TSTP Solution File: SET007-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET007-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 14:31:58 EDT 2023
% Result : Unsatisfiable 0.14s 0.64s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 32
% Syntax : Number of formulae : 98 ( 19 unt; 15 typ; 0 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 197 ( 84 ~; 113 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 8 >; 12 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 120 ( 8 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,
union: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
g: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
intersection: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
h: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
b: $i ).
tff(decl_31,type,
c: $i ).
tff(decl_32,type,
bUc: $i ).
tff(decl_33,type,
a: $i ).
tff(decl_34,type,
aIb: $i ).
tff(decl_35,type,
aIc: $i ).
tff(decl_36,type,
aI_bUc: $i ).
cnf(member_of_set2_is_member_of_union,axiom,
( member(X4,X3)
| ~ union(X1,X2,X3)
| ~ member(X4,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_set2_is_member_of_union) ).
cnf(b_union_c,axiom,
union(b,c,bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_union_c) ).
cnf(member_of_intersection_is_member_of_set2,axiom,
( member(X4,X2)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set2) ).
cnf(a_intersection_c,axiom,
intersection(a,c,aIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_c) ).
cnf(subsets_axiom2,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).
cnf(subsets_axiom1,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).
cnf(a_intersection_b,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_b) ).
cnf(member_of_set1_is_member_of_union,axiom,
( member(X4,X3)
| ~ union(X1,X2,X3)
| ~ member(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_set1_is_member_of_union) ).
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/sandbox2/benchmark/Axioms/SET001-2.ax',member_of_both_is_member_of_intersection) ).
cnf(a_intersection_bUc,axiom,
intersection(a,bUc,aI_bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_bUc) ).
cnf(membership_in_subsets,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',membership_in_subsets) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( member(X4,X1)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set1) ).
cnf(union_axiom1,axiom,
( union(X1,X2,X3)
| member(g(X1,X2,X3),X1)
| member(g(X1,X2,X3),X2)
| member(g(X1,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',union_axiom1) ).
cnf(union_axiom3,axiom,
( union(X1,X2,X3)
| ~ member(g(X1,X2,X3),X2)
| ~ member(g(X1,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',union_axiom3) ).
cnf(union_axiom2,axiom,
( union(X1,X2,X3)
| ~ member(g(X1,X2,X3),X1)
| ~ member(g(X1,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',union_axiom2) ).
cnf(member_of_union_is_member_of_one_set,axiom,
( member(X4,X1)
| member(X4,X2)
| ~ union(X1,X2,X3)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_union_is_member_of_one_set) ).
cnf(prove_aIb_union_aIc_is_aI_bUc,negated_conjecture,
~ union(aIb,aIc,aI_bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aIb_union_aIc_is_aI_bUc) ).
cnf(c_0_17,axiom,
( member(X4,X3)
| ~ union(X1,X2,X3)
| ~ member(X4,X2) ),
member_of_set2_is_member_of_union ).
cnf(c_0_18,axiom,
union(b,c,bUc),
b_union_c ).
cnf(c_0_19,axiom,
( member(X4,X2)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_intersection_is_member_of_set2 ).
cnf(c_0_20,axiom,
intersection(a,c,aIc),
a_intersection_c ).
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,
( member(X1,bUc)
| ~ member(X1,c) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( member(X1,c)
| ~ member(X1,aIc) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
subsets_axiom1 ).
cnf(c_0_25,axiom,
intersection(a,b,aIb),
a_intersection_b ).
cnf(c_0_26,plain,
( subset(X1,bUc)
| ~ member(member_of_1_not_of_2(X1,bUc),c) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( subset(aIc,X1)
| member(member_of_1_not_of_2(aIc,X1),c) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
( member(X4,X3)
| ~ union(X1,X2,X3)
| ~ member(X4,X1) ),
member_of_set1_is_member_of_union ).
cnf(c_0_29,plain,
( member(X1,b)
| ~ member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_30,axiom,
( member(X4,X3)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X2)
| ~ member(X4,X1) ),
member_of_both_is_member_of_intersection ).
cnf(c_0_31,axiom,
intersection(a,bUc,aI_bUc),
a_intersection_bUc ).
