TSTP Solution File: SET005-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET005-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %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  : 300s
% DateTime : Thu Aug 31 14:31:57 EDT 2023

% Result   : Unsatisfiable 0.21s 0.59s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   70 (  14 unt;  12 typ;   0 def)
%            Number of atoms       :  131 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  127 (  54   ~;  73   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   6   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-3 aty)
%            Number of variables   :   86 (   4 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    member: ( $i * $i ) > $o ).

tff(decl_23,type,
    subset: ( $i * $i ) > $o ).

tff(decl_24,type,
    member_of_1_not_of_2: ( $i * $i ) > $i ).

tff(decl_25,type,
    equal_sets: ( $i * $i ) > $o ).

tff(decl_26,type,
    intersection: ( $i * $i * $i ) > $o ).

tff(decl_27,type,
    h: ( $i * $i * $i ) > $i ).

tff(decl_28,type,
    a: $i ).

tff(decl_29,type,
    b: $i ).

tff(decl_30,type,
    aIb: $i ).

tff(decl_31,type,
    c: $i ).

tff(decl_32,type,
    bIc: $i ).

tff(decl_33,type,
    aIbIc: $i ).

cnf(member_of_intersection_is_member_of_set2,axiom,
    ( member(X4,X2)
    | ~ intersection(X1,X2,X3)
    | ~ member(X4,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set2) ).

cnf(a_intersection_bIc,axiom,
    intersection(a,bIc,aIbIc),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_bIc) ).

cnf(member_of_intersection_is_member_of_set1,axiom,
    ( member(X4,X1)
    | ~ intersection(X1,X2,X3)
    | ~ member(X4,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set1) ).

cnf(b_intersection_c,axiom,
    intersection(b,c,bIc),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_intersection_c) ).

cnf(subsets_axiom1,axiom,
    ( subset(X1,X2)
    | member(member_of_1_not_of_2(X1,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).

cnf(subsets_axiom2,axiom,
    ( subset(X1,X2)
    | ~ member(member_of_1_not_of_2(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).

cnf(intersection_axiom2,axiom,
    ( member(h(X1,X2,X3),X3)
    | intersection(X1,X2,X3)
    | member(h(X1,X2,X3),X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom2) ).

cnf(membership_in_subsets,axiom,
    ( member(X1,X3)
    | ~ member(X1,X2)
    | ~ subset(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',membership_in_subsets) ).

cnf(member_of_both_is_member_of_intersection,axiom,
    ( member(X4,X3)
    | ~ intersection(X1,X2,X3)
    | ~ member(X4,X2)
    | ~ member(X4,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_both_is_member_of_intersection) ).

cnf(a_intersection_b,axiom,
    intersection(a,b,aIb),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_b) ).

cnf(intersection_axiom3,axiom,
    ( intersection(X1,X2,X3)
    | ~ member(h(X1,X2,X3),X3)
    | ~ member(h(X1,X2,X3),X2)
    | ~ member(h(X1,X2,X3),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom3) ).

cnf(intersection_axiom1,axiom,
    ( member(h(X1,X2,X3),X3)
    | intersection(X1,X2,X3)
    | member(h(X1,X2,X3),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom1) ).

cnf(prove_aIb_intersection_c_is_aIbIc,negated_conjecture,
    ~ intersection(aIb,c,aIbIc),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aIb_intersection_c_is_aIbIc) ).

cnf(c_0_13,axiom,
    ( member(X4,X2)
    | ~ intersection(X1,X2,X3)
    | ~ member(X4,X3) ),
    member_of_intersection_is_member_of_set2 ).

cnf(c_0_14,axiom,
    intersection(a,bIc,aIbIc),
    a_intersection_bIc ).

cnf(c_0_15,axiom,
    ( member(X4,X1)
    | ~ intersection(X1,X2,X3)
    | ~ member(X4,X3) ),
    member_of_intersection_is_member_of_set1 ).

cnf(c_0_16,axiom,
    intersection(b,c,bIc),
    b_intersection_c ).

cnf(c_0_17,plain,
    ( member(X1,bIc)
    | ~ member(X1,aIbIc) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,axiom,
    ( subset(X1,X2)
    | member(member_of_1_not_of_2(X1,X2),X1) ),
    subsets_axiom1 ).

cnf(c_0_19,plain,
    ( member(X1,b)
    | ~ member(X1,bIc) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,plain,
    ( subset(aIbIc,X1)
    | member(member_of_1_not_of_2(aIbIc,X1),bIc) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,axiom,
    ( subset(X1,X2)
    | ~ member(member_of_1_not_of_2(X1,X2),X2) ),
    subsets_axiom2 ).

cnf(c_0_22,plain,
    ( subset(aIbIc,X1)
    | member(member_of_1_not_of_2(aIbIc,X1),b) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,axiom,
    ( member(h(X1,X2,X3),X3)
    | intersection(X1,X2,X3)
    | member(h(X1,X2,X3),X2) ),
    intersection_axiom2 ).

cnf(c_0_24,axiom,
    ( member(X1,X3)
    | ~ member(X1,X2)
    | ~ subset(X2,X3) ),
    membership_in_subsets ).

cnf(c_0_25,plain,
    subset(aIbIc,b),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,axiom,
    ( member(X4,X3)
    | ~ intersection(X1,X2,X3)
    | ~ member(X4,X2)
    | ~ member(X4,X1) ),
    member_of_both_is_member_of_intersection ).

cnf(c_0_27,axiom,
    intersection(a,b,aIb),
    a_intersection_b ).

