TSTP Solution File: COM011-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM011-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %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 : Fri Jul 15 01:32:30 EDT 2022
% Result : Unsatisfiable 0.20s 0.38s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 12 unt; 4 nHn; 25 RR)
% Number of literals : 60 ( 0 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 57 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)) ).
cnf(cls_Set_ODiffE_1,axiom,
( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| c_in(V_c,V_A,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_UNITY_Oconstrains__weaken__L_0,axiom,
( ~ c_in(V_F,c_UNITY_Oconstrains(V_A,V_A_H,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| c_in(V_F,c_UNITY_Oconstrains(V_B,V_A_H,T_a),tc_UNITY_Oprogram(T_a)) ) ).
cnf(cls_WFair_OensuresI_0,axiom,
( ~ c_in(V_F,c_UNITY_Oconstrains(c_minus(V_A,V_B,tc_set(T_a)),c_union(V_A,V_B,T_a),T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_WFair_Otransient(c_minus(V_A,V_B,tc_set(T_a)),T_a),tc_UNITY_Oprogram(T_a))
| c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ) ).
cnf(cls_WFair_OleadsTo__Basis_0,axiom,
( ~ c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
| c_in(V_F,c_WFair_OleadsTo(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ) ).
cnf(cls_WFair_Otransient__strengthen_0,axiom,
( ~ c_in(V_F,c_WFair_Otransient(V_A,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| c_in(V_F,c_WFair_Otransient(V_B,T_a),tc_UNITY_Oprogram(T_a)) ) ).
cnf(refute_0_0,plain,
( ~ c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a))
| c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(subst,[],[cls_WFair_OleadsTo__Basis_0:[bind(T_a,$fot(t_a)),bind(V_A,$fot(v_A)),bind(V_B,$fot(v_B)),bind(V_F,$fot(v_F))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(c_Main_OsubsetI__1(c_minus(X_19,X_17,tc_set(X_18)),X_19,X_18),X_19,X_18)
| c_lessequals(c_minus(X_19,X_17,tc_set(X_18)),X_19,tc_set(X_18)) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(X_18)),bind(V_A,$fot(c_minus(X_19,X_17,tc_set(X_18)))),bind(V_B,$fot(X_19))]]) ).
cnf(refute_0_2,plain,
( c_in(c_Main_OsubsetI__1(c_minus(X_9,X_10,tc_set(X_8)),V_B,X_8),c_minus(X_9,X_10,tc_set(X_8)),X_8)
| c_lessequals(c_minus(X_9,X_10,tc_set(X_8)),V_B,tc_set(X_8)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_8)),bind(V_A,$fot(c_minus(X_9,X_10,tc_set(X_8))))]]) ).
cnf(refute_0_3,plain,
( ~ c_in(c_Main_OsubsetI__1(c_minus(X_9,X_10,tc_set(X_8)),V_B,X_8),c_minus(X_9,X_10,tc_set(X_8)),X_8)
| c_in(c_Main_OsubsetI__1(c_minus(X_9,X_10,tc_set(X_8)),V_B,X_8),X_9,X_8) ),
inference(subst,[],[cls_Set_ODiffE_1:[bind(T_a,$fot(X_8)),bind(V_A,$fot(X_9)),bind(V_B,$fot(X_10)),bind(V_c,$fot(c_Main_OsubsetI__1(c_minus(X_9,X_10,tc_set(X_8)),V_B,X_8)))]]) ).
cnf(refute_0_4,plain,
( c_in(c_Main_OsubsetI__1(c_minus(X_9,X_10,tc_set(X_8)),V_B,X_8),X_9,X_8)
| c_lessequals(c_minus(X_9,X_10,tc_set(X_8)),V_B,tc_set(X_8)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_minus(X_9,X_10,tc_set(X_8)),V_B,X_8),c_minus(X_9,X_10,tc_set(X_8)),X_8) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( c_in(c_Main_OsubsetI__1(c_minus(X_19,X_17,tc_set(X_18)),X_19,X_18),X_19,X_18)
| c_lessequals(c_minus(X_19,X_17,tc_set(X_18)),X_19,tc_set(X_18)) ),
inference(subst,[],[refute_0_4:[bind(V_B,$fot(X_19)),bind(X_10,$fot(X_17)),bind(X_8,$fot(X_18)),bind(X_9,$fot(X_19))]]) ).
