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