TSTP Solution File: SET009-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET009-1 : 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 : n001.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 14:31:59 EDT 2023
% Result : Unsatisfiable 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 41 ( 10 unt; 11 typ; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 30 ~; 33 |; 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 : 14 ( 6 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 46 ( 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,
difference: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
k: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
d: $i ).
tff(decl_29,type,
a: $i ).
tff(decl_30,type,
b: $i ).
tff(decl_31,type,
bDa: $i ).
tff(decl_32,type,
bDd: $i ).
cnf(member_of_difference_or_set2,axiom,
( member(X1,X4)
| member(X1,X3)
| ~ member(X1,X2)
| ~ difference(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-3.ax',member_of_difference_or_set2) ).
cnf(b_minus_d,hypothesis,
difference(b,d,bDd),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_minus_d) ).
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(d_is_a_subset_of_a,hypothesis,
subset(d,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_a_subset_of_a) ).
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(member_of_difference,axiom,
( member(X4,X1)
| ~ difference(X1,X2,X3)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-3.ax',member_of_difference) ).
cnf(b_minus_a,hypothesis,
difference(b,a,bDa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_minus_a) ).
cnf(not_member_of_difference,axiom,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ difference(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-3.ax',not_member_of_difference) ).
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(prove_bDa_is_a_subset_of_bDd,negated_conjecture,
~ subset(bDa,bDd),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_bDa_is_a_subset_of_bDd) ).
cnf(c_0_10,axiom,
( member(X1,X4)
| member(X1,X3)
| ~ member(X1,X2)
| ~ difference(X2,X3,X4) ),
member_of_difference_or_set2 ).
cnf(c_0_11,hypothesis,
difference(b,d,bDd),
b_minus_d ).
cnf(c_0_12,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
membership_in_subsets ).
cnf(c_0_13,hypothesis,
subset(d,a),
d_is_a_subset_of_a ).
cnf(c_0_14,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
subsets_axiom2 ).
cnf(c_0_15,hypothesis,
( member(X1,d)
| member(X1,bDd)
| ~ member(X1,b) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,axiom,
( member(X4,X1)
| ~ difference(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_difference ).
cnf(c_0_17,hypothesis,
difference(b,a,bDa),
b_minus_a ).
cnf(c_0_18,axiom,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ difference(X4,X2,X3) ),
not_member_of_difference ).
cnf(c_0_19,hypothesis,
( member(X1,a)
| ~ member(X1,d) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,hypothesis,
( subset(X1,bDd)
| member(member_of_1_not_of_2(X1,bDd),d)
| ~ member(member_of_1_not_of_2(X1,bDd),b) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,hypothesis,
( member(X1,b)
| ~ member(X1,bDa) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
subsets_axiom1 ).
cnf(c_0_23,hypothesis,
( ~ member(X1,bDa)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_24,hypothesis,
( subset(X1,bDd)
| member(member_of_1_not_of_2(X1,bDd),a)
| ~ member(member_of_1_not_of_2(X1,bDd),b) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,hypothesis,
( subset(bDa,X1)
| member(member_of_1_not_of_2(bDa,X1),b) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ subset(bDa,bDd),
prove_bDa_is_a_subset_of_bDd ).
cnf(c_0_27,hypothesis,
( subset(bDa,X1)
| ~ member(member_of_1_not_of_2(bDa,X1),a) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_28,hypothesis,
member(member_of_1_not_of_2(bDa,bDd),a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 11:59:00 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.58 % Version : CSE_E---1.5
% 0.20/0.58 % Problem : theBenchmark.p
% 0.20/0.58 % Proof found
% 0.20/0.58 % SZS status Theorem for theBenchmark.p
% 0.20/0.58 % SZS output start Proof
% See solution above
% 0.20/0.58 % Total time : 0.010000 s
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58 % Total time : 0.013000 s
%------------------------------------------------------------------------------