cnf(c_0_28,plain,
    ( member(X1,a)
    | ~ member(X1,aIbIc) ),
    inference(spm,[status(thm)],[c_0_15,c_0_14]) ).

cnf(c_0_29,plain,
    ( intersection(X1,X2,X2)
    | member(h(X1,X2,X2),X2) ),
    inference(ef,[status(thm)],[c_0_23]) ).

cnf(c_0_30,plain,
    ( member(X1,b)
    | ~ member(X1,aIbIc) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,axiom,
    ( intersection(X1,X2,X3)
    | ~ member(h(X1,X2,X3),X3)
    | ~ member(h(X1,X2,X3),X2)
    | ~ member(h(X1,X2,X3),X1) ),
    intersection_axiom3 ).

cnf(c_0_32,plain,
    ( member(X1,aIb)
    | ~ member(X1,b)
    | ~ member(X1,a) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_33,plain,
    ( intersection(X1,aIbIc,aIbIc)
    | member(h(X1,aIbIc,aIbIc),a) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,plain,
    ( intersection(X1,aIbIc,aIbIc)
    | member(h(X1,aIbIc,aIbIc),b) ),
    inference(spm,[status(thm)],[c_0_30,c_0_29]) ).

cnf(c_0_35,plain,
    ( intersection(X1,X2,X2)
    | ~ member(h(X1,X2,X2),X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_29]) ).

cnf(c_0_36,plain,
    ( intersection(X1,aIbIc,aIbIc)
    | member(h(X1,aIbIc,aIbIc),aIb) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).

cnf(c_0_37,plain,
    ( member(X1,b)
    | ~ member(X1,aIb) ),
    inference(spm,[status(thm)],[c_0_13,c_0_27]) ).

cnf(c_0_38,axiom,
    ( member(h(X1,X2,X3),X3)
    | intersection(X1,X2,X3)
    | member(h(X1,X2,X3),X1) ),
    intersection_axiom1 ).

cnf(c_0_39,plain,
    intersection(aIb,aIbIc,aIbIc),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_40,plain,
    ( member(X1,bIc)
    | ~ member(X1,c)
    | ~ member(X1,b) ),
    inference(spm,[status(thm)],[c_0_26,c_0_16]) ).

cnf(c_0_41,plain,
    ( intersection(aIb,X1,X2)
    | member(h(aIb,X1,X2),b)
    | member(h(aIb,X1,X2),X2) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,plain,
    ( member(X1,aIb)
    | ~ member(X1,aIbIc) ),
    inference(spm,[status(thm)],[c_0_15,c_0_39]) ).

cnf(c_0_43,plain,
    ( member(X1,aIbIc)
    | ~ member(X1,bIc)
    | ~ member(X1,a) ),
    inference(spm,[status(thm)],[c_0_26,c_0_14]) ).

cnf(c_0_44,plain,
    ( intersection(X1,c,X2)
    | member(h(X1,c,X2),bIc)
    | member(h(X1,c,X2),X2)
    | ~ member(h(X1,c,X2),b) ),
    inference(spm,[status(thm)],[c_0_40,c_0_23]) ).

cnf(c_0_45,plain,
    ( intersection(aIb,X1,aIbIc)
    | member(h(aIb,X1,aIbIc),b) ),
    inference(spm,[status(thm)],[c_0_30,c_0_41]) ).

cnf(c_0_46,negated_conjecture,
    ~ intersection(aIb,c,aIbIc),
    prove_aIb_intersection_c_is_aIbIc ).

cnf(c_0_47,plain,
    ( member(X1,aIb)
    | ~ member(X1,bIc)
    | ~ member(X1,a) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_48,plain,
    member(h(aIb,c,aIbIc),bIc),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_17]) ).

cnf(c_0_49,plain,
    ( member(h(aIb,c,aIbIc),aIb)
    | ~ member(h(aIb,c,aIbIc),a) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_50,plain,
    ( intersection(X1,X2,aIbIc)
    | member(h(X1,X2,aIbIc),a)
    | member(h(X1,X2,aIbIc),X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_38]) ).

cnf(c_0_51,plain,
    ( intersection(X1,X2,aIbIc)
    | ~ member(h(X1,X2,aIbIc),bIc)
    | ~ member(h(X1,X2,aIbIc),a)
    | ~ member(h(X1,X2,aIbIc),X2)
    | ~ member(h(X1,X2,aIbIc),X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_43]) ).

cnf(c_0_52,plain,
    member(h(aIb,c,aIbIc),aIb),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_46]) ).

cnf(c_0_53,plain,
    ( ~ member(h(aIb,c,aIbIc),a)
    | ~ member(h(aIb,c,aIbIc),c) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_48]),c_0_52])]),c_0_46]) ).

cnf(c_0_54,plain,
    ( member(X1,c)
    | ~ member(X1,bIc) ),
    inference(spm,[status(thm)],[c_0_13,c_0_16]) ).

cnf(c_0_55,plain,
    ~ member(h(aIb,c,aIbIc),a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_48])]) ).

cnf(c_0_56,plain,
    ( member(X1,a)
    | ~ member(X1,aIb) ),
    inference(spm,[status(thm)],[c_0_15,c_0_27]) ).

cnf(c_0_57,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_52])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n020.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    : 300
% 0.14/0.35  % DateTime   : Sat Aug 26 12:15:29 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 0.21/0.59  % Version  : CSE_E---1.5
% 0.21/0.59  % Problem  : theBenchmark.p
% 0.21/0.59  % Proof found
% 0.21/0.59  % SZS status Theorem for theBenchmark.p
% 0.21/0.59  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.018000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.021000 s
%------------------------------------------------------------------------------