cnf(c_0_32,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
membership_in_subsets ).
cnf(c_0_33,plain,
subset(aIc,bUc),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,axiom,
( member(X4,X1)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_intersection_is_member_of_set1 ).
cnf(c_0_35,plain,
( member(X1,bUc)
| ~ member(X1,b) ),
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_36,plain,
( subset(aIb,X1)
| member(member_of_1_not_of_2(aIb,X1),b) ),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_37,plain,
( member(X1,aI_bUc)
| ~ member(X1,bUc)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
( member(X1,bUc)
| ~ member(X1,aIc) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( member(X1,a)
| ~ member(X1,aIc) ),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_40,plain,
( subset(aIb,X1)
| member(member_of_1_not_of_2(aIb,X1),bUc) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,axiom,
( union(X1,X2,X3)
| member(g(X1,X2,X3),X1)
| member(g(X1,X2,X3),X2)
| member(g(X1,X2,X3),X3) ),
union_axiom1 ).
cnf(c_0_42,plain,
( subset(X1,aI_bUc)
| ~ member(member_of_1_not_of_2(X1,aI_bUc),bUc)
| ~ member(member_of_1_not_of_2(X1,aI_bUc),a) ),
inference(spm,[status(thm)],[c_0_21,c_0_37]) ).
cnf(c_0_43,plain,
( subset(aIc,X1)
| member(member_of_1_not_of_2(aIc,X1),bUc) ),
inference(spm,[status(thm)],[c_0_38,c_0_24]) ).
cnf(c_0_44,plain,
( subset(aIc,X1)
| member(member_of_1_not_of_2(aIc,X1),a) ),
inference(spm,[status(thm)],[c_0_39,c_0_24]) ).
cnf(c_0_45,plain,
subset(aIb,bUc),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_46,plain,
( member(X1,bUc)
| ~ member(X1,aI_bUc) ),
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_47,plain,
( union(aIc,X1,X2)
| member(g(aIc,X1,X2),c)
| member(g(aIc,X1,X2),X1)
| member(g(aIc,X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_48,plain,
subset(aIc,aI_bUc),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_49,axiom,
( union(X1,X2,X3)
| ~ member(g(X1,X2,X3),X2)
| ~ member(g(X1,X2,X3),X3) ),
union_axiom3 ).
cnf(c_0_50,plain,
( member(X1,bUc)
| ~ member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_32,c_0_45]) ).
cnf(c_0_51,plain,
( union(aIc,X1,aI_bUc)
| member(g(aIc,X1,aI_bUc),bUc)
| member(g(aIc,X1,aI_bUc),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_22]) ).
cnf(c_0_52,axiom,
( union(X1,X2,X3)
| ~ member(g(X1,X2,X3),X1)
| ~ member(g(X1,X2,X3),X3) ),
union_axiom2 ).
cnf(c_0_53,plain,
( member(X1,aI_bUc)
| ~ member(X1,aIc) ),
inference(spm,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_54,plain,
( union(X1,X2,aI_bUc)
| ~ member(g(X1,X2,aI_bUc),bUc)
| ~ member(g(X1,X2,aI_bUc),a)
| ~ member(g(X1,X2,aI_bUc),X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_37]) ).
cnf(c_0_55,plain,
( union(aIc,aIb,aI_bUc)
| member(g(aIc,aIb,aI_bUc),bUc) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
( member(X1,a)
| ~ member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_57,plain,
( union(X1,X2,aI_bUc)
| ~ member(g(X1,X2,aI_bUc),bUc)
| ~ member(g(X1,X2,aI_bUc),a)
| ~ member(g(X1,X2,aI_bUc),X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_37]) ).
cnf(c_0_58,plain,
( member(X1,a)
| ~ member(X1,aI_bUc) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_59,plain,
( union(X1,X2,aI_bUc)
| ~ member(g(X1,X2,aI_bUc),aIc)
| ~ member(g(X1,X2,aI_bUc),X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_53]) ).
