1,axiom,
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_conjecture_2,negated_conjecture,
c_in(v_x,v_X,t_a) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_in(v_x,v_Z,t_a) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_in(v_x,v_Y,t_a) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_lessequals(v_X,V_U,tc_set(t_a))
| ~ c_lessequals(v_Z,V_U,tc_set(t_a))
| ~ c_lessequals(v_Y,V_U,tc_set(t_a)) ) ).
cnf(refute_0_0,plain,
( ~ c_in(v_x,c_union(v_Y,v_Z,t_a),t_a)
| c_in(v_x,v_Y,t_a)
| c_in(v_x,v_Z,t_a) ),
inference(subst,[],[cls_Set_OUnE_0:[bind(T_a,$fot(t_a)),bind(V_A,$fot(v_Y)),bind(V_B,$fot(v_Z)),bind(V_c,$fot(v_x))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(V_c,v_X,t_a)
| ~ c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a))
| c_in(V_c,c_union(v_Y,v_Z,t_a),t_a) ),
inference(subst,[],[cls_Set_OsubsetD_0:[bind(T_a,$fot(t_a)),bind(V_A,$fot(v_X)),bind(V_B,$fot(c_union(v_Y,v_Z,t_a)))]]) ).
cnf(refute_0_2,plain,
( ~ c_lessequals(v_Y,c_union(X_126,v_Z,t_a),tc_set(t_a))
| ~ c_lessequals(v_Z,c_union(X_126,v_Z,t_a),tc_set(t_a))
| c_lessequals(v_X,c_union(X_126,v_Z,t_a),tc_set(t_a)) ),
inference(subst,[],[cls_conjecture_5:[bind(V_U,$fot(c_union(X_126,v_Z,t_a)))]]) ).
cnf(refute_0_3,plain,
( ~ c_in(c_Main_OsubsetI__1(X_124,c_union(X_123,X_124,X_125),X_125),c_union(X_123,X_124,X_125),X_125)
| c_lessequals(X_124,c_union(X_123,X_124,X_125),tc_set(X_125)) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(X_125)),bind(V_A,$fot(X_124)),bind(V_B,$fot(c_union(X_123,X_124,X_125)))]]) ).
cnf(refute_0_4,plain,
( c_in(c_Main_OsubsetI__1(X_11,V_B,X_9),X_11,X_9)
| c_lessequals(X_11,V_B,tc_set(X_9)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_9)),bind(V_A,$fot(X_11))]]) ).
cnf(refute_0_5,plain,
( ~ c_in(c_Main_OsubsetI__1(X_11,V_B,X_9),X_11,X_9)
| c_in(c_Main_OsubsetI__1(X_11,V_B,X_9),c_union(X_10,X_11,X_9),X_9) ),
inference(subst,[],[cls_Set_OUnCI_0:[bind(T_a,$fot(X_9)),bind(V_A,$fot(X_10)),bind(V_B,$fot(X_11)),bind(V_c,$fot(c_Main_OsubsetI__1(X_11,V_B,X_9)))]]) ).
cnf(refute_0_6,plain,
( c_in(c_Main_OsubsetI__1(X_11,V_B,X_9),c_union(X_10,X_11,X_9),X_9)
| c_lessequals(X_11,V_B,tc_set(X_9)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_11,V_B,X_9),X_11,X_9) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( c_in(c_Main_OsubsetI__1(X_124,c_union(X_123,X_124,X_125),X_125),c_union(X_123,X_124,X_125),X_125)
| c_lessequals(X_124,c_union(X_123,X_124,X_125),tc_set(X_125)) ),
inference(subst,[],[refute_0_6:[bind(V_B,$fot(c_union(X_123,X_124,X_125))),bind(X_10,$fot(X_123)),bind(X_11,$fot(X_124)),bind(X_9,$fot(X_125))]]) ).
cnf(refute_0_8,plain,
c_lessequals(X_124,c_union(X_123,X_124,X_125),tc_set(X_125)),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_124,c_union(X_123,X_124,X_125),X_125),c_union(X_123,X_124,X_125),X_125) )],[refute_0_7,refute_0_3]) ).
cnf(refute_0_9,plain,
c_lessequals(v_Z,c_union(X_126,v_Z,t_a),tc_set(t_a)),
inference(subst,[],[refute_0_8:[bind(X_123,$fot(X_126)),bind(X_124,$fot(v_Z)),bind(X_125,$fot(t_a))]]) ).
cnf(refute_0_10,plain,
( ~ c_lessequals(v_Y,c_union(X_126,v_Z,t_a),tc_set(t_a))
| c_lessequals(v_X,c_union(X_126,v_Z,t_a),tc_set(t_a)) ),
inference(resolve,[$cnf( c_lessequals(v_Z,c_union(X_126,v_Z,t_a),tc_set(t_a)) )],[refute_0_9,refute_0_2]) ).