cnf(refute_0_6,plain,
c_lessequals(c_minus(X_19,X_17,tc_set(X_18)),X_19,tc_set(X_18)),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_minus(X_19,X_17,tc_set(X_18)),X_19,X_18),X_19,X_18) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
c_lessequals(c_minus(v_A,X_17,tc_set(t_a)),v_A,tc_set(t_a)),
inference(subst,[],[refute_0_6:[bind(X_18,$fot(t_a)),bind(X_19,$fot(v_A))]]) ).
cnf(refute_0_8,plain,
( ~ c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| ~ c_lessequals(X_79,v_A,tc_set(t_a))
| c_in(v_F,c_UNITY_Oconstrains(X_79,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(subst,[],[cls_UNITY_Oconstrains__weaken__L_0:[bind(T_a,$fot(t_a)),bind(V_A,$fot(v_A)),bind(V_A_H,$fot(c_union(v_A,v_B,t_a))),bind(V_B,$fot(X_79)),bind(V_F,$fot(v_F))]]) ).
cnf(refute_0_9,plain,
( ~ c_lessequals(X_79,v_A,tc_set(t_a))
| c_in(v_F,c_UNITY_Oconstrains(X_79,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[$cnf( c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) )],[cls_conjecture_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ c_lessequals(c_minus(v_A,X_17,tc_set(t_a)),v_A,tc_set(t_a))
| c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,X_17,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(subst,[],[refute_0_9:[bind(X_79,$fot(c_minus(v_A,X_17,tc_set(t_a))))]]) ).
cnf(refute_0_11,plain,
c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,X_17,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
inference(resolve,[$cnf( c_lessequals(c_minus(v_A,X_17,tc_set(t_a)),v_A,tc_set(t_a)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
inference(subst,[],[refute_0_11:[bind(X_17,$fot(v_B))]]) ).
cnf(refute_0_13,plain,
( ~ c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
| c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(subst,[],[cls_WFair_OensuresI_0:[bind(T_a,$fot(t_a)),bind(V_A,$fot(v_A)),bind(V_B,$fot(v_B)),bind(V_F,$fot(v_F))]]) ).
cnf(refute_0_14,plain,
( ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
| c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[$cnf( c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a))
| ~ c_lessequals(X_32,v_A,tc_set(t_a))
| c_in(v_F,c_WFair_Otransient(X_32,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(subst,[],[cls_WFair_Otransient__strengthen_0:[bind(T_a,$fot(t_a)),bind(V_A,$fot(v_A)),bind(V_B,$fot(X_32)),bind(V_F,$fot(v_F))]]) ).
cnf(refute_0_16,plain,
( ~ c_lessequals(X_32,v_A,tc_set(t_a))
| c_in(v_F,c_WFair_Otransient(X_32,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[$cnf( c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)) )],[cls_conjecture_1,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ c_lessequals(c_minus(v_A,X_17,tc_set(t_a)),v_A,tc_set(t_a))
| c_in(v_F,c_WFair_Otransient(c_minus(v_A,X_17,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(subst,[],[refute_0_16:[bind(X_32,$fot(c_minus(v_A,X_17,tc_set(t_a))))]]) ).
cnf(refute_0_18,plain,
c_in(v_F,c_WFair_Otransient(c_minus(v_A,X_17,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)),
inference(resolve,[$cnf( c_lessequals(c_minus(v_A,X_17,tc_set(t_a)),v_A,tc_set(t_a)) )],[refute_0_7,refute_0_17]) ).
cnf(refute_0_19,plain,
c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)),
inference(subst,[],[refute_0_18:[bind(X_17,$fot(v_B))]]) ).
cnf(refute_0_20,plain,
c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(resolve,[$cnf( c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) )],[refute_0_19,refute_0_14]) ).
cnf(refute_0_21,plain,
c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(resolve,[$cnf( c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)) )],[refute_0_20,refute_0_0]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)) )],[refute_0_21,cls_conjecture_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM011-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 16 17:31:04 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.38
% 0.20/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.39
%------------------------------------------------------------------------------