cnf(c_0_60,plain,
( union(aIc,aIb,aI_bUc)
| ~ member(g(aIc,aIb,aI_bUc),aIb) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_61,plain,
( member(X1,aIb)
| ~ member(X1,b)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_62,axiom,
( member(X4,X1)
| member(X4,X2)
| ~ union(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_union_is_member_of_one_set ).
cnf(c_0_63,plain,
( union(aIc,aIb,aI_bUc)
| ~ member(g(aIc,aIb,aI_bUc),aIc) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_55]),c_0_39]) ).
cnf(c_0_64,plain,
( union(X1,X2,aI_bUc)
| member(g(X1,X2,aI_bUc),a)
| member(g(X1,X2,aI_bUc),X1)
| member(g(X1,X2,aI_bUc),X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_41]) ).
cnf(c_0_65,plain,
( union(aIc,X1,aI_bUc)
| ~ member(g(aIc,X1,aI_bUc),aIc) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_51]),c_0_39]),c_0_59]) ).
cnf(c_0_66,plain,
( member(X1,aIc)
| ~ member(X1,c)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_67,plain,
( union(aIc,aIb,aI_bUc)
| ~ member(g(aIc,aIb,aI_bUc),b)
| ~ member(g(aIc,aIb,aI_bUc),a) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,plain,
( member(X1,b)
| member(X1,c)
| ~ member(X1,bUc) ),
inference(spm,[status(thm)],[c_0_62,c_0_18]) ).
cnf(c_0_69,plain,
( union(aIc,aIb,aI_bUc)
| member(g(aIc,aIb,aI_bUc),a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_60]) ).
cnf(c_0_70,plain,
( union(aIb,X1,X2)
| member(g(aIb,X1,X2),b)
| member(g(aIb,X1,X2),X1)
| member(g(aIb,X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_41]) ).
cnf(c_0_71,plain,
( union(aIc,X1,aI_bUc)
| ~ member(g(aIc,X1,aI_bUc),c)
| ~ member(g(aIc,X1,aI_bUc),a) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
( union(aIc,aIb,aI_bUc)
| member(g(aIc,aIb,aI_bUc),c) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_55]),c_0_69]) ).
cnf(c_0_73,plain,
( union(aIb,X1,aI_bUc)
| member(g(aIb,X1,aI_bUc),bUc)
| member(g(aIb,X1,aI_bUc),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_70]),c_0_35]) ).
cnf(c_0_74,negated_conjecture,
~ union(aIb,aIc,aI_bUc),
prove_aIb_union_aIc_is_aI_bUc ).
cnf(c_0_75,plain,
union(aIc,aIb,aI_bUc),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_69]) ).
cnf(c_0_76,plain,
member(g(aIb,aIc,aI_bUc),bUc),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_73]),c_0_74]) ).
cnf(c_0_77,plain,
( member(X1,aIc)
| member(X1,aIb)
| ~ member(X1,aI_bUc) ),
inference(spm,[status(thm)],[c_0_62,c_0_75]) ).
cnf(c_0_78,plain,
~ member(g(aIb,aIc,aI_bUc),aIc),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_76]),c_0_74]),c_0_39]) ).
cnf(c_0_79,plain,
( member(X1,aIb)
| member(X1,aIc)
| ~ member(X1,bUc)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_77,c_0_37]) ).
cnf(c_0_80,plain,
~ member(g(aIb,aIc,aI_bUc),aIb),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_76]),c_0_74]),c_0_56]) ).
cnf(c_0_81,plain,
~ member(g(aIb,aIc,aI_bUc),a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_76])]),c_0_80]) ).
cnf(c_0_82,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_64]),c_0_74]),c_0_81]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sat Aug 26 09:58:28 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.48 start to proof: theBenchmark
% 0.14/0.64 % Version : CSE_E---1.5
% 0.14/0.64 % Problem : theBenchmark.p
% 0.14/0.64 % Proof found
% 0.14/0.64 % SZS status Theorem for theBenchmark.p
% 0.14/0.64 % SZS output start Proof
% See solution above
% 0.14/0.65 % Total time : 0.147000 s
% 0.14/0.65 % SZS output end Proof
% 0.14/0.65 % Total time : 0.150000 s
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