cnf(refute_0_11,plain,
( ~ c_lessequals(v_Y,c_union(v_Y,v_Z,t_a),tc_set(t_a))
| c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a)) ),
inference(subst,[],[refute_0_10:[bind(X_126,$fot(v_Y))]]) ).
cnf(refute_0_12,plain,
( ~ c_in(c_Main_OsubsetI__1(X_250,c_union(X_250,X_251,X_249),X_249),c_union(X_250,X_251,X_249),X_249)
| c_lessequals(X_250,c_union(X_250,X_251,X_249),tc_set(X_249)) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(X_249)),bind(V_A,$fot(X_250)),bind(V_B,$fot(c_union(X_250,X_251,X_249)))]]) ).
cnf(refute_0_13,plain,
( c_in(c_Main_OsubsetI__1(X_24,V_B,X_23),X_24,X_23)
| c_lessequals(X_24,V_B,tc_set(X_23)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_23)),bind(V_A,$fot(X_24))]]) ).
cnf(refute_0_14,plain,
( ~ c_in(c_Main_OsubsetI__1(X_24,V_B,X_23),X_24,X_23)
| c_in(c_Main_OsubsetI__1(X_24,V_B,X_23),c_union(X_24,X_25,X_23),X_23) ),
inference(subst,[],[cls_Set_OUnCI_1:[bind(T_a,$fot(X_23)),bind(V_A,$fot(X_24)),bind(V_B,$fot(X_25)),bind(V_c,$fot(c_Main_OsubsetI__1(X_24,V_B,X_23)))]]) ).
cnf(refute_0_15,plain,
( c_in(c_Main_OsubsetI__1(X_24,V_B,X_23),c_union(X_24,X_25,X_23),X_23)
| c_lessequals(X_24,V_B,tc_set(X_23)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_24,V_B,X_23),X_24,X_23) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( c_in(c_Main_OsubsetI__1(X_250,c_union(X_250,X_251,X_249),X_249),c_union(X_250,X_251,X_249),X_249)
| c_lessequals(X_250,c_union(X_250,X_251,X_249),tc_set(X_249)) ),
inference(subst,[],[refute_0_15:[bind(V_B,$fot(c_union(X_250,X_251,X_249))),bind(X_23,$fot(X_249)),bind(X_24,$fot(X_250)),bind(X_25,$fot(X_251))]]) ).
cnf(refute_0_17,plain,
c_lessequals(X_250,c_union(X_250,X_251,X_249),tc_set(X_249)),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_250,c_union(X_250,X_251,X_249),X_249),c_union(X_250,X_251,X_249),X_249) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
c_lessequals(v_Y,c_union(v_Y,v_Z,t_a),tc_set(t_a)),
inference(subst,[],[refute_0_17:[bind(X_249,$fot(t_a)),bind(X_250,$fot(v_Y)),bind(X_251,$fot(v_Z))]]) ).
cnf(refute_0_19,plain,
c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a)),
inference(resolve,[$cnf( c_lessequals(v_Y,c_union(v_Y,v_Z,t_a),tc_set(t_a)) )],[refute_0_18,refute_0_11]) ).
cnf(refute_0_20,plain,
( ~ c_in(V_c,v_X,t_a)
| c_in(V_c,c_union(v_Y,v_Z,t_a),t_a) ),
inference(resolve,[$cnf( c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a)) )],[refute_0_19,refute_0_1]) ).
cnf(refute_0_21,plain,
( ~ c_in(v_x,v_X,t_a)
| c_in(v_x,c_union(v_Y,v_Z,t_a),t_a) ),
inference(subst,[],[refute_0_20:[bind(V_c,$fot(v_x))]]) ).
cnf(refute_0_22,plain,
c_in(v_x,c_union(v_Y,v_Z,t_a),t_a),
inference(resolve,[$cnf( c_in(v_x,v_X,t_a) )],[cls_conjecture_2,refute_0_21]) ).
cnf(refute_0_23,plain,
( c_in(v_x,v_Y,t_a)
| c_in(v_x,v_Z,t_a) ),
inference(resolve,[$cnf( c_in(v_x,c_union(v_Y,v_Z,t_a),t_a) )],[refute_0_22,refute_0_0]) ).
cnf(refute_0_24,plain,
c_in(v_x,v_Z,t_a),
inference(resolve,[$cnf( c_in(v_x,v_Y,t_a) )],[refute_0_23,cls_conjecture_4]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( c_in(v_x,v_Z,t_a) )],[refute_0_24,cls_conjecture_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET834-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.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 03:25:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------